research paper on math anxiety

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• Published: 02 October 2023

Strategies for remediating the impact of math anxiety on high school math performance

• Rachel G. Pizzie   ORCID: orcid.org/0000-0002-2309-7170 1 &
• David J. M. Kraemer 2  

npj Science of Learning volume  8 , Article number:  44 ( 2023 ) Cite this article

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Students with math anxiety experience excessive levels of negative emotion, including intrusive and distracting thoughts, when attempting to learn about math or complete a math assignment. Consequently, math anxiety is associated with maladaptive study skills, such as avoidance of homework and test preparation, creating significant impediments for students to fulfill their potential in math classes. To combat the impact of math anxiety on academic performance, we introduced two classroom-based interventions across two samples of high school math students: one intervention focused on emotion regulation (ER) using cognitive reappraisal, a technique for reframing an anxious situation, and the other intervention encouraged students to improve their study habits. The Study Skills (SS) intervention was associated with increased grades for highly anxious students during the intervention period, whereas the ER intervention was less efficacious in countering anxiety-related decreases in grade performance. The SS intervention encouraged highly math-anxious students to incorporate self-testing and overcome avoidant behaviors, increasing academic performance and ameliorating performance deficits associated with increased anxiety that were observed in both groups prior to intervention, and that persisted in the ER group. Notably, the benefits observed for the SS group extended to the post-intervention quarter, indicating the potential lasting effects of this intervention. These results support the hypothesis that using better study strategies and encouraging more frequent engagement with math resources would help highly-anxious students habituate to their math anxiety and ameliorate the negative effects of anxiety on performance, ultimately increasing their math comprehension and academic achievement.

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Anxiety in the classroom can have significant negative effects on students’ well-being and academic performance 1 , 2 . Math anxiety is hypothesized to impact academic performance through two mechanisms: students’ performance is impacted by distraction from the task at hand through pervasive, intrusive anxious thoughts, or by a failure to develop effective study techniques such that the information cannot be easily accessed during a high-pressure testing scenario 1 , 2 . In the present study, we compare two classroom interventions targeted at ameliorating the deficits associated with math anxiety in high school math classrooms: one intervention focused on emotion regulation techniques 3 targeting the negative thoughts that distract from performance, and another intervention focused on improving study skills through “desirable difficulties” such as self-testing 4 .

Previous research has suggested that math anxiety is negatively associated with math performance through intrusive worries that co-opt working memory resources, detracting cognitive resources from the task at hand 5 , 6 , 7 . Here we propose two different intervention techniques that would target anxiety in different ways. In an Emotion Regulation (ER) intervention strategy, students learn techniques to reframe or rethink their negative and anxious emotional experience while engaging with math. In this way, students learn how to downregulate their anxious response to mathematics, and thereby reduce the negative impact of anxiety on performance 8 , 9 , 10 . In a Study Skills (SS) intervention strategy 11 , 12 , 13 , students learn evidence-based strategies to improve their math studying and learning. This intervention was hypothesized to interact with anxiety in two potential ways: a) by improving learning of mathematical concepts, making them more robust to any anxiety that might detract from performing these skills, and/or b) by helping students to overcome the tendency to avoid mathematics by encouraging students to approach math more often, using better skills like self-testing to learn math, and helping students to habituate their anxiety. Across both the ER and SS interventions, both interventions were designed to ameliorate the negative effects of math anxiety on math performance, and in this study, we compared the effects of both interventions on grades in high school math classes.

The Study Skills intervention was focused on improving study habits through spaced studying and self-testing 14 , 15 , 16 , 17 . One potential approach to ameliorating math anxiety is to strengthen students’ study skills and thereby reduce the amount which anxiety interferes in math performance 13 , 18 . Indeed, maladaptive study behaviors such as avoidance of effortful study strategies contribute to performance deficits in math anxiety 19 , 20 . Implementing course curricula that emphasize self-testing increases learning, increases test performance, and remediates the negative effects of test anxiety on performance 11 , 21 . These techniques have all been shown to increase task performance in both laboratory procedures and real-world classroom settings 14 , 22 , and there is some evidence to suggest that implementing curricula focused on retrieval practice is not only linked to better learning 12 , 14 but is also associated with a reduction in anxiety in academic environments 11 . Increased self-testing may serve as a method to reduce negative feelings and reduce the impact of anxiety on performance by providing further instruction in the material, as well as providing increased exposure and desensitization for anxiety. A math-focused study used 8 weeks of individualized tutoring to examine the changes in math anxiety and brain plasticity in children 13 . An additional study that compared improved study skills to an anxiety intervention found that not only did math strategy training result in improved math achievement, but also resulted in a reduction of anxiety 18 . Over the course of this intensive tutoring period, students who showed remediation of math anxiety also showed reduced activity in the amygdala. However, due to the time and potential monetary expense associated with this method, this tutoring intervention would be difficult to implement on a large scale.

In contrast to these promising approaches that are focused on improving student retention of academic content, a separate area of research targeting feelings of anxiety has shown some success in reducing negative affect as well as improving performance 2 , 9 , 10 , 23 , 24 , 25 . Interventions that focus on therapy and alleviating anxiety have been effective in reducing self-reported math anxiety and have varied effectiveness in terms of their effect on mathematical performance. However, individualized therapy can be costly, time-consuming, and outcome measures evaluating math performance have frequently been constrained to tasks completed in the lab. To address these limitations, here we examine the effects of an anxiety-reducing Emotion Regulation strategy in the classroom that is quick, easy, and free to implement.

At the core of many of the therapy-based strategies is an emphasis on emotion regulation 26 , 27 , 28 . Emotion regulation is the mental process designed to change or alter one’s emotional experience, either augmenting a positive response or regulating and reducing negative feelings. Two common emotion regulation techniques include expressive suppression, or hiding one’s feelings 29 , 30 , and cognitive reappraisal, or rethinking or reframing the context of the emotional experience in order to change or decrease affect 31 , 32 . Particularly, cognitive reappraisal has been shown to decrease physiological arousal, increase cognitive control and decrease negative emotion. Cognitive reappraisal has been shown to improve reactivity to mathematics for highly math-anxious individuals 9 , 10 , 33 , 34 . In a study exploring the relationship between math accuracy and arousal in high vs. low math anxious individuals, cognitive reappraisal attenuated the relationship between physiological arousal (measured by electrodermal activity, EDA) and math task performance, such that even elevated physiological arousal (likely due to anxiety) was no longer associated with poor performance 10 .

Previous work has utilized neuroimaging to investigate a cognitive reappraisal strategy and its effects on math performance and neural activity in regions of the brain associated with arithmetic processing 9 . Whereas using a cognitive reappraisal strategy was associated with improved performance for highly math-anxious individuals, this was also associated with increased neural activity in regions of the brain associated with arithmetic processing, namely the intraparietal sulcus. These results suggest that not only is cognitive reappraisal associated with increased accuracy for highly math-anxious individuals, but this is also associated with a tandem increase in neural activity in regions of the brain that would support processing mathematical information. Although these results show promising results in a lab setting, the present research was designed to explore whether these cognitive reappraisal strategies would be efficacious in a real-world classroom setting.

Strategies that incorporate aspects of reappraisal have also been effective in improving performance in classrooms, specifically reducing anxiety related to math tests and ameliorating the negative effects of anxiety on performance 33 . Expressive writing reduces the interference created by rumination in math anxiety by allowing students to write about test-related worries before a test or other math task 24 , 25 , 35 . This technique provides the ideal context for “cognitive strategies that change the meaning of a stressful situation” 24 , allowing students to rethink or reframe their feelings of anxiety, reducing the negative attributions of the situation.

Following these two separate lines of investigation regarding effective study strategies and emotion regulation techniques, this research is targeted at reducing the deficits in mathematical performance associated with math anxiety by introducing two intervention approaches into real-world high school mathematics classrooms. We sought to test both intervention techniques, one targeting emotion regulation (ER), and the other focusing on utilizing better study skills (SS) in high school mathematics classrooms. One intervention was focused on an approach that should already be somewhat familiar to students – namely, using better study habits when reviewing material and preparing for exams. In fact, there is the possibility that highly math-anxious students will respond negatively to the requirement of increased exposure to math materials that this approach necessitates. The second intervention is aimed directly at reducing the negative feelings that anxious students experience when they encounter math by providing them with techniques to use for regulating their own emotions.

Both intervention techniques were designed to introduce the intervention strategy in small group discussions with high school students at the beginning of the second semester, then students were followed with questionnaires throughout the semester, and both groups completed a short writing task relevant to their assigned technique immediately before the midterm exam 24 . Introduction of these intervention strategies during the second semester allowed us to compare each student to their own pre-intervention class performance. Both intervention strategies were designed to be easy and cost-free to implement in a classroom setting, aiding students by introducing flexible, intuitive strategies that could reduce avoidance of mathematics, and reduce the decline in performance associated with anxiety, thus encouraging students to reach their full potential.

In this research, we aim to address two main questions:

When the intervention is introduced during second semester, do we observe increases in grade performance in either or both intervention groups relative to first semester performance?

Is one intervention more effective than the other in reducing the negative impact of math anxiety on grade performance?

We will also address additional follow-up analyses to address the following questions:

Comparing grades for Quarter 3 and Quarter 4, does the effect of the intervention last across the second semester, even beyond the main active intervention period?

Do other sources of anxiety, such as trait anxiety or test anxiety, explain our results?

Analysis design

The majority of the analyses in this project were conducted using linear mixed models (LMM), as these models allow us to account for the fixed effects of our experimental effects (i.e., intervention strategy, individual differences in anxiety), and still account for the important random effects inherent to doing research in a real-world educational setting. We evaluated whether course subject (i.e., algebra, geometry), teacher, and school accounted for differences in math grades. Using a LMM evaluating course subject as a fixed factor and random effects accounting for each individual participant, we found significant differences between course subjects on math grades, χ 2 (3) = 37.17, p  < .001. We used a LMM evaluating teacher as a fixed factor and random effects for each individual participant, we found significant differences between teachers on math grades, χ 2 (6) = 53.87, p  < .001. We used a LMM evaluating school as a fixed factor and random effects for each individual participant, we did not find significant differences between schools for math grades, χ 2 (1) = 0.30, p  = 0.58.

As a result, we decided to include course subject and teacher as random effects in our models in order to control for differences in grades created by these factors, and we did not include school as a factor in these models. In addition, we also included previous math grade to control for previous math performance as a within-subject control for math performance before the intervention was implemented. In the following analyses, we evaluated grades during the third and fourth quarter as outcome measures, with random effects accounting for individual differences in participants, course subject, teacher, and previous math class performance. In the Supplementary Material, we included analyses that evaluated quadratic models of math anxiety to account for a potential curvilinear model (negative quadratic) model of anxiety or stress, as has been demonstrated in previous studies 36 . We found that the quadratic models did not account for additional variance above and beyond the linear models included in the main manuscript. In some cases where we directly evaluate scores from before the intervention, or directly use difference scores to calculate the difference from pre-intervention grades to during the intervention, we utilize linear models. For descriptive statistics associated with this dataset, please see Table 1 .

Evaluating the effects of group assignment in pre-intervention semester

Prior to evaluating the effects of the intervention, we first evaluated whether there were inherent differences between the groups during first semester, before the intervention was implemented. Using an average of pre-intervention grades (an average of quarter 1 and quarter 2 grades), we evaluated the differences between intervention groups using a linear model, while accounting for class subject matter and teacher. Before the intervention was implemented, we find a main effect of math anxiety on pre-intervention grades F (1192) = 55.69, p  < 0.001, such that increased math anxiety is associated with decreased grade performance during the pre-intervention semester. When we examine grades before the intervention groups were introduced, there are no significant differences between intervention groups, F (1, 192) = 0.16, p  = 0.69, and there was no interaction between intervention group and math anxiety on pre-intervention grades, F (1192) = 1.27, p  = 0.26. These results confirm that our pseudo-random assignment of students to groups did not inadvertently result in groups that differed substantially in their math performance or effects of math anxiety on performance prior to our study. However, we do observe, as expected, that math anxiety was associated with decreased grade performance across all students before the intervention was introduced (Fig. 1 , Left).

Left Before the intervention is introduced, the two groups do not differ on grades, p  > 0.05, nor is there a significant interaction between group and anxiety on grade performance, p  > 0.05, however, there is a significant main effect of math anxiety on grades before the intervention was introduced, F (1, 192) = 55.69, p  < 0.001. Right) After the intervention is introduced, we observe a significant interaction between math anxiety and intervention group, collapsing across quarter grades in the second semester (Q3 and Q4 grades), χ 2 (1) = 6.73, p  = 0.010. For the emotion regulation group, we observe that as MA is increased, grades decrease, indicating that the ER intervention may not have had much effect in reversing the relationship between math anxiety and grade performance. However, for the study skills group, the relationship between math anxiety and grade performance is ameliorated, such that students who have higher anxiety performed better in the study skills group compared to the emotion regulation group. This suggests that the study skills intervention may be more effective at reversing the negative effects of anxiety on performance. Clouds represent standard error bars.

Evaluating effects of the interventions

In developing these interventions, our intention was to create approaches that could be leveraged by students highest in math anxiety, as these are the students who are mostly likely to suffer deficits in math performance. During second semester, we analyzed grades as an outcome measure, we utilized a LMM to evaluate the interaction between math anxiety (AAI-Math) and intervention group as fixed factors, and random effects were included in the model for individual participants, course subject, teacher, and previous math performance. Overall, we observe a significant effect of math anxiety, χ 2 (1) = 8.42, p  = 0.004, such that increased math anxiety is associated decreased grade performance ( β  = −3.87, t (160.89) = −2.90), as it was during the first semester. While there was no significant main effect of group on grades, χ 2 (1) = 0.003, p  = 0.95, there was a significant interaction between the AAI-Math scores and intervention group for math grades, χ 2 (1) = 6.73, p  = 0.010 (Fig. 1 , Right). This result indicates that one of the interventions was effective at reducing the negative impact of math anxiety on academic performance, while the other was not.

For the ER intervention group, as AAI-Math scores increase math grade performance is decreased, as was the case prior to the intervention. However, the negative impact of math anxiety on performance is ameliorated in the SS intervention group ( β  = −3.17, t (135.59) = −2.59). For the individuals who were highest in math anxiety, participating in the SS intervention group compared to the ER intervention group was associated with increased math grade performance. On average, for students highest in math anxiety, students in the Study Skills group had grades that were approximately half a letter grade higher compared to their peers that were randomly assigned to the Emotion Regulation group (6.29 grade points, calculated as a difference score between groups in the 4th quartile of anxiety scores). For students lower in math anxiety, these results suggest that the Emotion Regulation Intervention was associated with better math performance – possibly because these students may have already been using their own effective study strategies. Students highest in math anxiety tend to have the lowest grades in these courses, and these results indicate that the students highest in math anxiety are able to improve their grade performance by implementing the approaches provided by the study skills intervention.

To further examine the effect of intervention group, we directly compared grades during the main intervention period (Quarter 3) to previous grade performance during the pre-intervention timeframe by calculating a Pre/Post-Intervention Grade Difference score. In order to get an estimate of pre-intervention grade performance, we calculated an average grade from Quarter 1 and Quarter 2 math grades. Then, we subtracted this value from grades earned during the main intervention quarter (Quarter 3). Overall, all grades decreased over the course of the school year, likely reflecting the increased difficulty of the course content. Therefore, almost all of the observed difference values are negative, because we are subtracting the earlier term grades from the later term grades. Scores around zero or positive scores indicate that the student’s math grade performance was maintained or improved during the intervention quarter compared to the student’s previous performance in the class.

In this analysis, we used a linear model predicting Pre/Post-Intervention Grade Difference (Q3 – [Average of Q1 and Q2]) as an outcome measure, evaluating the interaction between intervention group and standardized math anxiety score (AAI-Math), and controlling for course subject and teacher (Fig. 2 ). The intervention groups did not differ in measures of average grade performance (Q1 and Q2 average) before the interventions were introduced, t (220.6) = −0.29, p  = 0.77. Before the intervention groups were introduced, average math grade performance across both groups was equivalent (ER group = 80.88, SS Group = 81.4). There was no significant main effect of math anxiety on Pre-/Post-Intervention Grade Difference scores, F (1,174) = 0.01, p  = 0.93, and no significant main effect of group, F (1,174) = 0.39, p  = 0.53. However, there was a statistically significant interaction between intervention group and math anxiety for the Pre-/Post-Intervention Grade Difference scores, F (1,174) = 4.72, p  = 0.03. For the ER intervention group, higher levels of math anxiety were associated with greater decreases in math grades compared to their previous class performance. Similar to the previous analysis, the negative association observed between Pre-/Post-Intervention Grade Difference scores and anxiety is ameliorated in the SS group ( β  = −2.19, t (174) = −2.17). In the SS intervention group, students who were more highly math-anxious were the most likely to maintain their math grades. Compared to the ER group, the SS group was associated with better grade performance for more highly math-anxious students, directly comparing to students’ own previous grade performance before the introduction of the intervention groups. Using students as their own within-subject controls, we observe that the SS intervention is associated with maintained or better grade performance compared to students enrolled in the ER intervention group for students who experience math anxiety.

To compare performance during the intervention to students’ own performance before the interventions were introduced, we calculated an Intervention Grade Difference Score. This score is calculated as the difference between students’ math grades during the intervention quarter, subtracting an average of their quarter grades during the previous semester (Q3 – [Average (Q1, Q2)]). We observe an interaction between math anxiety (Z-scored AAI-Math scores) and intervention group on the difference scores, F (1,174) = 4.72, p  = 0.03. For the ER intervention group, we observe a negative relationship between MA and grades, such that more anxious students were more likely to have decreased grades compared to their own previous performance. For the SS intervention group, the pattern was reversed: as math anxiety increased, students were more likely to maintain or improve their grade performance compared to their grade performance before the intervention. Overall, grades in the second semester are lower than those in the first semester, corresponding to the increased difficulty of the math content. Error bars represent standard error.

Duration of intervention effects

In order to examine the duration of the effects of the interventions, we also evaluated how math grades were affected by the intervention groups over the full course of second semester by exploring grade performance within each quarter (Fig. 3 ). We might expect that the interventions would have the greatest effect during the third quarter, while the intervention activity was highest, but then these effects might wane over time, e.g., once the researchers stopped reminding students to utilize their assigned intervention before each exam. Conversely, finding that the effects extended into the fourth quarter would indicate the potential lasting benefits of the interventions. In order to address this question, we conducted a LMM analysis with grades as the outcome measure, exploring the interaction between math anxiety, intervention group, and quarter as fixed factors, and random effects for participants, course subject, teacher, and previous math performance.

For second semester grades, following the introduction of the intervention we observe a significant interaction between math anxiety (AAI-Math, z-scored) and intervention group, χ 2 (1) = 6.74, p  = 0.010. For the Emotion Regulation Group, as math anxiety increases, we observe a characteristic decrease in grade performance. However, for the Study Skills Group, we see that this relationship is ameliorated, such that those higher in math anxiety show improved grade performance compared to those in the ER group. This relationship is maintained across both quarters, such that we do not observe a decrease in the effectiveness of the intervention across time. Between the two quarters of the second semester, the three-way interaction between math anxiety, intervention group, and quarter was not statistically significant, χ 2 (1) = 0.03, p  = 0.86. Error bars represent standard error.

In this analysis, we again found a main effect of math anxiety (z-scored AAI-Math scores) on math grades, χ 2 (1) = 8.44, p  = 0.004, and a main effect of quarter, χ 2 (1) = 24.64, p  < 0.001, such that overall grades decreased from third to fourth quarter. As before, there was no significant main effect of intervention group on math grades, χ 2 (1) = 0.004, p  = 0.95. For the post-intervention semester (i.e., 3rd and 4th quarters), there was no significant interaction between math anxiety and quarter, χ 2 (1) = 1.53, p  = 0.22, such that the detrimental effects of math anxiety were not associated with changes from one quarter to the next. Notably, for math grades, we again observe a significant interaction between math anxiety and intervention group, χ 2 (1) = 6.74, p  = 0.010, as previously discussed (Fig. 2 ). There was not a significant interaction between intervention and quarter for math grades, χ 2 (1) = 3.75, p  = 0.053. Finally, for math grades, there was no significant three-way-interaction between math anxiety, intervention group, and quarter, χ 2 (1) = 0.03, p  = 0.86. These results confirm that the effects observed in 3rd quarter extend to the 4th quarter. Specifically, the SS intervention was associated with ameliorating math anxiety-related deficits in math class, and this effect was maintained throughout the second semester, including in the quarter after the active intervention period had ended.

Other sources of anxiety

We also explored whether other sources of anxiety were associated with grade performance or had differential effects based on intervention group. We constructed similar LMMs with grades as the outcome, and utilized fixed factors for intervention group, anxiety, and quarter, with random effects for individual participants, course subject matter, teacher, and previous math performance. In all of these analyses, there were no interactions between anxiety and group, all p ’s > 0.05. There were no significant two-way interactions between anxiety and quarter, all p ’s > 0.05, and no significant three-way interactions between other sources of anxiety, intervention group, and quarter, all p ’s > 0.05. This suggests that the associations between math anxiety and grade performance in these math courses is relatively specific and cannot be accounted for by general experiences of anxiety.

Based on past associations between gender and math anxiety, we also explored whether the effects of math anxiety and group were also associated with gender (coded as a binary: male and female). We constructed a LMM with grades as the outcome, and used fixed factors for intervention group, math anxiety, and gender, with random effects for individual participants, course subject matter, teacher, and previous math performance. There was a main effect of gender on course grades, χ 2 (1) = 10.73, p  = 0.001, such that female students had higher course grades ( M  = 80.8, SE  = 5.41, 95% CI : 65.4–96.2) than male students ( M  = 72.2, SE  = 5.47, 95% CI : 57.0–87.5). However, there were no interactions between gender and math anxiety on grades, χ 2 (1) = .23, p  = 0.63, no interaction between group and gender, χ 2 (1) = 0.01, p  = 0.89, and no three-way interaction between math anxiety, intervention group, and gender, χ 2 (1) = 0.003, p  = 0.96.

This study evaluated the relative effects of two interventions on grades in high school math classes, investigating whether either of these interventions might be valuable tools for ameliorating the negative effects of math anxiety on math grade performance. There were no overall differences in grades between the intervention groups, suggesting that for all students, there was not one intervention that resulted in better grade performance than the other. However, improving math class performance for highly math-anxious individuals is a priority. Controlling for previous math performance before the intervention, our results suggest an interaction between math anxiety and Emotion Regulation or Study Skills intervention groups when we evaluate math grades.

Especially for highly math-anxious individuals, individuals assigned to the Study Skills Intervention group had increased math grade performance compared to those assigned to the Emotion Regulation Intervention. For individuals lower in math anxiety, individuals assigned to the Emotion Regulation intervention had better math grades relative to those assigned to the Study Skills intervention. These effects were maintained from the intervention quarter (third quarter) and longitudinally across the rest of the semester (fourth quarter). Compared to previous performance, more highly math-anxious students in the SS intervention were able to maintain or increase their grade performance compared to highly anxious students in the ER intervention, whose grade performance decreased in the intervention quarter. These results suggest that especially for highly math-anxious individuals who are likely to struggle to achieve in math classes, an in-class intervention focused on improving study skills by spaced studying and self-testing resulted in better math grades.

The SS intervention provides a simple, easy-to-administer technique that is intuitive for students to understand, and was effective in increasing math grades. This intervention emphasized self-testing and utilizing practice problems as an effective study strategy, and this technique was associated with better performance for highly math-anxious students, increasing grades up to half a letter grade higher than students assigned to the other intervention. Notably, relative to the ER intervention, the positive effects of the SS intervention were strongest for students who rated at the high end of measures of math anxiety. That these positive effects on grades can be generated from a 20-minute discussion at the beginning of a term, short reminders during study periods and before tests suggests that ameliorating the negative impact of anxiety on mathematics does not necessarily require drastic changes in the classroom.

The results of this intervention are consistent with previous work on utilizing self-testing as a study strategy 11 , and provide further evidence that increases in math grades in study strategies impact those highest in anxiety, increasing their performance 21 . These results also suggest that when students take an active role in implementing changes in their own study techniques – gaining practice in completing math problems and potentially habituating to the effects of anxiety – we see a resulting increase in math grades and a reduction in the effects of anxiety on performance. The impact of the SS intervention had promising results during the intervention quarter, and these effects extend to the subsequent final quarter when reminders about the technique are given, suggesting that students may require continued support, reminders, and implementation of the writing task before testing in order for the positive effects of the intervention to continue.

These results are consistent with our hypotheses that the Study Skills Intervention strategy would help more highly math-anxious students to habituate some of their anxiety, perhaps decreasing the negative impact of math anxiety and improving math performance. Because avoidance is a common feature of math anxiety 19 , 20 , engaging in better study skills may have helped more highly math-anxious individuals to approach math more often. During the intervention discussions, students often reported difficulty in knowing how to study for their math classes, often rereading the chapter or reviewing notes from class, strategies that have been suggested to be less effective for learning 11 . In this intervention, more highly math-anxious students who may have avoided studying or engaged in maladaptive strategies in the past were encouraged to engage in learning techniques that may have resulted in better math learning, such as spaced studying and self-testing. Our results suggest that encouraging math-anxious students to engage with math more often and use techniques that encourage better learning did not result in exacerbated effects of anxiety. Instead, the Study Skills Intervention was associated with better math grades for more highly math-anxious individuals, providing a boost in math performance to students who would otherwise struggle to achieve in math classes.

Although the ER intervention had limited impact on students, emotion regulation behaviors still seem to play a role in math classes. Although unexpected based on our hypotheses, students who reported lower levels of math anxiety who were assigned to the ER intervention had increased math grades compared to those assigned to the SS intervention. For individuals low in math anxiety, we speculate that perhaps the improved math performance observed in the ER group is attributed to the idea that cognitive reappraisal is a working memory-intensive strategy. The ability to look at an emotional situation through reframing or rethinking requires a lot of working-memory-intensive thoughts 37 . This emotion regulation strategy is effortful, and may be difficult to implement, especially when cognitive resources are already compromised by anxiety, or when learning a difficult new math skill. Because low math-anxious individuals may have had increased capacity for these emotion regulation strategies, this is a plausible explanation for why the ER intervention resulted in improved grade performance for low math-anxious individuals relative to the SS group.

This result conflicts with previous work on cognitive reappraisal and math anxiety done in a lab setting, but we must consider how context impacts cognitive capacity to engage in reappraisal 9 , 10 . These previous studies suggest that more highly math-anxious individuals are able to utilize a cognitive reappraisal strategy to improve math performance, suggesting that highly math-anxious individuals benefitted most from the cognitive reappraisal intervention in a lab setting. However, in these studies, participants were in a laboratory setting and were utilizing math skills that had previously been mastered (order of operations arithmetic problems). In other words, individuals may have been able to utilize a cognitive reappraisal strategy when they had the capacity to do so, such as in a low-stakes lab task, and performing a skill that was previously learned. Compared to the context of the current study, where students were in a scenario where their performance on the task resulted in real-world outcomes (grade performance), and where they were learning new information and skills, highly anxious participants in the previous lab studies may have had more cognitive capacity to utilize cognitive reappraisal skills. In the present study, individuals with lower math anxiety may have had a greater cognitive capacity to utilize cognitive reappraisal skills given the demands of the learning environment, and this may have resulted in improved math class performance relative to the study skills group.

Another possibility explaining the improved performance for highly math-anxious individuals in the SS intervention could be partially attributed to our use of a writing task in both intervention groups. Although past research suggests that the emotion-centered writing exercise was associated with improved performance for more anxious individuals 24 , 25 , 35 , it is possible that asking individuals in the SS intervention to write about the kinds of problems they thought would appear on the test would also result in a release of physiological arousal and decreased anxiety. Although the writing intervention for the SS group did not specifically focus on feelings or anxiety, writing out the kinds of problems they would expect to see on the test may have freed up working memory resources, helped students bring to mind the kinds of problems that they studied, thereby alleviating anxiety. In this way, students in the SS condition may have gotten a “double dose” of intervention, such that they may have had the benefit of both improving study skills and reducing anxiety through the writing intervention. Future studies could focus on the combined intervention of both study skills and anxiety support, as it’s possible that these may yield promising results for ameliorating the effects of math anxiety.

Indeed, another reason for the comparative success of the study skills intervention may be interrelation between anxiety and math performance. Over time, improved study skills and knowledge may have contributed to lessened feelings of anxiety and improved performance in a bidirectional relationship (Reciprocal theory 38 ). Past research has suggested that poorer math performance is likely a driving factor in the development of math anxiety 39 , especially in younger populations in elementary school 40 , 41 . In addition to math achievement, additional factors and attitudes like math mindset 40 and self-efficacy 42 also contribute to the relation between math anxiety and math achievement. These previous results suggest that our study skills intervention may have capitalized on this reciprocal relation between math achievement and math anxiety, with improved study skills training contributing not only to improved math understanding and achievement, but also to reduced feelings of anxiety that may have further improved achievement. These two factors have a reciprocal relation that may gone from a “vicious cycle,” with negative emotion contributing to underachievement and vice versa, to a “virtuous cycle” where increased achievement and understanding may have a reciprocal relation with decreased anxiety. Although the present study is not well-suited to explore the longitudinal reciprocal relations between achievement and anxiety, we hope that future studies will explore the effects of these longitudinal relationships as future interventions are implemented.

This analysis and these studies also had some important limitations. For example, as in all studies that are implemented in a real-world educational environment, there are variations between the two samples of students, resulting in very different educational environments, and variation in the availability of identical measures across schools (i.e., variation in the assignments included in grade outcomes, timing and frequency of assessments, etc.). By using random effects in our models, we have attempted to control for some of this variability. If anything, these variations likely would have weakened the effects we observed of the SS intervention. Instead, whether the schools are analyzed in a combined sample or separately (See Supplementary Material), our results consistently illustrate that for more highly anxious students, the study skills intervention resulted in improved math class grades. Finally, although the current sample sizes limited the inclusion of a third, no-intervention control group within the same cohort, further investigations using similar intervention techniques should include a no-contact/waitlist control group in order to bolster the conclusions that these interventions increase mathematics grades. In the present study we addressed this concern by matching groups on prior achievement and performing within-subjects comparisons across academic terms, but future research would benefit from the addition of such a control group as well.

In summary, the results of these experiments suggest that the study skills intervention is a promising technique for reversing the effects of math anxiety on academic performance and increasing math grades. Improvements in study techniques, especially the frequency with which students use self-testing to learn and review material, likely encourages students to overcome their tendencies to avoid mathematics. Especially for highly anxious students in the study skills intervention, this process ameliorates the performance deficits associated with anxiety. These results suggest that interventions targeting study techniques have important implications for students who struggle with anxiety. Empowering students to improve their strategies for learning may decrease the deficits caused by anxiety in the classroom, encouraging students to excel.

Participants

Participants in this study were recruited from two different school districts in geographically distinct regions of the US. School 1 was a small high school in rural New England. Classes were taught along different timescales: including semester-long, and year-long courses. At School 1, all students enrolled in these classes were invited to participate and parents were asked to opt-out of the study if they chose not to participate (parents were sent a letter informing of the study prior to the start of the study). The local superintendent, school administration, and Dartmouth Committee for the Protection of Human Subjects (CPHS #28333) approved these procedures that a written informed consent was not needed and that an opt-out sampling protocol was approved. No parents opted-out of the study. All students provided verbal assent to complete study procedures. One-hundred-nine adolescent participants were recruited for the study from their math classes (algebra I and II, geometry) taught by two instructors. From this sample, two students opted-out of the surveys, and 16 students had incomplete survey or grade data due to absences or technical difficulties with the online surveys. From the overall sample of N  = 91 across six classes, students were between the ages of 13 and 18 ( M age  = 15.34, SD age  = 1.05), and the sample was 60% female. Demographic information was provided by each school. For our analyses, we use the term “gender” to refer to masculine or feminine identity, as this encompasses the cultural and social context of gender roles, and our study does not refer to any biological measures of sex characteristics. The researchers realize there are a variety of identities that can be encompassed by gender identity, but for the purposes of these analyses, the researchers use the binary terms “male” and “female” to refer to the participants’ gender identity as this was the information provided by each school. For additional information about this sample, please see the Supplementary Material.

At School 2, approximately 272 students from a diverse high school in the mid-Atlantic region were invited to participate in this study, and parents provided a signed consent form for their student to opt-in to enroll in the study. Students were enrolled in Algebra I, Algebra II, and Algebra II honors classes, and were recruited from 13 year-long classes taught by six instructors. Out of this sample, 167 students had parents who provided a signed informed consent in order to participate in the study (59% response rate, 6 students not enrolled because they were enrolled in a different math class). In addition to the consent provided by parents, all students gave verbal assent. A total of 156 students were included in the dataset for analysis after an additional 5 students were excluded for incomplete grade information ( N  = 156, 53% female, M age  = 15.46, SD age  = .92, Range age  = 14–19; n  = 21 Algebra I students, 43% female; n  = 100 Algebra II students, 58% female; n  = 34 Algebra II honors students, 44% female). For more information about the demographics of this sample, please see the Supplementary Material. Supplementary materials, an appendix of materials, and preprint versions of this manuscript are available through the Open Science Framework through PsyArXiv: https://osf.io/43q6y/ .

All procedures were approved by the Dartmouth College Committee for the Protection of Human Subjects and each local high school’s administration. This study and its analyses were not preregistered. Students enrolled at School 2 did not receive monetary compensation for this study in accordance with school district regulations. At School 1, participants were entered in a gift card raffle by participating in follow-up surveys. The Authors declare no competing financial or non-financial interests.

Across both studies, all students were pseudo-randomly assigned to an intervention strategy group. To account for random effects created by class subject or teacher, each class was split in half, and half of the participating students in each class was assigned to each intervention group. Assignment to intervention groups were counterbalanced for gender, previous grade performance (School 2) and/or GPA and/or standardized test performance (School 1). Half of the students were assigned to an intervention technique focused on improving study skills (SS), half were assigned to an intervention technique focused on emotion regulation (ER) using cognitive reappraisal. In this way, we were able to establish that even within each class, the intervention groups would be relatively balanced in terms of gender composition and academic performance before the intervention was introduced.

This procedure of splitting each class in half also contributed to the decision to use two active intervention conditions in the study, instead of using a no-contact or waitlist control. Because classes needed to be split in half, this resulted in smaller groups within each class, and inclusion of an additional group would have further decreased the numbers of students assigned to each group, limiting our ability to draw conclusions about the impact of the interventions. Because no intervention materials were introduced during the first semester, we consider the first semester to be a within-subject control condition, as grades during the previous term or previous class could not have been affected by the assigned intervention. Because we were able to use a within-subject control for each students’ math performance, the researchers wanted to introduce two strategies that were both likely to have a positive impact on grade performance.

The intervention techniques were introduced during the second semester, with the main in-class intervention introduced at the beginning of the third quarter, with additional follow-up throughout the third quarter, and longitudinal follow-up with grades throughout the fourth quarter (Fig. 4 ). The main intervention was introduced in a short in-classroom session where students were split into small groups (approximately 2–10 students depending on the size of the class) based on assigned intervention strategy. Within each small group, students spent 20–30 min working on a worksheet in a structured discussion with a study team member who led the discussion. The interventions were designed to be personally relevant to the students, to encourage the student to consider how the assigned technique might be interesting or important to improving the way they react to anxiety in academic situations (Emotion Regulation Intervention Strategy) or improving their experience with different techniques designed to encourage students to study more efficiently (Study Skills Intervention Strategy). Continuing to observe grades and follow-up throughout second semester allowed us to observe the intervention over a longer timescale.

During first semester, no interventions were introduced, and we utilized grades during this period as within-subject control data. During second semester, an intervention was administered as a 20 min structured small-group discussion with a member of the research team during a class period. Each class was split in half and pseudo-randomly assigned to an Emotion Regulation (ER) Intervention group or Study Skills (SS) Intervention group. Groups were followed throughout the third quarter, with additional follow-up in the form of short surveys, reminders, and expressive writing tasks administered before major tests. During the 4th quarter, grades were recorded, and students received 2 brief survey prompts/reminders to determine how they implemented their intervention, but experimenters did not provide in-person sessions.

Intervention strategies

Students were assigned to either an Emotion Regulation Intervention or a Study Skills Intervention. Both interventions were designed to be introduced in such a way that students saw their relevance to their daily lives, and could think about specific personal situations where they might have struggled with academic skills in the past, and how the intervention strategy could potentially help them in scenarios when students encountered academic challenges. In these structured discussions (20–30 min), the research team member asked students to explain how they would use the assigned strategy, and why it was useful. If students produced responses that were off-topic or incorrect, the research team member would redirect the response. Please see the Supplementary Material for an Appendix of in-class handouts.

The ER intervention was focused on how to use cognitive reappraisal in academic settings such as math class. The ER intervention focused on using an emotional distancing strategy encouraging the students to view the situation from a more objective perspective (“Imagine you’re explaining the problem to your best friend”). The ER intervention also introduced a reframing technique that aims to change the cognitive appraisals associated with a stress response, instead focusing on the possible positive associations with increased physiological arousal (“Think about the situation as a challenge rather than an obstacle,” “Stress may help you perform better, use these feelings to help you focus and overcome this challenge;” [ 33 , 34 ]). This strategy was intended to allow students to reframe their reactions to math problems by changing their perspective and focusing on a mindset that would encourage them to approach mathematics, regulate their reactions, and face the problems at hand.

The SS intervention focused on two study skills: spaced studying 16 and retrieval practice 4 , 11 , 43 , 44 . In spaced studying, students were encouraged to avoid cramming, and set aside time to review key information on a regular basis. In retrieval practice, students were encouraged to practice bringing information to mind by using self-testing, such as doing practice problems, taking practice quizzes or tests, and making flashcards as effective ways to study for their math class. As in the ER intervention, the discussion was structured to focus on what students were already doing to study, where they were encountering problems, and where they could change their behaviors to focus on building study habits that were supported by spaced studying and retrieval practice to make these behaviors more personally-relevant to each student.

After completing the small group discussions, students completed a series of questionnaires. These survey measures were meant to assess a baseline measure of various types of academic anxiety. Students completed standardized measures of test anxiety (Test Anxiety Inventory, TAI 45 , math anxiety (Math Anxiety Rating Scale, MARS 46 , trait anxiety (State-Trait Anxiety Inventory, STAI 47 , and the Emotion Regulation Questionnaire (ERQ 48 Students also completed the Academic Anxiety Inventory (AAI), a self-report measure designed to test math anxiety, as well as anxiety related to tests, science, writing, and trait levels of anxious emotion 49 .

Follow-up intervention activities

In addition to the in-class structured discussion, students received reminders to implement their assigned intervention strategy throughout the term. Before an exam in their math class, students were asked to write about their assigned intervention strategy, similar to previous research on expressive writing interventions 24 , 25 . In the Emotion Regulation Intervention, students were asked to write about the thoughts and feelings they would experience while taking the upcoming test (for example: “please write as openly as possible about some of the thoughts and feelings you might experience on your upcoming test”), and were also asked to write about what reappraisal strategies they would use during the test to rethink or reframe their experience. In the Study Skills Intervention, students were asked what kinds of math problems they thought would appear on the upcoming test, and what strategies they might use to solve these problems on the test. Students were directed to write a few sentences in response to each question, and responses were collected on a pencil-and-paper worksheet. For school 1, students completed this writing activity before a midterm exam given during the third quarter. For school 2, students completed the writing activity during summary unit tests completed throughout second semester (approximately 4 tests).

In addition to the pre-test writing activities, students were also expected to fill out short questionnaires during the third quarter, and continuing with lower frequency during fourth quarter. Students completed a 6-question survey that involved answering brief questions about feelings of anxiety, understanding, confidence, as well as how frequently students had used aspects of the intervention techniques in the past few days. This short questionnaire was repeated several times throughout the semester over the course of the intervention. In School 1, the researchers received feedback that some students had difficulty remembering the material from their assigned strategy. Subsequently, for School 2 these short surveys were combined with additional reminders about the assigned intervention strategy (See Supplementary Material for implementation differences between schools). In order to remind students about their assigned technique, students were given short reminders to identify the correct intervention technique, and were asked to write down ways they could use their assigned technique while working on assignments for math class. Additional reminders were administered during class time or during study hall periods (see Supplementary Materials for examples). In the present manuscript, we focused on grade performance, and analyses evaluating additional survey outcomes are included in the Supplementary Material.

In this study, our main outcome measures were the grades given in these real-world math classes. However, for each school, grade composition differed slightly. For School 1, we analyzed quarter grades in the third and fourth quarter of the school year, which included tests (including the midterm exam which included the test-related intervention activities), homework, quizzes, and other miscellaneous assignments within the 8–10 week quarter. Previous grades were also provided to account for previous mathematics performance, which included grades within the same course for year-long courses, and overall grade for the previous mathematics course for semester-long courses. For School 2, we focused on analyzing grades from classwork, homework and quizzes, as these grades only reflected performance during the quarters where the intervention strategies had been introduced, as cumulative quarter grades also included previous course performance from the first semester. For year-long classes, the previous math performance was drawn from previous quarter grades. For more details about grade information for each sample, please see Supplementary Material.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

Some materials associated with this project will be shared in the Open Science Framework online repository ( https://osf.io/43q6y/ ). These data include educational data from underage minors. Sharing of these data is restricted based on FERPA regulations and research agreements with the participating local schools. Due to the nature of the data, deidentified data and code will be shared by request from the authors, but complete de-identified data will not be shared in an online repository due to privacy restrictions and the sensitive nature of the educational data. Interested parties can contact the corresponding author, Rachel Pizzie ([email protected]) to request access to the data and should receive a response to requests within two weeks. Interested parties will be asked to describe how they will ensure privacy and confidentiality of the data and maintain the security of the data. Interested parties must agree not to share these data beyond the parties included in the request, and do not have permission to publish the data themselves.

Code availability

Corresponding to the sensitive nature of the data, code for this project will be shared by request from the authors, but will not be shared in an online repository due to privacy restrictions and the sensitive nature of the educational data.

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Acknowledgements

Financial support for this research was provided by the Dartmouth College Department of Education. The authors would like to acknowledge the team of research assistants who made this study possible: Nikita Raman, Josh Cetron, Justin Hayes, Lauren Peterson, Dee Longhi, Cassidy McDermott, Emma Sisson, Ji Soo Song, Connor O’Leary, Tyler Salem. We also would like to thank the school administrators and teachers who made this research possible. They would also like to express gratitude for all the students who participated in this research.

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R.P. and D.K. were both responsible for the idea and design of this study. D.K. provided resources and logistical support for data collection. R.P. and D.K. designed study materials, and R.P. led data collection efforts with help and guidance from DK. RP cleaned and analyzed the data with guidance and assistance from D.K. R.P. wrote primary drafts of the manuscript, with additional edits, feedback, and guidance from D.K.

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Pizzie, R.G., Kraemer, D.J.M. Strategies for remediating the impact of math anxiety on high school math performance. npj Sci. Learn. 8 , 44 (2023). https://doi.org/10.1038/s41539-023-00188-5

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What impact does maths anxiety have on university students?

• Eihab Khasawneh   ORCID: orcid.org/0000-0002-9106-9008 1 , 2 ,
• Cameron Gosling 1 &
• Brett Williams 1  

BMC Psychology volume  9 , Article number:  37 ( 2021 ) Cite this article

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Maths anxiety is defined as a feeling of tension and apprehension that interferes with maths performance ability, the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations. Our aim was to identify the facilitators and barriers of maths anxiety in university students.

A scoping review methodology was used in this study. A search of databases including: Cumulative Index of Nursing and Allied Health Literature, Embase, Scopus, PsycInfo, Medline, Education Resources Information Centre, Google Scholar and grey literature. Articles were included if they addressed the maths anxiety concept, identified barriers and facilitators of maths anxiety, had a study population comprised of university students and were in Arabic or English languages.

Results and discussion

After duplicate removal and applying the inclusion criteria, 10 articles were included in this study. Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. The following themes emerged from the included papers: gender, self-awareness, numerical ability, and learning difficulty. The pattern in which gender impacts maths anxiety differs across countries and disciplines. There was a significant positive relationship between students’ maths self-efficacy and maths performance and between maths self-efficacy, drug calculation self-efficacy and drug calculation performance.

Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. Developing anxiety toward maths might be affected by gender; females are more prone to maths anxiety than males. Maths confidence, maths values and self-efficacy are related to self-awareness. Improving these concepts could end up with overcoming maths anxiety and improving performance.

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Introduction

Maths anxiety can be defined as a feeling of tension, apprehension and anxiety that interferes with maths performance ability the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations [ 1 ]. According to Olango [ 2 ] maths anxiety consists of an affective, behavioural and cognitive response to a perceived threat to self-esteem that occurs as a response to situations involving mathematics. Maths anxiety, which is rooted in emotional factors, can be differentiated from dyscalculia, which is characterized by a specific cognitive deficit in mathematics [ 3 ], in two ways. Firstly, maths anxiety can exist in people who have maths capability even though they may dislike maths. Secondly, maths anxiety has an emotional component which is not the case in dyscalculia [ 4 ].

Maths anxiety may occur in all levels of education from primary school to university education. Harari et al. [ 5 ] reported that negative reactions and numerical confidence are the most salient dimensions of maths anxiety in a sample of first-grade students. Similar findings were also observed at tertiary levels across multiple disciplines, including health care professions. For example, Roykenes and Larsen [ 6 ] studied 116 baccalaureate nursing students and found that there was a negative relationship between previous mathematic likes/dislikes and self-assessment of mathematic ability.

Many factors may contribute to or facilitate the maths anxiety. These factors or facilitators may include teachers, parents, peers and society. Negative experiences of maths learning in classroom or home can lead to maths anxiety [ 7 ]. Firstly, the teacher plays important role in making the class more attractive and reducing anxieties. Good maths teachers can create a learning environment in which students have a positive expectation about their learning [ 8 ]. Secondly, parents play an important part in developing or reducing the maths anxiety of their children. Parents' behaviours and relations with children are very important in this aspect [ 7 ]. By discussing the anxieties and the fears that their children might face, the parents are able to pinpoint any learning problem at early stage [ 8 ]. This might prevent the developing of any learning anxieties that the students might face later in life. Moreover, parents’ maths anxiety causes their children to learn less maths over the school year and to have more maths anxiety by the school year's end [ 9 ]. Thirdly, peers play important role in facilitating maths anxiety [ 7 ]. Peers at any stage of learning may have a negative impact on their colleagues, for example when students might feel inferior in front of their colleagues when they make mistakes [ 7 ]. Finally, society can contribute to the development of maths anxiety due to the misconception about mathematics, or maths myths [ 7 ].

Maths anxiety has negative impacts on individuals; many students who suffer from mathematics anxiety have little confidence in their ability to do mathematics and tend to take the minimum number of required mathematics courses, which greatly limits their career [ 10 ]. Fortunately, certain strategies can act as barriers, or prevent maths anxiety occurring. Uusimaki and Kidman [ 11 ] stated that whenever the persons become self-aware of maths anxiety and its consequences, their abilities to overcome it might increase [ 11 ]. On the other hand, activity-based learning and online/distance learning may reduce the fear of looking stupid in front of peers [ 12 ]. Another strategy is the use of untimed/unassessed (low stakes) tests to reduce the maths anxiety as well as to increase confidence [ 13 ]. Relevancy of studying maths can reduce maths anxiety; applying mathematics and statistics to real-life examples rather than pure maths can reduce maths anxiety [ 13 ].

Empirical investigations first began on maths anxiety in the 1950s, and Dreger and Alken [ 14 ] introduced the concept of maths anxiety to describe students’ attitudinal difficulty with maths. The aim of this study was to identify the facilitators and barriers of maths anxiety in university students using a scoping review methodology.

A scoping review methodology was used in conducting this study to allow for a greater breadth of literature to be investigated. Scoping reviews identify and map existing literature on a selected subject. This scoping review utilised the Arksey and O’Malley framework which includes six methodological steps: identifying the research question, identifying relevant studies, selecting studies, charting the data, collating, summarising and reporting the results and consulting experts [ 15 ]. The scoping approach systematically maps and reviews existing literature on a selected topic [ 16 ] including evidence from both peer-reviewed research and the non-peer reviewed literature.

Identify the research question

After several review iterations, the research team agreed on the question that guided this review: What are the barriers and facilitators of maths anxiety in university students? This question was broad so it could cover a wide literature in different disciplines that allowed a better summary of the available literature.

Identify relevant studies

A list of search terms was compiled from the available literature and previous research into maths anxiety and students. Suitable Medical Subject Headings (MeSH) terms and free text keywords were identified (Table 1 ). A search of databases included: Cumulative Index of Nursing and Allied Health Literature (CINHAL), Embase, Scopus, PsycInfo, Medline, ERIC, Trove, Google Scholar and Grey literature. The search involved any related studies from July-2018 backward. Studies in Arabic and English languages were filtered from the search yield and the abstracts scanned. The databases search were conducted by one of the researchers (EK). The search yield resulted in 656 records which were exported to EndNote17 referencing for screening.

Duplicates and irrelevant studies were removed by one of the researchers (EK) and potentially relevant abstracts were complied. The selection process was conducted at two levels: a title and abstract review and full-text review. The title and abstract of the retrieved studies were independently screened (EK and BW) for inclusion based on predetermined criteria. In the second stage, the selected studies full text of potentially eligible studies were assessed and inclusion confirmed by two of the authors (EK and BW). After removing the duplicates, (EK and BW) conducted the title and abstract review of 656 articles. After applying the inclusion criteria 20 articles resulted. These 20 articles were reviewed by (EK and BW) for the second time which ended in 10 articles to be involved in the scoping review.

Study selection (Fig.  1 )

Flow chart of study selection

Articles that met the following inclusion criteria were selected.

Research articles (of any design) available in full text.

The article addressed the maths anxiety concept.

The article identified the barriers and the facilitators of maths anxiety.

The article had a study population comprised of university students.

The article was in Arabic or English languages.

Articles that are systematic and scoping reviews, abstracts, editorials and letters for editors were excluded.

Charting the data

This stage allows data extraction from the included studies for more data description. A narrative review method was used to extract the data from each study. Narrative reviews summarise studies from which conclusions can be drawn into more holistic interpretation by the reviewers [ 17 ]. The data included: the author and the year of publication, the country the study was conducted in, the study design or type, the sample size, results and the theme emerges from the study (Table 2 ). Four themes emerged following full-text review of the 10 included papers, these included: gender, self-awareness, numerical ability and learning difficulties.

Collating, summarising and reporting the results

The data extracted from the included studies are reported in Table 2 . The table shows a summary of the selected articles in this scoping review study. It presents data on the different scales used to evaluate the maths anxiety across the different disciplines. Key outcome data from each of the included studies is presented and includes some of the causes or predictors of maths anxiety in university students such as gender and self-efficacy.

Consultation (optional)

Two experts were contacted for consultation to ensure no new or existing literature was missed; however no new articles were added following this consultation.

Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. Literature analysed in this scoping review spanned disciplines as diverse as education, engineering, health and science while covering diverse geographical locations such as United States (US), Austria, United Kingdom (UK), Israel, Portugal and Canada. The included articles utilised an array of varied study designs, including, cross-sectional, randomised control trial, and prospective cohort studies. The main themes that emerged from this review include gender, self-awareness, numerical ability, and learning difficulty each of these will now be synthesised and discussed.

Six articles addressed the gender concept; two American studies, three European and one Israeli study with mixed findings for the role gender plays in maths anxiety. Some of these articles found that gender has a role in maths anxiety [ 18 , 18 , 20 , 21 ], while others found there was no significant difference between males and females [ 20 , 22 ]. For example, a study of female psychology students in the US reported more maths anxiety than males [ 19 ] whereas there was no significant difference between males and females in maths anxiety in psychology students reported in the UK [ 20 ]. Psychology female students in the US [ 19 ] and Austria [ 21 ], and social science and education female students in Israel showed more maths anxiety than male students [ 22 ]. While in another study there was no significant difference in maths anxiety between males and females in the Portuguese engineering students [ 23 ].

The reasons why females frequently report higher maths anxiety than males is not well understood [ 24 ]. One explanation might be the different gender socialisation during childhood may differentially affect the anxiety experienced by males and females in certain situations which is known as the sex-role socialization hypothesis [ 24 ]. The sex-role socialization hypothesis argues that because mathematics has been traditionally viewed as a male domain, females may be socialised to think of themselves as mathematically incompetent and therefore females may avoid mathematics. When females do participate in mathematical activities they may experience more anxiety than males [ 24 ].

The pattern of gender effect on maths anxiety is different among disciplines and countries. In a recent study, Paechter et al. [ 21 ] administered the Revised Maths Anxiety Ratings Scale (R-MARS) to 225 psychology students at the University of Graz, Austria. This study showed that there were three antecedents of maths anxiety. Firstly, female gender who reported a higher level of maths anxiety β  = − 0.660. Secondly, a high proneness to experience anxiety in general report higher levels of maths anxiety β  = 0.385. Finally, poor grades in maths. According to Paechter et al. [ 21 ] maths anxiety is inversely related to maths grades β  = 0.393. Of the above three factors, female gender was the most strongly related to maths anxiety and is supported by the findings of other studies such as Devine et al. [ 23 ]. Developing anxiety toward maths might be effected by gender and highlights a specific area for future empirical work.

Self-awareness

Self-awareness helps people to manage themselves and improve performances while the opposite is true that lacking self-awareness leads to making the same mistakes repeatedly [ 25 ]. Being self-aware enables us to determine our strengths and areas that can be improved [ 25 ]. Four studies addressed the self-awareness concept in relation to maths anxiety, one American study, one UK study, one Israeli study and one Portuguese study. Under the self-awareness theme, a number of other subthemes emerged including self-efficacy, maths confidence, maths value, maths barriers and performance. McMullan et al. [ 26 ] developed a Drug Calculations Self-Efficacy Scale that measured critical skills of medication calculations (dose of liquid oral drugs, solid drugs, injections, percentage solutions and infusion and drip rates). McMullan et al. [ 26 ] reported that there was a significant positive correlation between students’ maths self-efficacy and maths performance and between maths self-efficacy, drug calculation self-efficacy and drug calculation performance. Low level of maths anxiety was demonstrated by 10% of the students, medium level by 70% and high level by 20% of the students. McMullan et al. [ 26 ] also noted that numerical skills can be improved by remedial approaches as lectures, study groups, workshops and computer assisted instructions [ 27 ]. The authors suggested that the lectures should be more student-directed not only didactic in nature. Study groups increase the cooperation and encourage students to exchange and clarify information leading to improve the self-efficacy.

Maths confidence, maths value and maths barriers are related to maths behaviour and performance. Hendy et al. [ 28 ] studied maths behaviours in 368 university maths students. They reported maths behaviours (attending class, doing homework, reading textbooks and asking for help) at week 8 of the 15 week-semester using self-reported questionnaires. The aim of their study was identify the subclasses of maths beliefs and their role in maths behaviours. The most commonly reported maths belief was maths confidence (mean rating = 3.79, SD = 0.90). This study reported that students with low maths confidence or high maths anxiety might benefit from the maths self-evaluation and self-regulation interventions. These interventions utilised suggestions which include: maths skills are learnable not innate, assessing current skills and believing in their development abilities, teaching student the specific strategies to solve maths problems and keeping self-regulatory records to track development in overcoming maths anxiety. These interventions may be used in overcoming maths anxiety. This study outlined the approach to develop interventional teaching methods that can be applied to students or course curriculum to help in reducing maths anxiety. Self-awareness might determine the person’s areas of strength that might help future career selection. Self-efficacy, maths confidence and values, maths barriers and performance are factors that related to self-awareness. Assessing these factors can determine the methods of improving self-awareness which may end in overcoming maths anxiety.

Numerical ability

Two articles addressed the numerical ability concept [ 25 , 2 ]. In their efforts to understand the origin of maths anxiety, Maloney et al. [ 29 ] investigated the processing of symbolic magnitude by high and low maths anxious individuals. They reported that high maths anxious individuals have less precise representations of numerical magnitude than their low maths anxious peers. Two experiments were performed on 48 undergraduate students in the University of Waterloo. A single Arabic digit in 18-font Arial font was presented at fixation. Numbers ranged from 1–4 to from 6–9. The participants were told to identify whether the number above five or below it. This study revealed that high maths anxious individuals have a less precise representation of numerical magnitude than the low maths anxious individuals. The results suggest that maths anxiety is associated with low level numerical deficits that compromise the development of higher level mathematical skills.

On the other hand, McMullan et al. [ 26 ] reported that numerical ability and maths anxiety are the main personal factors that might influence drug calculation ability in nursing students. The numerical ability test (NAT), used by McMullan et al. [ 26 ], is comprised of 15 questions that covered calculation operations like multiplication, addition, fraction, subtraction, percentage, decimals and conversion. McMullan et al. [ 26 ] reported that both numerical ability and drug calculation abilities of the participants (229 UK nursing students) were poor which might have been to an over-reliance on using calculators or not having adequate maths education in the past. Improving numerical ability and reducing maths anxiety can be achieved through teaching in a supportive environment using multiple teaching strategies that address the needs of all students and not being didactic [ 26 ]. Examples of these strategies include: accept and encourage students creative thinking, tolerate dissent, encourage students to trust their judgments, emphasise that everyone is capable of creativity, and serve as a stimulus for creative thinking through brainstorming and modelling [ 30 ].

Learning difficulty

Australian surveys have indicated that 10 to 16 per cent of students are perceived by their teachers to have learning difficulties according to Learning Difficulty Australia (LDA) (2012). Within the population of students with learning difficulties, there is a smaller subset of students who show persistent and long-lasting learning impairments and these are identified as students with a learning disability. It is estimated that approximately 4 per cent of Australian students have a learning disability (LDA 2012).

In this scoping review, one UK study addressed this concept, comparing undergraduate psychology students who represent 71% of the sample and nursing students who represent 14% of the sample who either had dyslexia ( n  = 28) or were assigned to the control group ( n  = 71). In 2014 Jordan et al. [ 31 ] reported that students with dyslexia had higher levels of maths anxiety relative to those without [ 31 ]. This study showed that significant correlations with maths anxiety were found for self-esteem ( r  = − 0.327; n  = 99, p .001), worrying ( r  = 393; n  = 99; p  < 0.001 the denial ( r  = 0.238; n  = 99; p  = 0.018, seeking instrumental support ( r  = 0.206; n  = 99; p  = 0.040 and positive reinterpretation ( r  = − 0.216; n  = 99; p  = 0.032). In addition, this study found that seeking instrumental support served as an indicator of students at high risk of maths anxiety. In explaining variation in maths anxiety. Jordan et al. [ 31 ] claimed that 36% of this variation is due to dyslexia, worrying, denial, seeking instrumental support and positive reinterpretation. The limitation of this study is that not all dyslexia cases were disclosed by the students. As long as some of the students with dyslexia are not reported, the generalisation of this study would be limited. This study recommends positive reframing and thought challenging as techniques to overcome difficult emotions and anxiety.

Limitations and future research

While multiple databases were used in this scoping review, some articles may be missed due to using specific terms in the search strategy. The disciplines covered in this scoping review were psychology, engineering, mathematics and some of the health disciplines such as nursing. Future research might focus on numerical ability and maths anxiety in university students who need maths and calculation in their future careers as engineers and health care professionals.

For example, the relationship between medication and drug calculation errors and maths anxiety in the health care field can be researched. Moreover, the relationship between self-awareness and numerical ability and maths anxiety and their impact on the performance and ability of the university students can be a future research topic. Finally, developing a new teaching package or strategy that reduces maths anxiety can be tested on university students.

Maths anxiety,which is an issue that affects many disciplines across multiple countries and sectors, is affected by gender, self-awareness, learning difficulties and numerical ability. Maths anxiety and its contributing factors at tertiary education should be researched more in the future addressing interventions and strategies to overcome maths anxiety. Maths anxiety level measuring tools should be used in determining its level among university students.

Availability of data and materials

It is a scoping review and all the articles that are analysed in this review are listed in the references section.

Abbreviations

Cumulative Index of Nursing and Allied Health Literature

Education Resources Information Centre

High Maths Anxious

Learning Difficulty Australia

Low Maths Anxious

Maths Barrier Scale

Maths Confidence Scale

Medical Subject Headings

Maths Value Scale

United Kingdom

United States

Revised Maths Anxiety Rating Scale

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EK conceived, designed and carried out the study, interpreted the analysis, and drafted and revised the manuscript. BW conceived, designed, drafted and revised the manuscript. CG helped conceive, drafted and revised the manuscript. All authors read and approved the final manuscript.

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Khasawneh, E., Gosling, C. & Williams, B. What impact does maths anxiety have on university students?. BMC Psychol 9 , 37 (2021). https://doi.org/10.1186/s40359-021-00537-2

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Systematic review article, reducing math anxiety in school children: a systematic review of intervention research.

• 1 Institute of Educational Research, University of Wuppertal, Wuppertal, Germany
• 2 Institute of Special Education, Leibniz University Hannover, Hanover, Germany
• 3 Department of Psychology, Federal University of Minas Gerais, Belo Horizonte, Brazil

Recent studies indicate that math anxiety (MA) can already be found in school-aged children. As early MA depicts a potential risk for developing severe mathematical difficulties and impede the socio-emotional development of children, distinct knowledge about how to reduce MA in school-aged children is of particular importance. Therefore, the goal of this systematic review is to summarize the existing body of research on MA interventions for children by identifying the approaches, designs, and characteristics as well as the effects of the interventions.

1 Introduction

In the last decade, a considerable amount of research focused on math anxiety (MA). Ramirez et al. (2018) sum up results of across 65 countries that participated in the 2012 PISA survey and highlight that “33% of 15-year-old students, on average, reported feeling helpless when solving math problems” (p.146). In accordance with the high prevalence in this age group, the majority of existing studies addressed MA in adolescents and young adults. However, more recent research described MA as early as in primary school children ( Ramirez et al., 2013 ; Cargnelutti et al., 2017 ; Gunderson et al., 2018 ; Sorvo et al., 2019 ; Primi et al., 2020 ) and highlighted negative impacts of early MA on their short- and long-term development and performance in mathematics ( Sorvo et al., 2017 ; Namkung et al., 2019 ; Zhang et al., 2019 ; Barroso et al., 2021 ). However, until now little attention has been paid to the investigation of interventions aiming at the reduction of MA in children ( Passolunghi et al., 2020 ). The paper at hand aims to systematically review the existing literature on interventions and approaches that target to reduce MA in school-aged children.

2 Theoretical Background

2.1 definition of ma.

MA can generally be defined as an “anxiety that interferes with manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” ( Richardson and Suinn, 1972 , p.551). There is, however, no consensus on the exact operationalization of MA in the field (e.g., Dowker et al., 2016 ). One important step towards a more precise definition and operationalization of MA is offered by the distinction of MA into trait and state anxiety. According to Spielberger (1972) trait anxiety refers to a relatively enduring individual disposition to feel anxious, whereas state anxiety refers to temporary and situational feelings of anxiety. Current MA studies either assess anxiety in math-related situations using hypothetical/retrospective questions (e.g., “How anxious would you feel if … ”) or assess anxiety about failure in math (e.g., “How worried are you if you have problems with … ”). The first type of question allows assumptions about state-like MA as not administered within the actual situation, the second type of question provides indications about trait MA ( Sorvo et al., 2017 ; Orbach et al., 2019 ). Considering empirical discrepancies between MA self-reports (see questions above) and real-time assessments ( Bieg, 2013 ), nowadays more studies apply questionnaires assessing state-MA within the actual mathematical situation (e.g., Vanbecelaere et al., 2021 ).

2.2 Explaining MA in Children

The development of MA and its relation to math performance has been investigated in only a few longitudinal studies ( Sorvo et al., 2019 ). According to these studies different etiological pathways have been suggested ( Carey et al., 2017 ; Sorvo et al., 2019 ) and it has been assumed that the MA-performance link is bidirectional ( Carey et al., 2016 ; Foley et al., 2017 ). In other words, MA can be considered as both the cause and the outcome of poor math performance ( Young et al., 2012 ).

Accordingly, MA could be elicited or increased over time because of math difficulties that often originate in early school years ( Ramirez et al., 2018 ). Ramirez et al. (2018) define this as reduced competency account and explain this link in two ways: A first explanation might be seen in lower numerical/spatial abilities which lead to underperformance in math and consequently to MA. Barroso et al. (2021) describe this association as the “deficit model” of MA (p.136). Ramirez et al. (2018) further summarize, that a second explanation could be seen in avoidance behavior that amplifies the development of math difficulties and consequent MA. In line with this, Ashcraft and Moore (2009) state that “avoidance of math is an overriding characteristic of math-anxious individuals” (p. 201). Therefore, experiencing math difficulties might cause a “vicious circle” ( Dowker et al., 2016 ) in which students avoid math-related situations leading to fewer opportunities to improve their math skills. Ramirez et al. (2018) consequently argue, that according to the assumption that MA may be the outcome of poor math performance, “interventions that aim to improve students’ math skills may be effective” to reduce MA (p. 156). Consequently, recent studies suggest a positive effect of mathematical interventions (MI) on MA in school children (e.g., Supekar et al., 2015 ; Passolunghi et al., 2020 ; Vanbecelaere et al., 2020 ).

Performance-inhibiting effects might, however, also be caused by MA. Such types of MA might be originally developed from environmental factors (e.g., adult role models: Casad et al., 2015 ; Lin et al., 2017 ) and genetic dispositions ( Wang et al., 2014 ; Malanchini et al., 2017 ). Such MA-related impacts on mathematical performance might be explained by the disruption of executive function processes and working memory ( disruption account ; Ramirez et al., 2018 ). This disruption may be caused by math-related worries (e.g., negative thoughts and rumination about one’s abilities or the consequences of failure). As a result, MA-evoking situations interfere with available cognitive resources (e.g., working memory) (e.g., Ramirez et al., 2013 ; Pizzie et al., 2020 ). Therefore, less resources are available for task-related problem-solving processes (e.g., arithmetical strategies). This might lead children either to switch to less sophisticated strategies (e.g., production deficiencies ) or apply advanced strategies unsuccessfully (e.g., utilization deficiencies ; Miller and Seier, 1994 ), both approaches leading to poorer performances. Barroso et al. (2021) summarize such links under the “processing efficiency theory” of MA (p.136). The links between MA and performance might additionally be influenced by the complexity of math tasks that children have to solve and the presence of time pressure. Studies using math assessments including more complex tasks show stronger MA-performance links ( Namkung et al., 2019 ; Zhang et al., 2019 ). Another stress-evoking factor might be seen in time pressure, as it seems to affect the arousal of children ( Caviola et al., 2017a ; Orbach et al., 2020 ). According to the assumption of a disruption of executive functions caused by math-related worries, cognitive-behavioral interventions (CBI) may help children to deal with maladaptive thoughts that e.g., attribute poor math grades to a lack of ability. Recent studies suggest a positive effect of CBI on MA in school children (e.g., Passolunghi et al., 2020 ).

2.3 Reducing MA in Children

With regard to the described manifold link between MA and mathematical performance, it becomes clear that reducing symptoms of MA might be a relevant approach in supporting children’s mathematical development ( Passolunghi et al., 2020 ). At the same time, the multiple explanations of the link between MA and mathematical performance might serve as a diverse foundation for designing appropriate interventional activities (e.g., addressing numerical/spatial abilities, executive functions, math self-concept). Previous work highlighted that the existing body of research can be subsumed into interventions that primarily target mathematical abilities as well as into cognitive-behavioral interventions that target anxiety related cognitions ( Dowker et al., 2016 ). Both directions can thereby be interpreted with regard to the described differential links between MA and mathematical performance.

As described, MI might be of particular relevance in light of the described reduced competency account ( Ramirez et al., 2018 ). They aim to break the vicious circle of MA and performance by promoting mathematical performance and thereby increasing math self-concept as well as decreasing MA. In line with this argument Dowker et al. (2016) propose that “interventions for children with mathematical difficulties may go some way toward preventing a vicious spiral, where mathematical difficulties cause anxiety, which causes further difficulties with mathematics” (p. 10). Similarly, math trainings moreover depict exposure interventions. Accordingly, Ramirez et al. (2018) argue that “the avoidance framework under the Reduced Competency Account states that avoidance tendencies may be responsible for the deficits in development (and explains why increased exposure is an effective solution)” (p. 156).

The effects of CBI can be mainly explained with regard to the described disruption account ( Ramirez et al., 2018 ) . Accordingly, CBI might decline the potential impact of anxiety-related cognitive processes and by that means improve mathematical performance. Dowker et al. (2016) as well as Ramirez et al. (2018) both highlight the potential impact of CBI such as re-appraisal and expressive writing on MA.

3 Objective of the Study and Research Questions

Most of the existing body of research on MA and MA interventions appears to focus on older adolescents and adults, as MA has been previously associated with more complex mathematics. At the same time, MA could already be observed in school-aged children and might be associated with early mathematical functioning and numeracy. Therefore, early identification and intervention of MA seems to be of high relevance to prevent negative developmental outcomes. As research on early MA interventions is limited, the exact conditions and characteristics of successful interventions in school-aged children remain unclear. To our knowledge, no existing work has summarized the existing evidence on the interventional approaches that target MA in childhood. Therefore, the objective of this study is to give an overview of interventional approaches in addressing MA in children and adolescents and to highlight potential characteristics of effective interventions. The study is guided by the following research questions:

1) What are the approaches, designs, and characteristics (e.g., setting, duration) of existing interventions aiming at the reduction of MA in school children?

2) What are the effects of these existing interventions?

Answers to these questions might contribute to the field of MA intervention research, as they might serve as a foundation and orientation for future intervention studies aiming at improving children’s emotional well-being and academic development in schools, especially regarding mathematics.

As MA has been addressed in previous research, we aim to identify characteristics of effective interventions based on the existing body of research. Therefore, we conduct a systematic (scoping) review. Thereby, we will describe the main findings of the included studies and highlight specific components using a narrative approach.

4.1 Search Procedure

To identify all relevant studies, we used a two-step approach. In a first step we conducted a systematic search in the most widely used electronic databases in psychological and educational research. Therefore, we focused on the databases PsycINFO and PubPsych. PubPsych is a multilingual database that includes entries from additional databases, such as PSYNDEX, MEDLINE and ERIC (Educational Resources Information Center). We used the descriptors: math (ematics) anxiety AND intervention OR treatment OR therapy OR program OR training OR tutoring OR support OR strategies OR best practice, AND alleviation as well as its synonyms reduction OR decrease OR remediation. Additionally, a German translation of the descriptors was used. To prevent the exclusion of relevant studies at an early stage no filters were used except the exclusion of dissertations as full texts are often difficult to access. We additionally identified studies by hand search, i.e., visually scanning reference lists from relevant studies or theoretical papers. The literature search was conducted in July 2020 and October 2021.

4.1.1 Inclusion and Exclusion Criteria

Studies were eligible for the systematic review if they met all the following inclusion criteria:

• Participants received intervention or a combination of interventions.

• Participants were assessed with a quantitative and/or qualitative measure of MA.

• Participants were of school-age (5–17 years old).

Studies were not eligible if they met one of the following exclusion criteria:

• The study was no intervention study (e.g., theoretical paper, literature review, meta-analysis, or correlation study).

• Participants did not match the target population (e.g., university students or (pre-service) teachers).

• The study was published in a language other than English or German.

The selection of eligible studies was conducted in two stages. Firstly, we employed an initial screening of titles and abstracts against the inclusion and exclusion criteria. Screening procedures followed PRISMA guidelines ( Moher et al., 2009 ). All studies were screened using the tool for systematic reviews Rayyan ( Ouzzani et al., 2016 ). Rayyan is an open access online application that enables a semi-automated collaborative screening process. Secondly, all studies that appeared to meet the inclusion criteria, or when a decision could not be made based on the title and/or abstract, were screened again based on their full texts.

4.2 Study Selection

The described inclusion and exclusion criteria were applied during the selection process (for an overview of the study selection process see Figure 1 ). The initial search in the databases PsycINFO and PubPsych led to the identification of 521 records. Additionally, 13 records were identified by hand search. After removing duplicates, the titles, and abstracts of 479 records were screened for potential eligibility. This step led to the exclusion of 452 records. The full texts of 27 records were consequently assessed for eligibility. As a result, three more records were excluded. These steps led to the inclusion of 24 records. A second search run was conducted in October 2021 to include most recent studies. This led to the inclusion of ten more studies. The final number of studies for the qualitative synthesis was 34.

FIGURE 1 . Study selection process following PRISMA guidelines.

4.3 Data Extraction and Coding Procedure

Next to general information about the studies, such as author(s), year of publication, and title, we extracted relevant data to address our specific research questions. Regarding our first research question (approaches, designs, and characteristics of existing interventions) we coded all information given by the author(s) about the study design, interventions, and their respective settings. This included information about the general study approach (quantitative, qualitative, mixed method), the study design (pre-post-test, follow up, control/comparison group), the operationalization of MA, as well as data about sample size and age group of the participants. Regarding the intervention we extracted information about the content as well as the intended goal of the interventions. We also coded the duration of the interventions (overall time span and number of sessions), the duration of single sessions, the intervention mode (computer-based, face-to-face), and the social arrangement (single, partner, small groups, class). Concerning our second research question (effects of these existing interventions) we coded the key results of the studies regarding the effectiveness of the intervention(s) to reduce MA as reported by the authors.

Relevant information has been coded using a spread sheet covering the previously described categories. The number of free text fields has been limited as much as possible to enable an unambiguous extraction and analysis of the data. Preferably fixed text such as yes/no decisions and drop-down lists has been used to code the data. The data extraction spread sheet has been previously piloted and adapted.

For a complete overview over all included studies (reference, sample, design, MA measure, operationalization type of MA, intervention, setting, and main findings) see Table 1 .

TABLE 1 . Overview of included studies.

5.1 Intervention Approach

Most of the included studies applied either a mathematical intervention (MI) approach (see section I in Table 1 ) or a cognitive-behavioral intervention (CBI) approach (see section II in Table 1 ). Four studies used other interventional approaches that could not clearly assigned to one of these two approaches (see section III in Table 1 ).

5.2 Sample and Study Design

The study samples differed between the two main intervention approaches (MI and CBI) in regards to the age groups of the participants. 82% of the MI studies targeted school age children (6–12 years), whereas 57% of the studies within the CBI approach focused on adolescents (13–17 years). Regarding the sample size and choice of study design there appears to be no systematic difference between MI and CBI studies. The majority of the included studies applied a quantitative study design to examine the effects of various interventions on MA. Thereby, the sample size of the included studies varies strongly, M = 138 ( SD = 171). Whilst some studies used large samples of over 300 participants ( Shapka and Keating, 2003 ; Brandenberger and Moser, 2018 ; Vanbecelaere et al., 2020 ), other studies only collected information of approximately 20 participants ( Kamann and Wong, 1993 ; Supekar et al., 2015 ; Choi-Koh and Ryoo, 2019 ). Most of the quantitative studies applied a pre-post design and included a control or comparison group. Whilst some studies used a waiting list procedure for the control group (i.e., the group received the same intervention with some time delay after the intervention group), other studies applied alternative interventions (e.g., Shapka and Keating, 2003 ; Asikhia and Mohangi, 2015 ) or applied modified version of the actual target intervention ( Kramarski et al., 2010 ; Huang et al., 2014 ). Four studies additionally followed up on their participants in the intervention and control group ( Sheffield and Hunt, 2006 ; Rauscher et al., 2017 ; Vanbecelaere et al., 2020 ; Vanbecelaere et al., 2021 ). Two of the identified studies applied single-case procedures to address potential effects of interventions on MA. LaGue et al. (2019) applied a multiple baseline approach within an experimental single-case design. Hord et al. (2018) used a qualitative approach to single-case research and focused on two eighth grade students with learning disabilities using a descriptive, qualitative microanalysis.

5.3 MA Measure

Different quantitative measures have been used to assess the level of MA (for an overview see Table 1 ). Some of the measures have been extensively researched and validated, such as the Math Anxiety Scale for children (MASC; Chiu and Henry, 1990 ) or the Math Anxiety Rating Scale—Revised (MARS-R; Plake and Parker, 1982 ). Often measures were translated and/or adapted for the specific contexts and needs of the studies. Some studies used measures that were self-developed or not as commonly known (e.g., Kramarski et al., 2010 ; Tok et al., 2015 ; Singh, 2016 ) Also, qualitative measures such as observational field notes and self-talk recordings have been used ( Kamann and Wong, 1993 ; Hord et al., 2018 ). According to the differentiations by Sorvo et al. (2017) and Orbach et al. (2019) , one study ( Vanbecelaere et al., 2021 ) used a real-time assessment measuring individuals math-related anxiety reaction during a math test situation (state-MA), 19 studies (approx. 54%) applied questionnaires with hypothetical/retrospective questions asking how anxious the individual would feel during a math-related situation (anxiety in math-related situations/statelike-MA) and nine studies (approx. 26%) used questionnaires with hypothetical/retrospective questions about anxiety in math-related situations (statelike-MA) and questions focusing anxiety about failure in math (trait-MA). Two studies used unclassifiable qualitative approaches ( Kamann and Wong, 1993 ; Hord et al., 2018 ). Four studies provided no clear information about the MA operationalization ( Idris, 2006 ; Lavasani et al., 2012 ; Mehdizadeh et al., 2013 ; Huang et al., 2014 ).

5.4 Intervention Activity

5.4.1 mathematical interventions.

The MI covered a wide range of different activities and programs, such as educational games or formalized math programs. Due to the amount of activities, only selected studies are presented in more detail below. The study selection does not constitute an evaluation of the quality of the studies. For a comprehensive overview of all MI see the first section of Table 1 .

Alanazi (2020) , Huang et al. (2014) , and Vanbecelaere et al. (2021) investigated the effect of educational math games on MA and performance in primary school children. The intervention group in Alanazi (2020) study participated in face-to-face recreational math games (e.g., movement games containing mathematical problems) in addition to their regular math teaching. The comparison group received regular math teaching. The intervention group obtained lower MA scores and higher math performance than the control group. Huang et al. (2014) and Vanbecelaere et al. (2021) applied a digital game-based learning approach. Huang et al. (2014) designed a digital math game to train basic arithmetic operations that provided the children in the intervention group with interactive diagnostic feedback. The children in the comparison group also played the game but without diagnostic feedback. Both groups obtained lower MA scores and enhanced levels of learning motivation. Vanbecelaere et al. (2021) compared an adaptive version with a nonadaptive version of the Number Sense Game ( Maertens et al., 2016 ). The Number Sense Game contained two types of exercises, a comparison game and a number line estimation game. Both groups obtained lower MA scores and improved on early numeracy skills.

Jansen et al. (2013) , Rauscher et al. (2017) , and Supekar et al. (2015) investigated the effect of formalized math training programs on primary school students’ math performance and anxiety. Jansen et al. (2013) and Rauscher et al. (2017) applied specific math training software, namely Math Garden ( Klinkenberg et al., 2011 ) and Calcularis ( Käser et al., 2013 ). In Jansen et al. (2013) study the control group received regular math teaching. Both groups obtained lower MA scores and the math performance only improved in the intervention group. Rauscher et al. (2017) compared the intervention group with two control groups; one was a waiting list group, the other received a control training. The results showed that the intervention group obtained lower MA scores than the waiting list control group, but there was no difference in MA between the intervention group and the control training group. Supekar et al. (2015) examined an adaption of MathWise ( Fuchs et al., 2013 ), a training program that aims to improve number knowledge, counting speed and the application of calculation strategies. Comparing children with high MA and low MA levels, the children with high MA significantly decreased their MA. In regards to math performance both groups benefited equally from the training.

5.4.2 Cognitive-Behavioral Interventions

The CBI also included different techniques and activities, such as coping strategy training or expressive writing. Due to the amount of activities, only selected studies are presented in more detail below. The study selection does not constitute an evaluation of the quality of the studies. For a comprehensive overview of all CBI see the second section of Table 1 .

Collingwood and Dewey (2018) , Kamann and Wong (1993) , Passolunghi et al. (2020) , and Ruff and Boess (2014) investigated the effect of coping strategy trainings on primary school students’ MA. Kamann and Wong (1993) examined a coping strategy based on cognitive behavior modification ( Meichenbaum, 1977 ) to reduce MA. They compared children with and without learning disabilities (LD) providing both groups with sample self-instruction statements on cue cards to assist them in applying those statements at each level of the coping process. The LD group showed increased positive self-talk compared to the group without LD indicating enhanced coping with MA. Collingwood and Dewey (2018) examined a multi-dimensional cognitive intervention called Thinking your problems away ( Martin, 2008 ) that encouraged (among other things such as self-regulation) the use of positive-self-coping statements based on Kamann and Wong (1993) . The control group was a waiting list control group. The intervention group showed no reduction of MA or enhancement of math self-concept but higher math performance than the control group. Passolunghi et al. (2020) trained the primary school children in strategy-based techniques (among others things such as the recognition of emotions) to decrease their MA. These techniques included breathing exercises, safe place visualizations and re-appraisal of negative thoughts based on Ellis and Bernard (2006) . The control group received a control training composed of playful activities with comic strips. The intervention group obtained lower MA scores but no increase in math performance compared to the control group.

Hines et al. (2016) and Ruark (2021) investigated the effect of expressive writing on MA in secondary school students. In the intervention group of Hines et al. (2016) study the participants wrote about their math related feelings 15 min a day for 3 days. The control group did the same amount of expressive writing but on a neutral topic. The intervention group reported reduced levels of general anxiety and MA, whereas the control group also indicated reduced levels of MA. The students in Ruark (2021) study wrote about their math homework problems every day for 2 weeks. The intervention group was requested to write about their feelings when encountering problems during math homework for at least 1 minute. The control group wrote about their math homework problems only. Both groups showed no reduction of MA.

5.5 Intervention Mode and Setting

The interventions were either carried out face-to-face (67.6%) or via computer (23.5%). Three studies (8.8%) did not fit into one of the two categories. Segumpan and Tan (2018) used both settings—face-to-face and computer—as they investigated the effect of a Flipped Classroom on secondary school students’ MA and performance. In Hines et al. (2016) and Ruark (2021) studies the participants performed expressive writing activities at home without specifications whether to use paper and pencil or a computer.

Within the mathematics intervention approach computers were predominantly used to train basic arithmetic operations in primary school children (e.g., Mevarech et al., 1991 ; Jansen et al., 2013 ; Huang et al., 2014 ; Rauscher et al., 2017 ). Jansen et al. (2013) , Rauscher et al. (2017) , and Vanbecelaere et al. (2021) explicitly mentioned the adaptivity of their training software, i.e. the selection of training tasks was regulated by an adaptive algorithm ( Klinkenberg et al., 2011 ). The only study within the CBI approach that utilized computers was Kim et al. (2017) . In this study secondary school students were guided through a computer-based learning environment by a so-called embodied agent. The learning environment covered fundamental algebra topics. In the intervention group the embodied agent provided not only instructional guidance (control condition) but also anxiety treating messages. Results indicated that both groups obtained lower MA scores and higher math performance. All other CBI were conducted face-to-face.

The interventions were either held in classrooms (29.4%), small groups (32.4%), or individual settings (26.5%). Four studies (11.8%) did not specify the setting of their intervention. There were no significant differences between the settings in regards to the intervention approach.

5.6 Intervention Length

On average, the included studies applied interventions for M = 7.04 weeks ( SD = 6.78). However, the span of the overall duration was large. The interventions ranged between a 1-h session ( Sheffield and Hunt, 2006 ) and one school year ( Brandenberger and Moser, 2018 ). Similarly, the number of training sessions varied between the included studies, M = 10.51 sessions ( SD = 7.86). Again, the span of the number of sessions was large. The interventions took between one session (e.g., Sheffield and Hunt, 2006 ) and 30 sessions ( Rauscher et al., 2017 ). Accordingly, the number of sessions per week differed, M = 2.6 sessions/week ( SD = 1.4). Moreover, the duration of the individual session varied, M = 46.82 min ( SD = 19.85), ranging from 15 min (e.g., Jansen et al., 2013 ) to 90 min of intervention time (e.g., Asanjarani and Zarebahramabadi, 2021 ) in each session.

5.7 Intervention Effects on MA

The intervention effects reported by the authors were mixed. 59% of the studies reported a positive effect of the intervention on MA in the intervention group compared to no effect in the control/comparison group (e.g., Kramarski et al., 2010 ; Tok et al., 2015 ; Alanazi, 2020 ; Passolunghi et al., 2020 ). In Passolunghi et al. (2020) study math strategy training influenced and improved not only math ability, but also contributed to a decrease in students’ MA level. In the same study the cognitive-behavioral MA training showed only effects in reducing MA level, but there was no improvement of math abilities. Verkijika and De Wet (2015) provided evidence that MA could be effectively reduced by means of neuropsychological feedback while playing a math game. LaGue et al. (2019) reported positive effects of mindfulness-based cognitive therapy on students’ MA levels using an experimental single-case study design.

21% of the studies found a positive effect of intervention(s) on MA in both the intervention as well as the control/comparison group (e.g., Jansen et al., 2013 ; Huang et al., 2014 ; Hines et al., 2016 ; Kim et al., 2017 ; Arias Rodriguez et al., 2019 ). Rauscher et al. (2017) showed that students who trained with the online math training Calcularis obtained significant lower MA scored compared the waiting list control group (intervention vs. waiting list control group). When compared to the control group that received a control training MA was, however, reduced equally in both groups (intervention vs. control training). Other studies reported a positive effect of the intervention(s) on MA for certain groups of students, such as highly anxious ( Supekar et al., 2015 ; Choi-Koh and Ryoo, 2019 ) or low achieving students (e.g., Mevarech et al., 1991 ).

15% of the studies did not find a positive effect of the intervention on the students’ level of MA (e.g., Shapka and Keating, 2003 ; Tok, 2013 ; Collingwood and Dewey, 2018 ; Vanbecelaere et al., 2020 ). Collingwood and Dewey (2018) reported a positive impact of intervention on the mathematical performance of students in the intervention group, however, no significant impact on the level of MA. Tok (2013) also found increased achievement after teaching students to use the Know-Want-Learn strategy as well as improved metacognitive abilities, but no significant impact on MA. Shapka and Keating (2003) did not find evidence that girls-only math teaching would reduce female students’ MA in comparison to co-educated math teaching.

The findings did not differ in relation to the applied MA questionnaires. The only study that used a real-time assessment (state-MA) reported a positive effect of a math training on MA, approx. 80% of the studies using questionnaires with hypothetical/retrospective items (statelike-MA/anxiety in math-related situations) reported lower MA after the intervention and approx. 90% of the studies using questionnaires focusing anxiety about failure (trait-MA) and anxiety in math-related situations (statelike-MA) reported lower MA after the intervention.

6 Discussion

The goal of this study was to summarize the existing body of research on MA interventions for school children. Therefore, we conducted a systematic (scoping) review and presented the results in a narrative manner. Table 1 gives a comprehensive overview of the included studies and their main characteristics. Note that not all studies provided all relevant information.

Generally, the overall number of eligible studies identified in this review was still relatively small, for example compared to general mathematical intervention studies ( Reynvoet et al., 2021 ). Given the potential negative impact of early MA on children’s short- and long-term development, one would have expected a greater attention to this field of research. This finding indicates that research on MA interventions is still emerging. The fact that most studies included in this review are relatively recent underpins this assumption. At the same time, the categorization of interventions into either MI or CBI as described in adults, can be similarly found in MA research in children and adolescents. The application of both approaches might be justified by different explanations of the MA-performance link (e.g., the reduced competency account and the disruption account of MA; Ramirez et al., 2018 ). Our findings do not justify any judgments on potential empirical advantages of either approach, as no direct comparisons of the described effects are possible. Future meta-analyses are required to address this issue. At the same time, our findings give qualitative insights into the existing body of research in MA interventions.

More than half of the included studies primarily focused on math performance rather than MA. Hence, MA was often assessed as an affective covariate but was not necessarily the actual target of the intervention. Despite that, almost half of the included MI still reported a positive side-effect of the intervention on students’ MA compared to the control/comparison group. This supports the assumption that MI can reduce anxiety responses, but might also allow children to re-evaluate dysfunctional cognitive beliefs (“I am bad at math”) and to stimulate the formation of new basic cognitive assumptions (e.g., increase of math self-concept).

As for the CBI, more than half of the included studies reported a positive effect of the intervention on the level of MA compared to the control/comparison group. At the same time, the effect of CBI on math performance was comparatively low. One possible explanation could be that the physiological arousal that comes with an anxious response (e.g., increased heart rate, faster breathing) can also support performance. Therefore, reducing this arousal through breathing or self-regulation exercises might not always be beneficial to enhance performance. Instead re-appraising the arousal as a sign of challenge or excitement rather than threat, might help children to capitalize on the performance enhancing effects of their physiological response see Biopsychological model of Challenge and Threat, ( Blascovich, 2008 ). Similar effects have already been observed in adults (e.g., Brooks, 2014 ; Jamieson et al., 2016 ).

The mixed effects of the MI and CBI on MA and performance might indicate that a combination of both approaches could be most beneficial for school children. This means, on the one hand, to develop sound arithmetic skills that build not only the foundation for more complex math content but would also help children to form a positive math self-concept. On the other hand, combined interventions could also provide children with cognitive-behavioral tools to cope with their anxious thoughts and arousal in math related situations. These tools should, however, take effect models into account, such as the Biopsychological model of Challenge and Threat ( Blascovich, 2008 ), that aim to capture the complex interrelations between cognitive processes and affective, physiological, and behavioral responses.

Furthermore, almost a quarter of the described studies, that either apply MI or CBI, reported positive effects on MA for both the intervention and the control/comparison group. This surprising result raises questions on potential third factors that led to a reduction of MA in these studies, and that have not yet been taken explicitly into account. These third factors could be school- and teaching-related variables that might be associated with the development of MA (e.g., teacher’s beliefs). At the same time, the differences between the control groups of the included studies hinder potential discussions of these third factor variables. Of course, methodological issues might explain the non-existing differences between control and intervention groups (e.g., non-randomized controls leading to an unbalanced study design, unknown background interventions). In addition, reductions in the level of MA in both groups might be explained by the applied MA measures. To make differentiated conclusions about impacts of intervention programs on math-related anxiety reactions and/or math anxious cognitive beliefs, it may be useful for future studies to carefully consider the conceptualizations of MA questionnaires. E.g., intervention programs focusing emotional-regulation strategies could benefit from real-time assessments, measuring math-related anxiety reactions (state-MA), whereas studies that incorporate CBI might be more likely to evaluate effects on cognitive beliefs and trait-dispositions. However, to account for all influences, it would be best to consider both situation- and disposition-related approaches.

When comparing the mode and settings of the MI and CBI, it becomes clear that the majority of CBI was based in a one-to-one or small group setting. A classroom-based application of CBI was rare. Hence, future research might try to apply CBI or to combine CBI and MI on a classroom level. Despite the fact that interventions addressing MA are of relevance for students with high levels of MA, all students might profit from adequate strategies targeting anxiety related cognitions.

To conclude, a few limitations of our systematic review need to be mentioned. Firstly, the review only included intervention studies that target MA. This approach might have excluded a range of studies and findings, that highlighted the relevance of potential variables that might also be associated with the development of MA but had not been part of an intervention study (e.g., environmental factors). Secondly, although we tried to capture all relevant information of the included studies as accurate and complete as possible, the transparency within the studies was lacking at times. This implies, that important information might be missing or incomplete for some of the included studies. Especially missing information on the format and duration of the interventions makes it difficult to compare the effectiveness of the different approaches. And thirdly, our review is not a meta-analysis. Insights in described effects are therefore on a descriptive level and do not allow a direct statistical comparison or aggregation of the described effects.

In the end, no clear picture can be drawn yet of how effective MA intervention for school children should look like. However, this literature review still offers valuable insights into the current state in the field of MA intervention research. Both approaches (MI and CBI) show potential positive effects. The findings of this review at hand might therefore serve as an orientation for future research and for the development of effective interventions that aim to reduce MA in children.

Data Availability Statement

The raw data supporting the conclusion of this article will be made available by the authors on request, without undue reservation.

Author Contributions

LO, MB and MB-R drafted the theoretical background. MB and MB-R were responsible for data analysis and discussion of the findings. All authors contributed to the article and approved the submitted version.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

We thank Julia Gehlhaus, Lisa Marie Flebbe, and Kristin Busse for their support in screening and evaluating the studies for this systematic review and for piloting the data extraction spread sheet as part of their Bachelor theses. We acknowledge support from the Open Access Publication Fund of the University of Wuppertal.

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Keywords: math anxiety, intervention, review, school, children

Citation: Balt M, Börnert-Ringleb M and Orbach L (2022) Reducing Math Anxiety in School Children: A Systematic Review of Intervention Research. Front. Educ. 7:798516. doi: 10.3389/feduc.2022.798516

Received: 20 October 2021; Accepted: 06 January 2022; Published: 03 February 2022.

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Copyright © 2022 Balt, Börnert-Ringleb and Orbach. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Miriam Balt, [email protected]

This article is part of the Research Topic

Cognitive and Affective Factors in Relation to Learning

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• Published: 07 September 2020

Mathematics anxiety among STEM and social sciences students: the roles of mathematics self-efficacy, and deep and surface approach to learning

• Dmitri Rozgonjuk   ORCID: orcid.org/0000-0002-1612-2040 1 , 2 ,
• Tiina Kraav 2 ,
• Kristel Mikkor 2 ,
• Kerli Orav-Puurand 2 &
• Karin Täht 2 , 3  

International Journal of STEM Education volume  7 , Article number:  46 ( 2020 ) Cite this article

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Although mathematics anxiety and self-efficacy are relatively well-researched, there are several uninvestigated terrains. In particular, there is little research on how mathematics anxiety and mathematics self-efficacy are associated with deep (more comprehensive) and surface (more superficial) approaches to learning among STEM and social sciences students. The aim of the current work was to provide insights into this domain.

Bivariate correlation analysis revealed that mathematics anxiety had a very high negative correlation with mathematics self-efficacy. However, while mathematics anxiety correlated positively with surface approach to learning in the STEM student sample, this association was not statistically significant in the social sciences student sample. Controlled for age and gender, regression analysis showed that lower mathematics self-efficacy and female gender predicted higher mathematics anxiety, while only mathematics self-efficacy predicted mathematics anxiety in the social sciences student sample. Interestingly, approaches to learning were not statistically significant predictors in multivariate analyses when mathematics self-efficacy was included.

Conclusions

The results suggest that mathematics self-efficacy plays a large role in mathematics anxiety. Therefore, one potential takeaway from the results of the current study is that perhaps improving students’ mathematics self-efficacy could also be helpful in reducing mathematics anxiety. Since the current study was cross-sectional, it could also be that reducing students’ mathematics anxiety could be helpful in boosting their mathematics self-efficacy. Future studies should aim to clarify the causal link in this relationship.

Introduction

One could argue that mathematics is an important component in science, technology, engineering, and mathematics (STEM) education, since most domains rely on applying mathematical thinking. Research on teaching and learning mathematics has received a lot of attention over the years, as mathematical knowledge is a crucial factor for students’ successful future careers (Claessens & Engel, 2013 ; Konvalina, Wileman, & Stephens, 1983 ). As mathematics is commonly perceived to be difficult (Fritz, Haase, & Räsänen, 2019 ), it has been proposed that instead of instructing the content and practices of mathematics, the main focus should be on students’ experience of the discipline and providing mathematical sense-making (Li & Schoenfeld, 2019 ). Research in tertiary mathematics education is also a growing field as the role of mathematics in learning other disciplines is widely acknowledged.

Little research has investigated the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning in the context of mathematics education among STEM and social sciences students. Do students with higher mathematics anxiety also have a more superficial approach to learning? Or does mathematics self-efficacy also contribute to a more thoughtful and integrative learning process? Are there significant differences in mathematics self-efficacy, mathematics anxiety, and approaches to learning between STEM and social sciences students? Thus far, these questions have not received a lot of attention in the academic literature. Therefore, the main aim of this study is to provide some insights into the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning, and the potential differences in those variables between STEM and social sciences students. While several associations have been investigated in earlier works (see below), this is the first study where the relationships between all these variables are compared among STEM and social sciences students.

Literature overview

Mathematics anxiety has been described as experiencing feelings of panic and helplessness when asked to solve a mathematical task or problem (Tobias & Weissbrod, 1980 ). Psychological as well as physiological symptoms may appear when feeling anxious about mathematics (Chang & Beilock, 2016 ). Mathematics anxiety is known as a common problem in K-12 as well as tertiary education (Ashcraft & Moore, 2009 ; Luttenberger, Wimmer, & Paechter, 2018 ; Yamani, Almala, Elbedour, Woodson, & Reed, 2018 ) and, therefore, has received considerable attention as a researched topic among educational scientists (Dowker, Sarkar, & Looi, 2016 ; Hoffman, 2010 ; Jansen et al., 2013 ). For instance, in the Programme for International Student Assessment (PISA) 2012, across the 34 participating Organisation for Economic Co-operation and Development (OECD) countries, 59% of the 15-year-old students reported that they often worry that math classes will be difficult for them and 31% reported they get very nervous doing math problems (OECD, 2013b ).

Mathematics anxiety can be caused by several different factors. For instance, unpleasant teaching and assessment strategies for students, like time testing (Ashcraft & Moore, 2009 ) and assigning mathematics as punishment (Oberlin, 1982 ), that are still widely in use in all school levels, may influence the spread of mathematics anxiety. Although mathematics anxiety may have been appearing relatively early in life, it has been shown that there are possibilities to reduce mathematics anxiety in all levels of schooling (Hembree, 1990 ). As appropriate mathematics-related instruction and teacher’s enthusiasm toward mathematics are important in the development of mathematics anxiety of students (Jackson & Leffingwell, 1999 ), reduction of pre-service teachers’ own mathematics anxiety is crucial and it could be helpful in reducing the students’ mathematics anxiety (Gresham, 2007 ; Vinson, 2001 ). Applying more active learning (such as group work) may also reduce anxiety (Cooper, Downing, & Brownell, 2018 ).

Mathematics anxiety has been shown to be associated with poorer performance in mathematics (Ashcraft & Faust, 1994 ; Devine, Fawcett, Szűcs, & Dowker, 2012 ; Fan, Hambleton, & Zhang, 2019 ). In addition, it has been shown, that mathematics anxiety also correlates with other variables (e.g., learning behavior, self-efficacy) that influence academic performance (Feng, Suri, & Bell, 2014 ; McMullan, Jones, & Lea, 2012 ). For example, Paechter, Macher, Martskvishvili, Wimmer, and Papousek ( 2017 ) investigated psychology students and showed a correlation between mathematics and statistics anxiety and learning behavior. In addition, Royse and Rompf ( 1992 ) compared social work and non-social work university students and found that the former had higher levels of mathematics anxiety than the latter group. Nevertheless, there are no studies comparing STEM and social sciences students with regard to mathematics anxiety.

Attitudes toward mathematics is another construct that plays an important role in mathematical studies, as well as its outcomes (Ahmed, Minnaert, Kuyper, & van der Werf, 2012 ; House, 2005 ). Mathematics attitudes and anxiety are often studied together; nevertheless, they cannot be equated with each other. As Zan and Martino ( 2007 ) describe, many studies about mathematics attitudes do not provide a clear definition for the construct. It always has an emotional dimension (positive or negative emotional disposition toward mathematics), usually also involving conceptualization of mathematics (Dowker et al., 2016 ), and/or mathematics-related behavior, depending on the specific research problem. In addition, one may argue that, to some extent, attitudes toward mathematics also reflect mathematics self-efficacy (Yusof & Tall, 1998 ). Self-efficacy could be defined as one’s belief in one’s ability to succeed in specific situations. The academic aspect of this concept is called academic self-efficacy, and is described as an individual’s belief that they can successfully achieve at a designated level on an academic task (Bandura, 1997 ). Mathematics self-efficacy is one’s belief about how their own action and effort could lead to success in mathematics (Luttenberger et al., 2018 ; OECD, 2013b ). Higher mathematics self-efficacy has been shown to be correlated with lower mathematics anxiety, more positive, and less negative attitudes toward mathematics (Akin & Kurbanoglu, 2011 ). In addition, higher mathematics anxiety is related to more negative attitudes toward mathematics (Vinson, 2001 ). These findings underscore the importance of mathematics anxiety in attitudes toward mathematics, as well as mathematics self-efficacy.

More general attitudes toward learning are also important to be considered. Marton and Säljö ( 1976 ) referred to a co-existence of intention and process of learning and described deep and surface learning approaches. Students with a deep approach to learning look for the meaning of the studied material and try to relate new knowledge with prior information, whereas students with a surface approach to learning use rote learning and un-meaningful memorization. How students approach to learning in higher education is an important factor when speaking about educational outcomes (Duff, Boyle, Dunleavy, & Ferguson, 2004 ; Fryer & Vermunt, 2018 ; Maciejewski & Merchant, 2016 ). Deep approach to learning is associated with better general academic outcomes, as well as, specifically, better mathematical performance (Murphy, 2017 ; Postareff, Parpala, & Lindblom-Ylänne, 2015 ). Although it is not the sole factor influencing mathematics achievement, it is still important to determine students’ approaches to learning mathematics, as it enables educators to analyze and shape the students’ classroom experience toward more effective learning.

Little research has been done in the domain of approaches to learning in relation to mathematics anxiety and self-efficacy in tertiary education. Anxiety in general is associated with higher surface and lower deep approach to learning (Marton & Säljö, 1984 ). In one study, surface approach to learning has been found to correlate with mathematics anxiety (Bessant, 1995 ). It has also been demonstrated that students with positive attitudes toward mathematics tend to use more deep and less surface approach when learning mathematics (Alkhateeb & Hammoudi, 2006 ; Gorero & Balila, 2016 ). Another common finding in educational research is that students who have higher self-efficacy adopt more deep approach to learning (Papinczak, Young, Groves, & Haynes, 2008 ; Phan, 2011 ; Prat-Sala & Redford, 2010 ).

There are not many studies investigating the role of deep and surface approaches to learning in mathematics anxiety. Although a study by Bessant ( 1995 ) showed that mathematics students scored lower on mathematics anxiety measure than psychology/sociology students, the relations between mathematics anxiety and approaches to learning in STEM and social sciences students is a largely unexplored area.

Conceptual framework

Several studies have aimed to explain the potential causes for mathematics anxiety. It has been proposed that the origins of mathematics anxiety could be categorized into three groups (Baloglu & Kocak, 2006 ): situational, dispositional, and environmental factors. Situational factors are direct stimuli related to feelings of anxiety in relation to mathematics. Dispositional factors include individual characteristics, such as personality traits; for instance, it has been shown that people with higher trait neuroticism (the tendency to experience negative effect; McCrae & Costa, 2003 ) worry more and tend to be more anxious in general (Costa & McCrae, 1985 ), although this typically decreases with age (Mõttus & Rozgonjuk, 2019 ). Finally, environmental factors include prior perceptions, attitudes, and experiences that may have affected the individual (Baloglu & Kocak, 2006 ).

In the current work, mathematics self-efficacy as well as approaches to learning could be conceptualized as environmental factors that could potentially affect the development of mathematics anxiety. Furthermore, students’ age, gender, and the curricula could be considered as environmental factors potentially affecting mathematics anxiety (Baloglu & Kocak, 2006 ).

Aims and hypotheses

The general aim of this study is to investigate how mathematics anxiety and self-efficacy, as well as approaches to learning (deep and surface), are related to each other. Furthermore, these relationships are also compared across STEM and social sciences student samples. Based on the previous literature, we have posed some hypotheses that are rather confirmatory of previous findings. Based on the previous literature, we hypothesize the following:

H1: Mathematics anxiety and mathematics self-efficacy are negatively correlated .

Previously it has been demonstrated that mathematics anxiety and self-efficacy are inversely associated (Akin & Kurbanoglu, 2011 ; Vinson, 2001 ).

H2: Mathematics anxiety is positively correlated with surface approach to learning and negatively with deep approach to learning . Even though one study found that mathematics anxiety correlates positively with surface approach to learning (Bessant, 1995 ), it would also be natural to assume that deep approach to learning is negatively associated with mathematics anxiety, since typically surface and deep approaches to learning are inversely correlated (Rozgonjuk, Saal, & Täht, 2018 ).

H3: Mathematics self-efficacy is positively associated with deep and negatively with surface approach to learning. It has previously been shown that high self-efficacy, in general, is associated with more deep and less surface approach to learning (Chou & Liang, 2012 ; Papinczak et al., 2008 ). Therefore, it would be logical to assume that also in the context of mathematics, these constructs would be correlated.

H4: STEM students have less mathematics anxiety than social sciences students . Previously, Bessant ( 1995 ) have demonstrated that mathematics students had lower scores on mathematics anxiety measure than psychology/sociology students. However, our study goes beyond comparing only mathematics students, and includes students from other disciplines (e.g., biology) as well, forming a more heterogeneous STEM student group.

H5: Approaches to learning and mathematics self-efficacy predict mathematics anxiety when age and gender are controlled for. Based on previous research and hypotheses mentioned above, there is evidence to believe that the associations between approaches to learning, mathematics self-efficacy, and mathematics anxiety would hold also when covariates are included.

There is relatively little research in this domain and knowing the associations between these variables may help educators to improve and adjust their teaching strategies to potentially improve the learning process. The results of this study aim to outline the important predictors of mathematics anxiety, and, therefore, expand the existing research in this field of study, and influence future teaching strategies. The results of this work could be helpful for the teacher/lecturer when he/she aims toward reducing mathematics anxiety by, e.g., using teaching strategies that could enhance deeper (and less surface) approach to learning, increase mathematics self-efficacy, or both.

Material and methods

Sample and procedure.

The study participants were students who either took an introductory calculus course (dealing with more elaborate topics than in secondary education) for university students or an introductory statistical modeling course at a major Estonian university. Importantly, these courses were mandatory in order to complete the student’s curriculum and, in most cases, were prerequisite courses for other courses in the curriculum. While most of the students in the introductory calculus course were STEM curricula students, mainly psychology and political sciences majors were enrolled in the statistical modeling course. However, because it is possible to take these courses as electives as well, students with various backgrounds could participate in these courses. This means that, theoretically, both student groups could enroll in either the calculus or statistical modeling course. For instance, as could be seen in Supplementary Table 1 there are some Economics students who enrolled in a Calculus course, while all other social sciences students were enrolled in the statistical modeling course. Students’ responses across variables of interest across curricula are depicted in Supplementary Figures 1 to 4 .

The data were collected during the start of both courses, in September 2019. Students were asked to take part in a web survey which aimed to investigate the role of different factors in mathematics education. Participation in the study was voluntary, anonymous, and in line with the Helsinki Declaration.

In total, there were 358 responses. However, many rows were empty or most of the data were missing, after some initial data cleaning, 234 rows of responses were kept. The reason for the aforementioned “missing data” lies in the fact that whenever a person opens the questionnaire environment, this gets logged as a response row. However, it does not necessarily mean that a person provides any responses to the questionnaire. Therefore, as mentioned, out of 358 rows logged, only 234 were actually partially or fully filled in with responses. Finally, because n = 3 people did not specify their major, we excluded those rows. Therefore, the effective sample comprised 231 students (age M = 21.39, SD = 5.12; 79 (34.2%) men, 152 (65.8%) women). There were 147 (63.6% of total sample) STEM students (age M = 20.55, SD = 4.51; 57 men, 90 women), and 84 (36.4%) social sciences students (age M = 22.87, SD = 5.78; 22 men, 62 women).

We queried about the study participants’ socio-demographic variables (e.g., age, gender, curriculum/major), mathematics anxiety and mathematics self-efficacy, and approaches to learning (deep and surface).

• Mathematics anxiety

Mathematics anxiety was measured with the 5-item mathematics anxiety questionnaire used in the international PISA 2012 survey (OECD, 2013a ). Students were asked to assess on a 4-point scale (1 = strongly disagree to 4 = strongly agree ) the extent of agreement with the following statements: (1) I often worry that mathematics classes will be difficult for me ; (2) I get very tense when I have to do mathematics homework ; (3) I get very nervous doing mathematics problems ; (4) I feel helpless when doing a mathematics problem ; (5) I worry that I will get poor grades in mathematics . The psychometric properties of this scale in an adolescent population could be found in OECD report ( 2014 ; Table 16.7 on page 320). As a side comment, we opted for using this measure as opposed to, e.g., the Abbreviated Mathematics Anxiety Scale (AMAS; Hopko, Mahadevan, Bare, & Hunt, 2003 ), because the PISA-study mathematics anxiety scale fits better with contemporary classroom where the role of digitalization is increasing (e.g., the AMAS items include words like “book” and “blackboard,” but not digital resources). Secondly, PISA mathematics anxiety scale has demonstrated good psychometric properties, it has probably been administered in a larger variety of cultural settings (as opposed to the AMAS), and it has been validated against mathematics aptitude test in all these cultures (e.g., see the report by OECD ( 2014 ), p. 320, Table 16.7, ANXMAT). Finally, in all PISA survey questionnaires, stringent quality-assurance mechanisms are implemented by experts in translation, sampling, and data collection, resulting in a high degree of reliability and validity (OECD, 2017 ). Cronbach’s alpha for the effective sample of this measure was very good, α = 0.90.

• Mathematics self-efficacy

Mathematics self-efficacy was measured with three items, measuring the extent of agreement on a four-point scale (1 = strongly disagree to 4 = strongly agree ) from Yusof and Tall ( 1998 ). All items from the mathematics self-efficacy scale (Yusof & Tall, 1998 ) were translated into Estonian by the members of our mathematics education team and were reviewed by a professional Estonian philologist. The questionnaire was then translated back into English by another translator, and the back-translated English version was reviewed by an English-speaking student in order to estimate the content and the similarities between the original and the back-translated items. The items were the following: (1) I usually understand a mathematical idea quickly; (2) I have to work very hard to understand mathematics ; (3) I can connect mathematical ideas that I have learned . Cronbach’s alpha for this three-item measure was α = 0.83.

• Approaches to learning

Approaches to learning were measured with the Estonian adaptation of the Revised Study Process Questionnaire (Biggs, Kember, & Leung, 2001 ; Valk & Marandi, 2005 ). It is a 16-item measure (8 items for deep and 8 items for surface approach to learning) that measures deep and surface approaches to learning on a five-point scale (1 = do not agree at all to 5 = totally agree ). Example items for the deep approach to learning scale are as follows: I find most new topics interesting and often spend extra time trying to obtain more information about them , and I learn because I want to understand the world . Example items for the surface approach to learning scale are as follows: I see no point in learning material which is not likely to be in the examination , and In case of difficult topics, learning by rote is one way to pass an exam . The internal consistency of deep and surface approaches to learning were acceptable, Cronbach’s α = 0.71 for both scales.

Data analysis was conducted in the R software version 3.5.3 (R Core Team, 2020 ). As mentioned in the “Sample and procedure” section, we first removed the data rows that were not valid responses (empty rows) or where people did not specify their major ( n = 3). After this procedure, there were no missing data in key variables. Internal consistency statistics were calculated with the alpha() function from the psych package (Revelle, 2018 ). Since the sample sizes were not equal, Mann-Whitney U tests to analyze the potential group differences between STEM and social sciences students in age, math anxiety and self-efficacy, and deep and surface approach to learning were used. Chi-square test was used to see if there are differences in gender distribution among those student groups.

We then computed descriptive statistics and conducted Spearman correlation analysis (with p values adjusted for multiple testing with the Holm’s method), using the rcorr.adjust() function from the RcmdrMisc package (Fox, 2020 ). Finally, we computed regression models where mathematics anxiety was treated as the outcome variable, either surface or deep approach to learning as the predictor, age and sex were covariates, and we also computed additional regression models where mathematics self-efficacy was additionally included as a predictor variable. We ran these analyses for the whole sample, as well as for STEM and social sciences students separately.

The data as well as the analysis script are included with this work as Supplementary Materials .

Firstly, we analyzed if STEM and social sciences students had group differences in key variables. There were no statistically significant group differences in deep and surface approaches to learning, mathematics anxiety, as well as in gender distribution (all ps > 0.01). However, the social sciences student group was slightly older ( M = 22.87, SD = 5.78) than the STEM student group ( M = 20.55, SD = 4.51), W = 9742, p < 0.001. In addition, STEM students ( M = 8.39, SD = 1.92) had higher mathematics self-efficacy scores than social sciences students ( M = 7.77, SD = 2.03), W = 5080.50, p = 0.023.

Descriptive statistics and correlations for mathematics anxiety and self-efficacy, and approaches to learning

The descriptive statistics and Spearman correlation coefficients between the variables are in Table 1 .

According to Table 1 , mathematics anxiety was very strongly negatively correlated to mathematics self-efficacy across all samples. Additionally, surface learning was positively significantly associated with mathematics anxiety in the total and STEM student sample, but it was not significant among social sciences students. Deep approach to learning and age were not statistically significantly associated with mathematics anxiety.

Mathematics self-efficacy was negatively significantly associated with surface approach to learning in total and STEM student samples, but not in social sciences students. Mathematics self-efficacy did not correlate with deep approach to learning.

Surface approach to learning was negatively correlated to deep approach to learning in total and STEM student samples (but not in social sciences student sample) and had a statistically significant negative correlation with age only in social sciences student sample. Deep approach to learning did not correlate with age.

Which factors predict mathematics anxiety?

Next, we computed several regression models where mathematics anxiety was treated as the outcome variable. We computed models for three samples of students: the full sample ( N = 231), the STEM student sample ( N = 147), and the social sciences students ( N = 84). For each sample of students, we computed two models. Model 1 included age, gender, and surface and deep approaches to learning as predictors. In model 2, mathematics self-efficacy was added as an additional predictor. For the full sample, we also included the student group (STEM vs social sciences) as a predictor.

According to results in Table 2 , when regression models are computed across the full sample, female students tend to have greater mathematics anxiety than male students. Approaches to learning, age, and being a STEM versus social sciences student did not predict mathematics anxiety. Finally, including the mathematics self-efficacy variable was negatively associated with mathematics anxiety in this multivariate model. In addition, it seems that mathematics self-efficacy explains a large proportion of mathematics anxiety, as inclusion of this variable improved the explained variance by almost 50% in the regression model full sample level.

However, the regression analysis results are somewhat different when the sample is broken down into the STEM and social sciences student group. In STEM students, it seems higher mathematics anxiety is associated with older age, female gender, and more surface and less deep approach to learning. However, when mathematics self-efficacy is included in the model, only gender and mathematics self-efficacy effects are significant.

Interestingly, when mathematics self-efficacy is not included as a predictor of mathematics anxiety, there are no statistically significant predictors in the social sciences student sample; however, once it is included in the regression model, mathematics self-efficacy is statistically significantly and negatively associated with mathematics anxiety.

The aim of the current study was to investigate the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning (deep and surface) among STEM and social sciences students. We had posed several hypotheses to meet that aim.

Based on the literature (Akin & Kurbanoglu, 2011 ; Vinson, 2001 ), we expected mathematics anxiety and mathematics self-efficacy to have a negative association (H1). This hypothesis found support from the data. The very high negative correlation of r = −0.768 (across the full sample) suggests that these variables explain each other’s variance relatively well. These results were expected, since students who perceive that they can succeed in mathematics and who have a more positive attitude toward this topic, should experience less anxiety; furthermore, as mentioned earlier, these findings are coherent with previous research (Akin & Kurbanoglu, 2011 ).

Our second hypothesis (H2) regarded the relationship between mathematics anxiety and approaches to learning. Specifically, we expected that mathematics anxiety correlates positively with surface approach to learning and negatively with deep approach to learning. While surface approach to learning should be associated with increased and deep approach to learning with decreased anxiety in general, a study found that only higher levels of surface approach to learning correlated with more mathematics anxiety (Bessant, 1995 ). The results of the current study supported this hypothesis on the full and STEM student sample level; however, surface approach to learning did not correlate significantly with mathematics anxiety in social sciences students. Furthermore, deep approach to learning was negatively correlated with mathematics anxiety in the STEM student sample. This is the first study demonstrating that there are discrepancies in approaches to learning in association with mathematics anxiety between STEM and social sciences students. Although it is hard to explain these discrepancies based on our data, it is certainly a topic that needs to be pursued further.

According to the third hypothesis (H3), we expected mathematics self-efficacy to be positively correlated with deep and negatively with surface approach to learning, in line with some previous findings (Alkhateeb & Hammoudi, 2006 ; Gorero & Balila, 2016 ). This hypothesis found partial support from the data. Deep approach to learning was not associated with mathematics self-efficacy, while surface approach to learning had a negative correlation with mathematics self-efficacy on the full and STEM student sample level.

We expected that STEM students have less mathematics anxiety than social sciences students in our fourth hypothesis (H4). Royse and Rompf ( 1992 ) compared groups of students who did and did not study social work and found that the former had higher mathematics anxiety. However, this was not the case in the current study. STEM and social sciences students did not differ from each other in group comparison analysis. Therefore, this hypothesis did not find support from data. These results are surprising, since one may logically think that if a student chooses to major in a subject that has a strong mathematics component, the student’s anxiety toward mathematics could be lower than among students who choose a curriculum where the share of mathematics may be rather small (on an undergraduate level). Furthermore, STEM students are more likely to have mathematics in different courses throughout their studies as well as professionally after graduation. Therefore, these results are certainly interesting, since they demonstrate that STEM and social sciences students are as much or as little anxious toward mathematics.

Finally, to understand how mathematics anxiety would be predicted from approaches to learning and mathematics self-efficacy when age and gender are controlled for, we conducted regression models on the total, STEM, and social sciences student samples. We hypothesized that approaches to learning and mathematics self-efficacy predict mathematics anxiety, also when age and gender are controlled for (H5) . The regression model results showed that among STEM student sample, older age, female gender, higher surface, and lower deep approach to learning predicted higher mathematics anxiety. However, when mathematics self-efficacy was included in the model, only female gender and lower mathematics self-efficacy were significant predictors of mathematics anxiety. Gender differences are somewhat in line with research finding that female students tend to experience more anxiety in STEM classroom settings (Pelch, 2018 ). Interestingly, only lower mathematics self-efficacy predicted higher mathematics anxiety in social sciences student sample.

One potential takeaway from the results of this study is that in order to lower one’s mathematics anxiety, it could be necessary to boost one’s mathematics self-efficacy. However, this may prove to be a rather difficult task, since there is a potential problem of a “vicious circle:” one’s mathematics self-efficacy may be dependent on one’s performance in mathematics, and vice versa (Carey, Hill, Devine, & Szücs, 2016 ). Therefore, if a student performs well on a mathematics task, their self-efficacy may get a boost, consequently lowering mathematics-related anxiety. On the other hand, if a student performs poorly, their self-efficacy may drop, followed by increased anxiety. Mathematics anxiety, in turn, could further hamper one’s mathematics performance, resulting in poorer perceived self-efficacy. It would be, therefore, necessary to further study—preferably experimentally and in a longitudinal study design—how working with one’s mathematics self-efficacy could be helpful against mathematics anxiety.

While we discussed the association between mathematics anxiety and self-efficacy, it is nevertheless noteworthy that approaches to learning seem to play a significant role in mathematics anxiety among STEM students. Somewhat coherent with previous findings, more surface approach to learning predicted more mathematics anxiety (Bessant, 1995 ). These results suggest that perhaps—at least among STEM students—there is a possibility to tailor the classroom experience so that it would promote more synthesis of study materials, and decrease fact-based, rote-learning. STEM subjects likely have more universal facts (e.g., equations, proofs) to be learned, possibly promoting superficial learning. Here, too, could be a potentially vicious circle in play: a student who has to study materials that may seemingly be isolated facts, could implement rote-learning. This results in superficial knowledge, which may not prove to be useful when synthesis with other materials is needed. In turn, this may lead to poor performance and higher mathematics anxiety due to that. As discussed earlier, mathematics self-efficacy also likely plays a crucial role in this process. On the other hand, this reasoning does not entirely explain why approaches to learning did not predict mathematics anxiety among social sciences students. It could be that STEM students differ in how they perceive mathematics in general due to having to use this more in their studies. We believe that this should receive more attention in future research.

The main contribution of this study is providing insights into the potential role of mathematics self-efficacy, and deep and surface approaches to learning in mathematics anxiety in STEM and social sciences students. All in all, it could be inferred from this study that while surface approach to learning may be, to some extent, an important factor possibly predicting mathematics anxiety, the role of mathematics self-efficacy should be further studied in combination with approaches to learning in order to understand mathematics anxiety. It could be further hypothesized that by improving mathematics self-efficacy, it could also be helpful in reducing mathematics anxiety, as well as surface approaches to learning. Interestingly, while STEM and social science students differ in attitudes toward mathematics (with STEM students scoring higher), there were no differences in mathematics anxiety between these student groups.

There are limitations that need to be mentioned. Firstly, we used self-reports in our study. It could be helpful to include other important variables, such as grades and test scores, to complement the results. In addition, methods such as experience sampling may also provide more valid results (Lehtamo, Juuti, Inkinen, & Lavonen, 2018 ). Secondly, there were significantly fewer social sciences students than STEM students in the total sample, and social sciences students were slightly older than STEM students. Although age was accounted for in multivariate analyses, future studies should aim toward equal sample sizes as well as higher similarity in other demographic characteristics (e.g., age, gender). A third limitation was the absence of controlling for students’ prior academic ability (e.g., grade point average, course grades, ability test results). It could be that there are inherent differences between the past performance in mathematics-related courses and mathematics self-efficacy and anxiety. Future works should include variables of prior academic ability as control variables. In addition, future works could also collect data among STEM and social sciences students across multiple semesters, providing more robust results. The fourth limitation regards the use of the mathematics anxiety scale that has been validated in a sample of adolescents. Some additional measures of mathematics anxiety designed for tertiary-education settings, such as the AMAS (Hopko et al., 2003 ), could further validate the findings. Finally, future studies could also include other external factors to models predicting mathematics anxiety (Martin-Hansen, 2018 ).

In conclusion, we found that STEM and social sciences students do not differ largely with regard to mathematics anxiety, while STEM students do have higher mathematics self-efficacy. It may be that surface approach to learning plays a larger role in mathematics anxiety in STEM students than in social sciences students. This is the first work to investigate the differences between STEM and social sciences students in mathematics anxiety and self-efficacy, as well as deep and surface approaches to learning. The results could be helpful for mathematics educators, as it is relevant for them to learn about and understand the interplay between deep and surface approach to learning, mathematics anxiety and self-efficacy, and students’ curricula. It could be that improving students’ mathematics self-efficacy, as well as facilitating more synthesis among the learned materials could help as a remedy against mathematics anxiety. This, however, should be investigated in future research that, preferably, implements an experimental and longitudinal study design.

Availability of data and materials

The data as well as analysis script are available among the supplementary materials .

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DR designed the study, collected and analyzed the data, and wrote the first draft; TK designed the study, collected the data, and revised the manuscript; KOP collected the data and revised the manuscript; KM collected the data, and revised the manuscript; KT collected the data, and revised the manuscript. The author(s) read and approved the final manuscript.

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Supplementary Table 1 Grouping of students to social sciences/STEM by self-reported curricula, and the distribution of students' curricula by course taken Notes . LT_Calc1 = Calculus I (LTMS.00.003); MT_Calc1 = Calculus I (MTMM.00.340); SH_StatM = Statistical Modeling (SHSH.00.002). Supplementary Figure 1: Students' mathematics anxiety summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 2: Students' mathematics self-efficacy summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 3: Students' deep approach to learning summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 4: Students' surface approach to learning summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Math anxiety study

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Rozgonjuk, D., Kraav, T., Mikkor, K. et al. Mathematics anxiety among STEM and social sciences students: the roles of mathematics self-efficacy, and deep and surface approach to learning. IJ STEM Ed 7 , 46 (2020). https://doi.org/10.1186/s40594-020-00246-z

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Current Trends in Math Anxiety Research: a Bibliometric Approach

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The aim of this study was to investigate current trends in research of math anxiety (MA) through bibliometric perspective. Three main clusters were formed based on author keywords: cognitive correlates (working memory, attention, numerical cognition, mental arithmetic), psychological factors and effects (self-concept and self-efficacy, motivation, confidence, attitudes), and educational context (PISA, measurement, gender differences, math achievement, math education, assessment). Analysis of the index keywords revealed somewhat different organization with two dominant clusters: the experimental cluster in which the most frequent are psychophysiological measures and terms and the correlational cluster in which the topics of MA psychosocial factors are most represented. The map of bibliographic coupling showed several relatively separated groups of authors with different focus in cited references. However, a map of co-citation of authors revealed closeness of these separated groups, with Beilock, S. L. and Ashcraft, M. H. by far the most-cited authors in this field.

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Radević, L., Milovanović, I. Current Trends in Math Anxiety Research: a Bibliometric Approach. Int J of Sci and Math Educ (2023). https://doi.org/10.1007/s10763-023-10424-4

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Mathematics Anxiety: What Have We Learned in 60 Years?

The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken ( 1957 ), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

Low achievement and low participation in mathematics are matters of concern in many countries; for example, recent concerns in the UK led to the establishment of the National Numeracy organization in 2012. This topic has received increasing focus in recent years, the ever-increasing importance of quantitative reasoning in a variety of educational and occupational situations, ranging from school examinations to management of personal finances.

Some aspects of mathematics appear to be cognitively difficult for many people to acquire; and some people have moderate or severe specific mathematical learning disabilities. But not all mathematical disabilities result from cognitive difficulties. A substantial number of children and adults have mathematics anxiety, which may severely disrupt their mathematical learning and performance, both by causing avoidance of mathematical activities and by overloading and disrupting working memory during mathematical tasks. On the whole, studies suggest that attitudes to mathematics tend to deteriorate with age during childhood and adolescence (Wigfield and Meece, 1988 ; Ma and Kishor, 1997 ), which has negative implications for mathematical development, mathematics education and adult engagement in mathematics-related activities. Also, while there are nowadays few gender differences in actual mathematical performance in countries that provide equal educational opportunity for boys and girls, females at all ages still tend to rate themselves lower in mathematics and to experience greater anxiety about mathematics than do males. It is important to understand children's and adults' attitudes and emotions with regard to mathematics if we are to remove important barriers to learning and progress in this subject.

Many studies over the years have indicated that many people have extremely negative attitudes to mathematics, sometimes amounting to severe anxiety (Hembree, 1990 ; Ashcraft, 2002 ; Maloney and Beilock, 2012 ). Mathematics anxiety has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in … ordinary life and academic situations” (Richardson and Suinn, 1972 ).

Although, many studies treat mathematics anxiety as a single entity, it appears to consist of more than one component. Wigfield and Meece ( 1988 ) found two separate dimensions of mathematics anxiety in sixth graders and secondary school students and found two different dimensions: cognitive and affective, similar to those that had been previously identified in the area of test anxiety by Liebert and Morris ( 1967 ). The cognitive dimension, labeled as “worry,” refers to concern about one's performance and the consequences of failure, and the affective dimension, labeled as “emotionality” refers to nervousness and tension in testing situations and respective autonomic reactions (Liebert and Morris, 1967 ).

People have been expressing mathematics anxiety for centuries: the verse “Multiplication is vexation … and practice drives me mad” goes back at least to the sixteenth century. From a research perspective, the construct has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken ( 1957 ), and has received increasing attention in recent years, in conjunction with the generally increased focus on mathematical performance.

Although, as will be discussed below, it is unclear to what extent mathematics anxiety causes mathematical difficulties, and to what extent mathematical difficulties and resulting experiences of failure cause mathematics anxiety; there is significant evidence that mathematics anxiety interferes with performance of mathematical tasks, especially those that require working memory. Moreover, whether a person likes or fears mathematics will clearly influence whether they take courses in mathematics beyond compulsory school-leaving age, and pursue careers that require mathematical knowledge (Chipman et al., 1992 ; Brown et al., 2008 ). Thus, mathematics anxiety is of great importance to the development and use of mathematical skills. It is also important in itself, as a cause of much stress and distress.

This paper will focus on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We will discuss what mathematics anxiety is, and how distinct it is from other forms of anxiety. We will discuss its relationship to attitudes to mathematics. We will then discuss the relationships between mathematics anxiety and mathematics performance and possible reasons for them. We will then discuss ways in which mathematics anxiety is measured, both by the commonest technique of questionnaires, and by physiological measures. We will then discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally and importantly, we will discuss some implications for treatment. We will conclude with a brief discussion of what still needs to be learned.

Is mathematics anxiety separable from other forms of anxiety?

Though, as will be discussed below, mathematics anxiety is closely related to mathematical performance, it cannot be reduced just to a problem with mathematics. It seems to be as much an aspect of “anxiety” as an aspect of “mathematics.” Indeed, before assuming that mathematics anxiety is an entity in its own right, it is necessary to consider relationships between mathematics anxiety and other forms of anxiety, especially test anxiety, and general anxiety. Several studies suggest that mathematics anxiety is more closely related to other measures of anxiety, especially test anxiety, than to measures of academic ability and performance (Hembree, 1990 ; Ashcraft et al., 1998 ). Such studies typically show correlations of 0.3 and 0.5 between measures of mathematics anxiety and test anxiety.

Mathematics anxiety has also generally been found to correlate with measures of general anxiety; and it is indeed possible that this may serve as a background variable explaining some of the correlation between mathematics anxiety and test anxiety. For example, Hembree ( 1990 ) found a mean correlation of 0.35 between the MARS and a measure of general anxiety. In a behavioral genetic study, to be discussed in more detail below, Wang et al. ( 2014 ) obtained evidence that genetically based differences in general anxiety contribute to genetic differences in mathematics anxiety.

However, mathematics anxiety cannot be reduced to either test anxiety or general anxiety. Different measures of mathematics anxiety correlate more highly with one another (0.5–0.8) than with test anxiety or general anxiety (Dew et al., 1983 ; Hembree, 1990 ; review by Ashcraft and Ridley, 2005 ).

People may exhibit performance anxiety not only about tests and examinations, but about a variety of school subjects. Mathematics is usually assumed to elicit stronger emotional reactions, and especially anxiety, than most other academic subjects, but this assumption needs more research (Punaro and Reeve, 2012 ). Although, the general assumption is that people show much more anxiety and other negative attitudes toward mathematics than other academic subjects, there have not been many studies directly comparing attitudes to mathematics and other subjects.

Certainly anxiety toward other subjects exists, especially when performance in these subjects takes place in front of others. People with dyslexia have been found to exhibit anxiety about literacy (Carroll et al., 2005 ; Carroll and Iles, 2006 ). It is well-known, that foreign language learning and use, especially by adults, is often inhibited by anxiety (Horwitz et al., 1986 ; Cheng et al., 1999 ; Wu and Lin, 2014 ). Music students, and even successful musicians, often demonstrate music performance anxiety (Kenny, 2011 ).

Drawing also elicits performance anxiety and lack of confidence, and there is a decline in confidence with age, which in some ways parallels findings with regard to mathematics. Most young children enjoy drawing, and will often draw spontaneously. Many authors report that interest in drawing seems to decline in most children at or before the transition to secondary school, and many older children and adults will insist that they “can't draw,” even though they had drawn frequently and enthusiastically some years earlier (Cox, 1989 ; Thomas and Silk, 1990 ; Golomb, 2002 ; but see Burkitt et al., 2010 for somewhat conflicting findings).

Punaro and Reeve ( 2012 ) reported a study that directly compared mathematics and literacy anxiety in Australian 9-year-olds and related their anxiety to their actual academic abilities. Although, children expressed anxiety about difficult problems in both mathematics and literacy, worries were indeed greater for mathematics than literacy. Moreover, anxiety about mathematics was related to actual mathematics performance, whereas anxiety about literacy was not related to actual literacy performance. This study would suggest that although mathematics is not the only subject that elicits anxiety, anxiety may indeed be more severe, and possibly affect performance more, for mathematics than for other subjects.

Mathematics anxiety and attitudes to mathematics

Attitudes to mathematics, even negative attitudes, cannot be equated with mathematics anxiety, as the former are based on motivational and cognitive factors, while anxiety is a specifically emotional factor. Nevertheless, attitude measures tend to correlate quite closely with mathematics anxiety. For example, Hembree ( 1990 ) found that in school pupils, mathematics anxiety showed a mean correlation of −0.73 with enjoyment of mathematics and −0.82 with confidence in mathematics. In college students, the equivalent mean correlations were a little lower than in schoolchildren, but still very high: −0.47 between mathematics anxiety and enjoyment of mathematics, and −0.65 between mathematics anxiety and confidence in mathematics.

Mathematics anxiety seems to be particularly related to self-rating with regard to mathematics. People who think that they are bad at mathematics are more likely to be anxious. Most studies indicate a negative relationship between mathematics self-concept and mathematics anxiety (Hembree, 1990 ; Pajares and Miller, 1994 ; Jain and Dowson, 2009 ; Goetz et al., 2010 ; Hoffman, 2010 ).

However, as most of these studies are correlational rather than longitudinal, it is hard once again to establish the direction of causation: does anxiety lead to a lack of confidence in one's own mathematical ability, or does a lack of confidence in one's mathematical ability make one more anxious? Ahmed et al. ( 2012 ) carried out a longitudinal study of 495 seventh-grade pupils, who completed self-report measures of both anxiety and self-concept three times over a school year. Structural equation modeling suggested that each characteristic influenced the other over time, but that the effect of self-concept on subsequent anxiety was significantly greater than the effect of anxiety on subsequent self-concept. The details of the results should be taken with some caution, because although the study was longitudinal, it was over a relatively short period (one school year) and also a different pattern might be seen among younger or older children. However, it provides evidence that the relationship between mathematics anxiety and mathematics self-concept is reciprocal: each influences the other.

A closely related construct is self-efficacy. Ashcraft and Rudig ( 2012 ) adapted Bandura's ( 1977 ) definition of self-efficacy to the topic of mathematics, stating that “self-efficacy is an individual's confidence in his or her ability to perform mathematics and is thought to directly impact the choice to engage in, expend effort on, and persist in pursuing mathematics” (p. 249). It is not precisely the same construct as self-rating, as it includes beliefs about the ability to improve in mathematics, and to take control of one's learning, rather than just about one's current performance; but there is of course significant overlap between the constructs. Studies have demonstrated an inverse relationship between self-efficacy and math anxiety (Cooper and Robinson, 1991 ; Lee, 2009 ).

Attitudes to mathematics also involve conceptualization of what mathematics is, and it is possible that this is relevant to mathematics anxiety. Many people seem to regard mathematics only as school-taught arithmetic, and may not consider other cultural practices involving numbers as mathematics (Harris, 1997 ). Also, people may not recognize that arithmetical ability (even without considering other aspects of mathematics) is made up of many components, not just a single unitary ability (Dowker, 2005 ). This can risk their assumption that if they have difficulty with one component, they must be globally “bad at maths,” thus increasing the risk of mathematics anxiety.

Most studies of mathematics anxiety have not differentiated between different components of mathematics, and it is likely that some components would elicit more anxiety than others and that the correlations between anxiety about different components might not always be very high. Indeed, studies which have looked separately at statistics anxiety and (general) mathematics anxiety in undergraduates have suggested that the two should be seen as separate constructs, and differ in important ways. For example, as will be discussed in the Section Gender and Mathematics Anxiety, most studies suggest that females show more mathematics anxiety than males, but there are no gender differences in statistics anxiety (Baloğlu, 2004 ).

Prevalence of mathematics anxiety

Estimates of the prevalence of mathematics anxiety vary quite widely, and are of course likely to be dependent on the populations being sampled, on the measures used (though many of the studies involve similar measures), and, perhaps especially, on what criteria are used to categorize people as “mathematics anxious.” Most measures of mathematics anxiety assess scores on continuous measures, and there is no clear criterion for how severe the anxiety must be for individuals to be labeled as high in mathematics anxiety.

Richardson and Suinn ( 1972 ) estimate that 11% of university students show high enough levels of mathematics anxiety to be in need of counseling. Betz ( 1978 ) concluded that about 68% of students enrolled in mathematics classes experience high mathematics anxiety. Ashcraft and Moore ( 2009 ) estimated that 17% of the population have high levels of mathematics anxiety. Johnston-Wilder et al. ( 2014 ) found that about 30% of a group of apprentices showed high mathematics anxiety, with a further 18% affected to a lesser degree. Chinn ( 2009 ) suggested the far lower figure of 2–6% of secondary school pupils in England, which may simply indicate the use of an unusually strict criterion for defining pupils as having high mathematics anxiety. There is no doubt, even when taking the lowest estimates, that it is a very significant problem.

Relationships between mathematics anxiety and mathematics performance

Numerous studies have shown that emotional factors may play a large part in mathematical performance, with mathematics anxiety playing a particularly large role (McLeod, 1992 ; Ma and Kishor, 1997 ; Ho et al., 2000 ; Miller and Bichsel, 2004 ; Baloğlu and Koçak, 2006 ). Mathematics anxiety scores correlate negatively with scores on tests of mathematical aptitude and achievement, while usually showing no significant correlation with verbal aptitude and achievement.

One possible reason for the negative association between mathematics anxiety and actual performance is that people who have higher levels of math anxiety are more likely to avoid activities and situations that involve mathematics. Thus, they have less practice (Ashcraft, 2002 ), which is in itself likely to reduce their fluency and their future mathematical learning.

Mathematics anxiety might also influence performance more directly, by overloading working memory (Ashcraft et al., 1998 ). Anxious people are likely to have intrusive thoughts about how badly they are doing, which may distract attention from the task or problem at hand and overload working memory resources. It has been found in many studies over the years that general anxiety as a trait is associated with working memory deficits (Mandler and Sarason, 1952 ; Eysenck and Calvo, 1992 ; Fox, 1992 ; Berggren and Derakhshan, 2013 ). It would appear likely that if anxiety affects working memory, it would have a particularly strong effect on arithmetic, as working memory has been found in many studies to be strongly associated with arithmetical performance, especially in tasks that involve multi-digit arithmetic and/or involve carrying (e.g., Hitch, 1978 ; Fuerst and Hitch, 2000 ; Gathercole and Pickering, 2000 ; Swanson and Sachse-Lee, 2001 ; Caviola et al., 2012 ). Thus, the load that mathematics anxiety and associated ruminations place on working memory could be a plausible explanation for decrements in mathematical performance.

Ashcraft and Kirk ( 2001 ) found that people with high maths anxiety demonstrated smaller working memory spans than people with less maths anxiety, especially in tasks that required calculation. In particular, they were much slower and made many more errors than others in tasks where they had to do mental addition at the same time as keeping numbers in memory.

DeCaro et al. ( 2010 ) asked adult participants to work out verbally based and spatially based mathematics problems in either low-pressure or high-pressure testing situations. Performance on problems that relied heavily on verbal WM resources was less accurate under high-pressure than under low-pressure tests. Performance on spatially based problems that do not rely heavily on verbal WM was not affected by pressure. Asking some individuals to focus on the problem steps by talking aloud helped to reduce pressure-induced worries and eliminated pressure's negative impact on performance.

While Ashcraft's theory emphasizes the ways in which mathematics anxiety impairs mathematical performance, some researchers such as Núñez-Peña and Suárez-Pellicioni ( 2014 ) put more emphasis on how pre-existing mathematical difficulties might cause or increase mathematics anxiety. Poor mathematical attainment may lead to mathematics anxiety, as a result of repeated experiences of failure.

Indeed, it appears that mathematics anxiety is associated not only with performance in high-level calculation skills that require the use of working memory resources, but also with much more basic numerical skills. For example, Maloney et al. ( 2011 ) gave high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. The authors suggest that HMA individuals have less precise representations of numerical magnitude than their LMA peers; and that this may be primary, and precede the mathematics anxiety. In other words, mathematics anxiety may be associated with low-level numerical deficits that compromise the development of higher-level mathematical skills. Núñez-Peña and Suárez-Pellicioni ( 2014 ) also found that people with HMA showed a larger distance effect as well as a larger size effect (longer reaction times to comparisons involving larger numbers) than LMA individuals. Maloney and Beilock ( 2012 ) proposed that mathematics anxiety is likely to be due both to pre-existing difficulties in mathematical cognition and to social factors, e.g., exposure to teachers who themselves suffer from mathematics anxiety. Additionally, they proposed that those with initial mathematical difficulties are also likely to be more vulnerable to the negative social influences; and that this may create a vicious circle.

Studies of the relationship between mathematics anxiety and performance also need to take into account that, as stated at the beginning of this paper, mathematics anxiety consists of different components, often termed “cognitive” and “affective.” The cognitive and affective dimensions seem to be differently related to achievement in mathematics. For example, in sixth graders and secondary school students, the affective dimension of math anxiety has found to be more strongly negatively correlated with achievement than the cognitive dimension (Wigfield and Meece, 1988 ; Ho et al., 2000 ). It also needs to be remembered that, even before considering the non-numerical aspects of mathematics, arithmetic itself is not a single entity, but is made up of many components (Dowker, 2005 ).

Assessments of mathematics anxiety

So far, we have been discussing mathematics anxiety without much reference to the methods used for studying it. However, in order to study mathematics anxiety, it is necessary to find suitable ways of assessing and measuring it. Most measures for assessing mathematics anxiety involve questionnaires and rating scales, and are predominantly used with adolescents and adults. The first such questionnaire to our knowledge is that of Dreger and Aiken ( 1957 ); and subsequent well-known examples include the Mathematics Anxiety Research Scale or MARS (Richardson and Suinn, 1972 ) and the Fennema–Sherman Mathematics Attitude Scales (Fennema and Sherman, 1976 ).

Some questionnaires, mainly including pictorial rating scales, have since been developed for use with primary school children; e.g., the Mathematics Attitude and Anxiety Questionnaire (Thomas and Dowker, 2000 ; Krinzinger et al., 2007 ; Dowker et al., 2012 ) and the Children's Attitude to Math Scale (James, 2013 ).

The reliability of mathematics anxiety questionnaires has generally been found to be good, whether measured through inter-rater reliability, test-retest reliability or internal consistency. The test whose psychometric properties have been most frequently assessed is the MARS, in its original form and in various adaptations, and it has been consistently found to be highly reliable (e.g., Plake and Parker, 1982 ; Suinn et al., 1972 ; Levitt and Hutton, 1984 ; Suinn and Winston, 2003 ; Hopko, 2003 ).

Good reliability has also been found for other mathematics anxiety measures such as Betz's ( 1978 ) Mathematics Anxiety Scale (Dew et al., 1984 ; Pajares and Urban, 1996 ) and the Fennema–Sherman scales (Mulhern and Rae, 1998 ). The mathematics anxiety scales developed specifically for children have also been found to have good reliability, including Thomas and Dowker's ( 2000 ) Mathematics Anxiety Questionnaire (Krinzinger et al., 2007 ); James' ( 2013 ) Children's Anxiety in Math Scale; and the scale developed by Vukovic et al. ( 2013 ).

Thus, it is unlikely that any ambiguous or conflicting results in different studies are likely to be due to unreliability of the measures. However, there are potential problems with questionnaire measures as such. In particular, a potential problem with questionnaire measures is that, like all self-report measures, they may be influenced both by the accuracy of respondents' self-perceptions and by their truthfulness in reporting. There are some studies that have attempted to combat this problem by using physiological measures of anxiety when exposed to mathematical stimuli: e.g., heart rate and skin conductance (Dew et al., 1984 ); cortisol secretion (Pletzer et al., 2010 ; Mattarella-Micke et al., 2011 ) and especially brain imaging measures ranging from EEG recordings (Núñez-Peña and Suárez-Pellicioni, 2014 , 2015 ); to functional MRI (Lyons and Beilock, 2012b ; Young et al., 2012 ; Pletzer et al., 2015 ).

Physiological measures: cortisol secretion

Cortisol secretion is a response to stress (Hellhammer et al., 2009 ), and therefore might be expected to be higher in people with high levels of mathematics anxiety when presented with mathematical stimuli or activities. Studies do indeed support this view, as well as giving some clues about the interactions between mathematics anxiety and other characteristics.

Pletzer et al. ( 2010 ) investigated people's changes in cortisol level in response to the stress of a statistics examination, and the relationship between these changes and their actual examination performance. They were also assessed on a questionnaire measure of mathematics anxiety (a version of the MARS) and on tests of magnitude judgements and arithmetic. With a few exceptions who showed other patterns, most participants either showed an increase in cortisol from the basal level just before the examination, and a decrease afterwards, or a decrease in cortisol from the basal level both before and after the examination. Neither absolute levels or cortisol nor patterns of change in cortisol production correlated with the MARS, with the arithmetical tests, or with performance in the examination itself. However, the cortisol response to the examination did influence the association of other predictor variables and statistics performance. Mathematics anxiety and arithmetic abilities predicted statistics performance significantly in the group who showed an increase in cortisol production before the examination with a subsequent decrease, but not in the group that showed a consistent decrease.

Mattarella-Micke et al. ( 2011 ) measured cortisol secretion levels just before and after participants were presented with challenging mathematics problems. They also assessed their working memory. The performance of individuals with low working memory scores was not associated with mathematics anxiety or cortisol secretion. For people with higher working memory scores, those with high mathematics anxiety showed a negative relationship between cortisol secretion and mathematics performance, while those with low mathematics anxiety showed a positive relationship between cortisol secretion and mathematics performance.

Thus, in the studies carried out so far, the relationship between mathematics anxiety and cortisol response are not absolutely straightforward. It appears that the cortisol secretion profile modulates the relationship between mathematics anxiety and mathematics performance, while mathematics anxiety modulates the relationship between cortisol and performance. Thus, there are modulatory relationships between these measures, which are well worth studying further; but no evidence as yet that cortisol response is a good indicator of mathematics anxiety, or should replace traditional questionnaires.

Physiological measures: what can measures of brain function tell us about mathematics anxiety?

Attempts at physiological measures of mathematics anxiety have more commonly involved some form of recording of brain function. Dehaene ( 1997 , p. 235) argues that the neuroscience of mathematics can and must involve emotional factors: “…(C)erebral function is not confined to the cold transformation of information according to logical rules. If we are to understand how mathematics can become the subject of so much passion or hatred, we have to grant as much attention to the computations of emotion as to the syntax of reason.” It is, however, only quite recently that we have had the ability to carry out functional brain imaging with sufficient numbers of participants to be able to examine correlations between individual differences in brain function and individual differences in behavioral characteristics. It is even more recently that we have been able to apply functional brain imaging to children.

It is important to remember that finding neural correlates of behavioral characteristics does not mean that the brain characteristics are causing the behavioral characteristics. They are at least as likely to be reflecting the behavioral characteristics. Nevertheless, examining brain-based correlates of mathematics anxiety may give us some clues as to the cognitive characteristics involved, even if it does not tell anything about the direction of causation. They may also give us ways of assessing mathematics anxiety without needing to rely on self-report measures.

Physiological measures: EEG/ERP

Núñez-Peña and Suárez-Pellicioni ( 2014 , 2015 ) carried out both ERP and behavioral measures of numerical processing in people with high and low mathematics anxiety as measured on the MARS questionnaire. In a magnitude comparison test, people with high mathematics anxiety had slower reaction times and showed larger size and distance effects than those with low mathematics anxiety. ERP measures showed that those with high mathematics anxiety showed higher amplitude in frontal areas for both the size and distance effects than did those with low mathematics anxiety: a component which has been proposed to be associated with numerical processing. They also looked at two-digit addition in people with high and low mathematics anxiety. They were presented with correct and incorrect answers to such problems, and asked to say whether each answer was right or wrong. Participants with high mathematics anxiety were significantly slower and less accurate than those with low mathematics anxiety. ERP analysis showed that people with high mathematics anxiety showed a P2 component of larger amplitude than did people with low mathematics anxiety. This component had been previously found to be associated with devoting attentional resources to emotionally negative stimuli. Thus, the studies suggest that people with high mathematics anxiety may be devoting extra attentional resources to their worries, possibly at the expense of task performance, though the direction of causation cannot be determined from a correlational study.

Physiological measures: functional MRI

There has been much evidence that stress affects the activation levels of regions of the prefrontal cortex, possibly interfering with the working memory functions associated with this area (Qin et al., 2009 ). These effects have been shown to be greater in people with high levels of general anxiety as a trait. For example, Bishop ( 2009 ) found that, even in the absence of threat stimuli, people with high trait anxiety showed less prefrontal activation in attentional control tasks than people with lower trait anxiety, and this was associated with less efficient performance. Basten et al. ( 2012 ) found that high trait anxiety was associated with high activation of the right dorsolateral prefrontal cortex (dLPFC) and left inferior frontal sulcus, which are generally found to be implicated in the goal-directed control of attention, and with strong deactivation of the rostral-ventral anterior cingulate cortex, a key region in the brain's default-mode network. The authors suggested that these activation patterns were likely to be associated with inefficient manipulations in working memory.

Lyons and Beilock ( 2012a ) carried out functional brain imaging studies with adults with high and low mathematics anxiety. The individuals with high mathematics anxiety tended to show less activity in the frontal and parietal areas in anticipating and carrying out mathematical tasks than did less anxious individuals. They also did less well in the mathematical tasks. However, there was a subgroup, that did show strong activation of these areas when anticipating a mathematics task, and these individuals performed much better than those who did not show such activation, and almost as well as those with low mathematics anxiety. This group of individuals also showed high activation during the mathematics task, not so much of the parietal and other cortical areas associated with arithmetic, but of subcortical areas associated with motivation and assessment of risk and reward. The authors suggested that the deficit in performance of individuals with high mathematics anxiety might be determined by their response and interpretation of their anxiety response, instead of the magnitude of those anxiety response or their mathematics skills per se .

Pletzer et al. ( 2015 ) carried out an fMRI study of two groups of people, matched for their mathematical performance on tests of magnitude judgment and arithmetic, but differing in levels of mathematics anxiety, as measured by a version of the MARS. Eighteen participants scored high and 18 low on the measure of mathematics anxiety. They underwent fMRI when carrying out two numerical tasks: number comparison and number bisection. For comparison, they were also given brief non-numerical cognitive tasks involving verbal reasoning and mental rotation. The groups did not differ in their brain activation patterns for the non-numerical tasks. In the numerical tasks, they did not differ with regard to the activation of areas known to be involved in number processing, such as the intraparietal sulcus (similar to findings of Lyons and Beilock, 2012a , b ) suggesting that performance deficits of high mathematics anxious individuals were unlikely to be due to lower mathematics skills; but the group with high mathematics anxiety showed more activity in other areas of the brain, especially frontal areas associated with inhibition. This suggests that processing efficiency may be impaired in people with high mathematics anxiety, requiring more effort to inhibit incorrect responses. The differences seemed to occur specifically for items that required magnitude processing, and were not found for items that involved multiplication and could readily be solved by fact retrieval.

Recently, functional brain imaging studies have indicated that 7- to 9-year-old children are already showing some of the same neural correlates of mathematics anxiety as adults. Young et al. ( 2012 ) carried out a functional MRI study with 7- to 9-year-old children, and found that mathematics anxiety was associated with high levels of activity in right amygdala regions that are involved in processing negative emotions and reduced activity in posterior parietal and dorsolateral prefrontal cortex regions associated with mathematical problem-solving (the latter finding was in contrast to Pletzer et al., 2015 , Lyons and Beilock, 2012a , b who found no activation differences in these areas). Children with high mathematics anxiety also showed greater functional connectivity between the amygdala and areas in the ventromedial prefrontal cortex that are associated with negative activity was also positively correlated with task activity in two subcortical regions: the right caudate nucleus and left hippocampus, both of which are known to be involved in memory processes. Crucially, these brain activity differences were mainly found, not during the actual mathematics task, but during the cue that preceded it (similar to Lyons and Beilock, 2012b ). Thus, the control processes that influence whether mathematics anxiety will inhibit performance seem to occur at the time of anticipation of the mathematics task, rather than during the task itself.

These studies have led to some interesting proposals about the most effective timing of cognitive treatments for mathematics anxiety. In particular, Lyons and Beilock ( 2012b , p. 2108) have proposed, on the basis of the above-mentioned brain-imaging studies and their own findings (greater activation in areas associated with visceral threat detection and pain perception with higher mathematics anxiety before but not during mathematics performance), that “emotional control processes that act early on the arousal of negative affective responses (e.g., reappraisal) are more effective at mitigating these responses and limiting concomitant performance decrements than explicit suppression of these responses later in the affective process.” As we shall see, this has implications for treatments.

Factors that influence mathematics anxiety: genetics

So far, we have been discussing the nature and assessment of mathematics anxiety, without much reference to the factors that influence it. One potential factor that has been investigated is genetics. Wang et al. ( 2014 ) carried out behavioral genetic studies of mathematics anxiety in a sample of 514 twelve-year-old twin pairs. They were given the Elementary Students version of the MARS as a measure of mathematics anxiety; the Spence Children's Anxiety Scale as a measure of test anxiety; a mathematical problem solving subtest of the Woodcock-Johnson III Tests of Achievement; and a reading comprehension test from the Woodcock Reading Mastery Test. Mathematics anxiety correlated significantly with general anxiety, and also correlated negatively with both mathematical problem solving and reading comprehension, while general anxiety did not correlate significantly with either academic measure. Univariate and multivariate behavioral genetic modeling indicated that genetic factors accounted for about 40% of the variance in mathematics anxiety, with most of the rest being explained by non-shared environmental factors.

It is unlikely that there are genetic factors specific to mathematics anxiety. Rather, the multivariate analyses suggested that mathematics anxiety was influenced by the genetic and environmental risk factors involved in general anxiety, and the genetic factors involved in mathematical problem solving. Thus, mathematics anxiety may result from a combination of negative experiences with mathematics, and predisposing genetic risk factors associated with both mathematical cognition and general anxiety.

Gender and mathematics anxiety

One of the factors that has received most study with regard to mathematics anxiety is that of gender. Much recent research indicates that males and females, in countries that provide equal education for both genders, show little or no difference in actual mathematical performance (Spelke, 2005 ). However, they do indicate that females tend to rate themselves lower and to express more anxiety about mathematics (Wigfield and Meece, 1988 ; Hembree, 1990 ; Else-Quest et al., 2010 ; Devine et al., 2012 ), though such differences are not huge (Hyde, 2005 ). Most studies suggest such gender differences only develop at adolescence, and that primary school children do not exhibit gender differences in mathematics anxiety (Dowker et al., 2012 ; Wu et al., 2012 ; Harari et al., 2013 ) though even in the younger age group boys often rate themselves higher in mathematics than girls do (Dowker et al., 2012 ). This increased anxiety may come from several sources, including exposure to gender stereotypes, and the influence and social transmission of anxiety by female teachers who are themselves anxious about mathematics (Beilock et al., 2010 ).

It may also be related to more general differences in anxiety between males and females. Many studies indicate that females tend to show higher levels of trait anxiety and the closely related trait of Neuroticism than males (e.g., Feingold, 1994 ; Costa et al., 2001 ; Chapman et al., 2007 ) and show higher prevalence of clinical anxiety disorders (McLean et al., 2011 ). They have been found to show greater anxiety than males even in subjects where their actual performance tends to be higher than that of males, such as foreign language learning (Park and French, 2013 ).

Also, males tend to show more confidence and rate themselves higher in a number of domains than females do (e.g., Beyer, 1990 ; Beyer and Bowden, 1997 ; Jakobsson et al., 2013 ). Thus, it is not surprising that this should also apply to mathematics, and, given the associations between anxiety and self-rating, that it might contribute to gender differences in mathematics anxiety.

However, there is some evidence that gender differences in mathematics anxiety cannot be reduced to gender differences in general academic self-confidence or in test anxiety. Devine et al. ( 2012 ) found that mathematics anxiety has an effect on mathematics performance, even after controlling for general test anxiety, in girls but not in boys. They asked 433 British secondary school children in school years 7, 8, and 10 (11-to 15-year-olds) to complete mental mathematics tests and Mathematics Anxiety and Test Anxiety questionnaires. Boys and girls did not differ in mathematics performance; but girls had both higher mathematics anxiety and higher test anxiety. Both girls and boys showed a positive correlation between mathematics anxiety and test anxiety and a negative correlation between mathematics anxiety and mathematics performance. Both boys and girls showed a negative correlation between mathematics anxiety and mathematics performance. However, regression analyses showed that for boys, this relationship disappeared after controlling for general test anxiety. Only girls continued to show an independent relationship between mathematics anxiety and mathematics performance.

By contrast, Hembree ( 1990 ) suggested that math anxiety is more negatively related to achievement in males than in females, and some other studies suggested that there are no gender differences in the relationship between mathematics anxiety and performance (Meece et al., 1990 ; Ma, 1999 ; Wu et al., 2012 ). However, most such studies have not controlled for general test anxiety. Gender effects on the relationship between mathematics anxiety and performance may also depend on whether one is examining the cognitive or affective component of mathematics anxiety, and on what aspects of mathematics are involved. Indeed, Miller and Bichsel ( 2004 ) found that mathematics anxiety was more related to basic mathematics scores in males, but to applied mathematics scores in females. More research is needed as to what influences gender differences in both mathematics anxiety itself, and in its influence on performance.

It is unlikely that such gender differences are the result of gender differences in working memory, as on the whole, studies show relatively few gender differences in working memory (Robert and Savoie, 2006 ) though some studies suggest that males may be better at visuo-spatial working memory and females at verbal working memory (Robert and Savoie, 2006 ). Intriguingly, Ganley and Vasilyeva ( 2014 ) carried out a mediation analysis that suggested that mathematics anxiety seemed to affect visuo-spatial working memory more in female than male college students, and that this led to a greater decrement in mathematics performance. However, since other studies suggest that mathematics anxiety affects verbal more than visuo-spatial working memory (DeCaro et al., 2010 ), there is still much room for further research here.

One possible explanation for greater mathematics anxiety in females than males is stereotype threat . Stereotype threat occurs in situations where people feel at risk of confirming a negative stereotype about a group to which they belong. In the domain of mathematics anxiety, this usually refers to females being reminded of the stereotype that males are better at mathematics than females, though it can also occur with regard to other stereotypes. For example, Aronson et al. ( 1999 ) found that white American men performed less well in mathematics when they were told that Asians tend to perform better in mathematics than white people, than when they were not exposed to this stereotype.

Most of the studies of the effects of stereotype threat on mathematics anxiety are somewhat indirect: they indicate that mathematics performance is worse when people are exposed to stereotype threat, but do not usually include direct measures of mathematics anxiety. While one likely explanation for the effects of stereotype threat is that it increases mathematics anxiety, there are other possibilities: e.g., that participants choose to conform to social expectations. This caution must be borne in mind when considering the evidence about the effects of stereotype threat on performance.

Schmader ( 2002 ) and Beilock et al. ( 2007 ) found that women performed less well on an arithmetic task if they were told that the researchers were studying why women do more poorly than men. Beilock et al. ( 2007 ) noted that, as is often found in studies of mathematics anxiety, the effect only occurred for problems that required the significant use of working memory resources.

Johns et al. ( 2005 ) gave participants a mathematics test under three conditions: one without any reference to gender stereotypes; one where they were told that the researchers were studying reasons why women performed less well in mathematics; and one where they were exposed to the same gender stereotype, but also taught explicitly about the nature of stereotype threat in this context, and how it could increase women's anxiety when doing mathematics. Females performed less well than men in the condition where the gender stereotype was presented without explanation, but there were no gender differences either in the condition where no gender stereotype was presented or in the condition where they were taught explicitly about the stereotype threat.

However, the effect of stereotype threat is not always found, especially in children. Ganley et al. ( 2013 ) carried out three studies with a total sample of 931 school children ranging from fourth to twelfth grade, and using several different methods from the implicit to the highly explicit to induce stereotype threat. There was no evidence of any effect of stereotype threat on girls' performance in any of these studies. It may be that stereotype threat only exerts an influence in very specific circumstances, or on the other hand that it always occurs and exerts an influence under all circumstances, so that the experimental manipulations exerted no additional effect. It may also be that the importance of stereotype threat has been overestimated at least with regard to children; or that the effects were greater in the past than now, due to changes in social attitudes.

Moreover, it may be that gender stereotypes are affecting not so much mathematics anxiety itself as self-perceptions of mathematics anxiety. Goetz and colleagues gave secondary school pupils questionnaires about mathematics anxiety as a trait , and also about their anxiety as a state during a mathematics class (Goetz et al., 2013 ; Bieg et al., 2015 ). Both boys and girls tended to report higher trait anxiety than state anxiety, but girls did so to a much greater extent. Girls reported higher trait anxiety than boys in both studies, but higher state anxiety only in one of the studies. One possible conclusion that girls do not in fact experience so much more mathematics anxiety than boys, but that due to gender stereotypes they expect to experience more mathematics anxiety, and this in itself may discourage them from pursuing mathematics activities and courses.

Factors that affect mathematics anxiety: age

On the whole, mathematics anxiety appears to increase with age during childhood. Most studies suggest that severe mathematics anxiety is uncommon in young children, though some researchers have found significant mathematics anxiety even among early primary school children (Wu et al., 2012 ). This apparent increase in mathematics anxiety with age is consistent with findings that show that other attitudes to mathematics change with age. Unfortunately, they tend to deteriorate as children get older (Ma and Kishor, 1997 ; Dowker, 2005 ; Mata et al., 2012 ). Blatchford ( 1996 ) found that two-thirds of 11-years-olds rate mathematics as their favorite subject, but that few 16-year-olds do so. Some studies suggest that the deterioration of attitudes begins even before the end of primary school (Wigfield and Meece, 1988 ).

There are a number of reasons why mathematics anxiety might increase with age: some relating more to the “anxiety” and some more to the “mathematics.” One reason is that general anxiety appears to increase with age during childhood and adolescence could also reflect increases in tendency to general anxiety. For example, it is generally found that the onset of clinical anxiety disorders peaks in early adolescence (Kiessler et al., 2005 ) though it is possible that such disorders in younger children are under-diagnosed due to lack of clear and appropriate diagnostic methods (Egger and Angold, 2006 ). It may be that a factor such as increasing intolerance of uncertainty or increasing awareness of social comparison is leading to both increased general anxiety and to increased mathematics anxiety in particular.

Reasons more specifically relating to mathematics may include exposure to other people's negative attitudes to mathematics; to social stereotypes, for example about the general difficulty of mathematics or about supposed gender differences in mathematics; to experiences of failure or the threat of it; and/or to changes in the content of mathematics itself. Arithmetic with larger numbers that make greater demands on working memory, and more abstract non-numerical aspects of mathematics, may arouse more anxiety than the possibly more accessible aspects of mathematics encountered by younger children.

Moreover, the relationships between attitudes and performance may change with age. A meta-analysis by Ma and Kishor ( 1997 ) indicated that the relationship between attitudes and performance increases with age. Some studies suggest that among young children, performance is not significantly related to anxiety (Cain-Caston, 1993 ; Krinzinger et al., 2009 ; Dowker et al., 2012 ; Haase et al., 2012 ), but is more related to liking for mathematics and especially to self-rating. However, different studies give conflicting results; and some studies do show a significant relationship between anxiety and performance in young children (Dossey et al., 1988 ; Newstead, 1998 ; Wu et al., 2012 ; Ramirez et al., 2013 ; Vukovic et al., 2013 ).

There are at least three possible explanations for the conflicting findings. One is that the results may vary according to the aspect of mathematics anxiety that is being studied. Studies that base their measures on Richardson and Suinn ( 1972 ). Mathematics Rating Scale (MARS) or MARS-Elementary (Suinn et al., 1988 ) have tended to show such a relationship even in young children (Wu et al., 2012 ; Vukovic et al., 2013 ), and this could reflect the fact that such measures tend to focus on the affective dimension of mathematics anxiety. Those that have used the Mathematics Anxiety Questionnaire (MAQ) developed by Thomas and Dowker ( 2000 ) have tended not to show such a relationship in younger children (Krinzinger et al., 2007 , 2009 ; Dowker et al., 2012 ; Haase et al., 2012 ; Wood et al., 2012 ), which could reflect the fact that this measure places more emphasis on the cognitive (“worry”) aspect of mathematics. The few studies that have included both dimensions of mathematics anxiety have suggested that performance in young children is related to the affective but not to the cognitive dimension (Harari et al., 2013 ), whereas studies of older children and adults suggest that performance is related to both, but is more strongly related to the affective dimension (Wigfield and Meece, 1988 ; Ho et al., 2000 ). More research is needed on how the relationship changes with age between performance and different components of mathematics anxiety.

A second explanation is that mathematics anxiety becomes more closely related to mathematics performance because of changes in working memory. Working memory of course increases with age in childhood (Henry, 2012 ), which could affect the relationship between anxiety and performance. One study does suggest that the relationship between anxiety and performance is greater in children with higher than lower levels of working memory. Vukovic et al. ( 2013 ) carried out a longitudinal study of 113 children, who were followed up from second to third grade. Mathematics anxiety was measured by items from the MARS-Elementary and from Wigfield and Meece's ( 1988 ) MAQ. Mathematics anxiety was negatively related to performance in calculation but not geometry. It was also negatively correlated with pupils' improvement from second to third grade, but only for children with higher levels of working memory. This is at first sight surprising given that working memory is generally positively correlated with mathematical performance, and especially in view of the theory that mathematics anxiety impedes performance by overloading working memory. We would suggest that a likely explanation is that among younger elementary school children, only those with high levels of working memory are already using mathematical strategies that depend significantly on working memory, and that therefore these may be the children whose progress is most impeded by mathematics anxiety. This could be one explanation for mathematics anxiety being more correlated with performance more in older than in younger children.

A third possible explanation is cultural. The studies that do show a relationship between mathematics anxiety and achievement among young children tend to be from the USA, though this could of course be a coincidence, and there are at present no obvious reasons why the relationship should be stronger in the USA than elsewhere. Nevertheless, there is evidence more generally for cultural influences on mathematics anxiety.

Culture, nationality, and mathematics anxiety

Some aspects of attitudes to mathematics seem to be common to many countries and cultures: e.g., the tendency for young children to like mathematics, and for attitudes to deteriorate with age (Ma and Kishor, 1997 ; Dowker, 2005 ). However, different countries differ not only in actual mathematics performance, but also in liking mathematics; in whether mathematics is attributed more to ability or effort; and how much importance is attributed to mathematics (Stevenson et al., 1990 ; Askew et al., 2010 ).

Some of these differences could affect mathematics anxiety, though the direction is not completely predictable. Children in high-achieving countries could be low in mathematics anxiety because they are doing well (and/or may do well because they are not impeded by mathematics anxiety). On the other hand, they could be high in mathematics anxiety, because such countries often attach high importance to mathematics and to academic achievement in general, making failure more threatening; and because such children are likely to be comparing themselves with high-achieving peers, rather than with lower-achieving children in other countries. Lee ( 2009 ) investigated mathematics anxiety scores in a variety of countries and found that the relationship between a country's overall mathematics achievement level, and the average level of mathematics anxiety among children in that country, was not consistent. Children in high-achieving Asian countries, such as Korea and Japan, tended to demonstrate high mathematics anxiety; while those in high-achieving Western European countries, such as Finland, the Netherlands, Liechtenstein, and Switzerland tended to demonstrate low mathematics anxiety. At present, the reason for these differences is not clear. They may be related to the fact that pressure to do well in examinations is probably significantly greater in Asian countries (e.g., Tan and Yates, 2011 ). They could also be related to some as yet undetermined specific aspects of the educational systems or curricula.

Another possible reason could involve cultural or ethnic differences either in willingness to admit to mathematics anxiety, or in the nature of the relationship between mathematics anxiety and mathematics performance. Several studies have suggested that ethnic minority students express more positive attitudes to mathematics than white pupils both in the USA (Catsambis, 1994 ; Lubienski, 2002 ) and in the UK (National Audit Office, 2008 ), which did not conform to actual differences in performance. However, the meta-analysis of Ma ( 1999 ) showed no ethnic differences with regard to the relationship between anxiety and performance.

There is overwhelming evidence that both the socio-economic status of individuals and the economic position of countries have a very large influence on mathematical participation and achievement (e.g., Chiu and Xihua, 2008 ), However, there has been little research specifically on the influence of socio-economic status on mathematics anxiety or attitudes to mathematics; and the research that has been done does not suggest a very strong SES effect on these variables (Jadjewski, 2011 ).

Potential treatments of mathematics anxiety

Research has already told us a lot about the nature of emotions and attitudes toward mathematics. So far, it tells us less about how such attitudes can be modified, and how mathematics anxiety may be treated, or, ideally, prevented. It is likely that early interventions for children with mathematical difficulties may go some way toward preventing a vicious spiral, where mathematical difficulties cause anxiety, which causes further difficulties with mathematics. Parents and teachers could attempt to model positive attitudes to mathematics and avoid expressing negative ones to children. This may, however, be difficult if the parents or teachers are themselves highly anxious about mathematics. There could be greater media promotion of mathematics as interesting and important. However, much more research is needed on the effectiveness of different strategies for improving attitudes to mathematics. In such research, it must be taken into account, both that mathematics has many components and that different strategies might be effective with different components; and that improving attitudes to mathematics means not only reducing anxiety and other negative emotions toward mathematics, but increasing positive emotions toward mathematics.

Treatments of already-established mathematics anxiety may involve both mathematics interventions as such, and treatments for anxiety such as systematic desensitization and cognitive behavior therapy. So far, no miracle cure seems to be in sight. However, there are new methods, based on recent research findings that appear to be promising.

In particular, researchers have recently attempted to use findings about the cognitive aspects of mathematics anxiety, and about cognitive treatments of anxiety more generally, to develop techniques involving reappraisal of the anxiety-provoking situation. A few recent studies suggest that instructing people to reappraise the nature and consequences of mathematics anxiety may reduce the negative effects, breaking a vicious circle, whereby people feel that their anxiety will worsen their performance or is a signal of inability to carry out the tasks. Johns et al. ( 2008 ) and Jamieson et al. ( 2010 ) found that informing people that arousal could actually improve performance led to better mathematics performance than in a control condition.

Beilock and colleagues have developed a promising intervention for mathematics anxiety that amounts to “writing out” the negative affect and worry (Ramirez and Beilock, 2011 ; Park et al., 2014 ). The researchers drew on previous findings that writing about traumatic and highly emotional events lowered ruminating behavior in individuals with clinical depression (Smyth, 1998 ). A possible mechanism for this could be that writing enables a form of reappraisal that interrogates the need to worry in the first place. This in turn frees working memory resources consumed by worrying, which can be deployed toward task performance. Ramirez and Beilock ( 2011 ) tested this proposition both in a laboratory environment and also in a high-stakes field experiment (i.e., an exam). Both the laboratory and field experiments showed that writing about one's worries before academic performance significantly improved performance compared to a control condition (e.g., writing about untested exam material). An exam can be stressful for anyone taking it. Most interesting, therefore, was the finding that 10 min of expressive writing before an exam was only beneficial for individuals with high test anxiety, compared to control writing. Individuals with low test anxiety did not experience any particular benefits from expressive writing. The authors attribute this to the extent to which individuals with high and low test anxiety differ in worrying about exams. Individuals with lower test anxiety, who presumably worry less, would therefore write about fewer worries during an expressive writing exercise. In other words, there is simply less worry that needs to be “written out” for individuals with low test anxiety, in contrast to individuals with high mathematics anxiety. The potential of this kind of intervention to facilitate a level playing field during exams is potentially large. Indeed, students in the expressive condition outperformed those in the control condition by 6%. In letter grades, the expressive condition students earned a B+ on average, while those in the control condition earned a B–. Could this kind of intervention be useful for mathematics anxiety? The same group of authors has suggested that this may be the case. In a recent paper, Park et al. ( 2014 ) explored the influence of expressive writing on the link between mathematics anxiety and mathematics performance. Parallel to the Ramirez and Beilock ( 2011 ) results, Park et al. ( 2014 ) found that expressive writing ameliorated performance on tasks of modular arithmetic (specially developed working memory-intensive mathematics problems) in high mathematics anxiety individuals compared to a control writing task. As stated earlier in this paper, one of the central tenets of current theories of mathematics anxiety is that the negative emotional state and associated ruminations absorb working memory resources necessary for task completion. Expressive writing seems to disrupt the negative emotional cognitions, and allows individuals to engage with the mathematical tasks rather than the attendant anxiety. Unlike Ramirez and Beilock ( 2011 ), Park et al. ( 2014 ) did not test these propositions in the field with an actual mathematics exam. Therefore, the benefit of expressive writing on mathematics examination performance remains a presumption in need of verification. However, a note of cautious optimism is permissible, given both the promising results from the earlier field experiments as well as evidence of higher performance on working memory-intensive problems reported in Park et al. ( 2014 ). Future research can easily investigate this possibility, as the only requirement is that proctors instruct students to engage in a writing task 10 min before the start of an exam.

Recently, the potential of cognitive tutoring to intervene with mathematics anxiety has been explored. Supekar et al. ( 2015 ) examined whether an intensive, 8-week one-on-one math-tutoring programme, MathWise that was developed by Fuchs et al. ( 2013 ) to improve mathematical skills could remediate math anxiety of children aged 7–9 years old. Children underwent three sessions of 40–50 min mathematics tutoring per week. They reported math anxiety levels using the Scale for Early Mathematics Anxiety (Wu et al., 2012 ) and were scanned using fMRI before and after training. During scanning, children performed on an arithmetic problem-solving task (Addition task) and number-identification (Control task). This study found that tutoring reduced math anxiety scores and remediated aberrant functional responses and connectivity in emotion-related circuits associated with the basolateral amygdala in children with high mathematics anxiety, but not those with low mathematics anxiety. In particular, they found that children with greater tutoring-associated decreases in their amygdala activity showed higher reductions in mathematics anxiety. The authors proposed that similar to models of exposure-based therapy for anxiety disorders, sustained exposure to mathematical stimuli could reduce mathematics anxiety, possibly through modulating the role of the amygdala. Together, this study showed that a relatively short and intensive one-on-one cognitive tutoring could remediate mathematics anxiety through modulation of neural functions.

As highlighted by Sokolowski and Necka ( 2016 ) however, interpretations of these findings should consider that since children were categorized through the extreme group approach (into high or low math-anxious using a median-split of pre-test SEMA scores) and were not recruited on the basis of their math anxiety levels, it is possible that children with nearly average SEMA scores might have been included in the high math anxious group (which is typically defined, for example by Ashcraft and Kirk ( 2001 ), as the highest 20% of this population). Such classification might affect the interpretations of “aberrant neural responses” attributed to children with high mathematics anxiety. Nonetheless, Supekar et al. ( 2015 ) provided a proof-of-concept that behavioral interventions with simultaneous neural, social and cognitive assessments could contribute to our understanding of the relationship between individual differences and efficacy of interventions.

Another potential form of treatment, which is just beginning to be explored, involves non-invasive brain stimulation. Non-invasive brain stimulation techniques are used by researchers to modulate neural activity on broad areas of the cortex. Transcranial electrical stimulation (tES) has emerged as a painless technique in which mild electrical currents are applied to the scalp and can be used to both upregulate and downregulate neuronal activity underneath the cortex.

Might such a technique be useful as an intervention for mathematics anxiety? As stated above, some brain imaging research has examined the neurophysiological signatures of mathematics anxiety. These include abnormal amygdala activation (Young et al., 2012 ) associated with fear processing, activation of the dorsoposterior insula, associated with pain perception (Lyons and Beilock, 2012a ), and hypoactivation of regions in the frontoparietal network such as the dorsolateral prefrontal cortex, associated with both cognitive control of negative emotions and with mathematical performance (Lyons and Beilock, 2012b ). Transcranial electrical stimulation enables researchers to modulate cortical activity in regions that may facilitate greater emotional control over the negative emotional response to mathematical stimuli, thereby improving performance. Transcranial direct current stimulation (tDCS) is the most widely used form of tES. tDCS is a non-invasive and painless neuromodulation technique wherein a low direct current, usually between 1 and 2 mA, is transmitted into cortical tissue through scalp-electrodes (Nitsche et al., 2008 ; Cohen Kadosh, 2013 ; Krause and Cohen Kadosh, 2014 ). The electrical signals in tDCS alter neuronal polarization, thereby manipulating the probability that the targeted neurons will fire; typically, anodal stimulation is known to facilitate neural firing, while cathodal stimulation inhibits neuronal firing of the stimulated cortical region (Nitsche and Paulus, 2000 ). In sham (placebo) stimulation, a burst of current is provided and turned-off, generating the same physical sensations as real stimulation (e.g., mild itching, burning, tingling, or stinging), but producing no change in cortical excitability. This serves as a reliable blinding method, and participants are generally unable to distinguish between real and sham stimulation (Gandiga et al., 2006 ). The brain region usually targeted in emotion-related tDCS research is the dorsolateral prefrontal cortex (dlPFC), which is implicated in working memory and affective regulation (Peña-Gómez et al., 2011 ), and is closely involved in the response and control of stress (Cerqueira et al., 2008 ).

Sarkar et al. ( 2014 ) investigated the effects of tDCS to the dlPFC on mathematics anxiety. High mathematics anxiety individuals received 1 mA of tDCS for 30 min (or 30 s, in the placebo condition) to their left and right dorsolateral prefrontal cortices to enhance cognitive control over the negative emotional response elicited by mathematical stimuli. A low mathematics anxiety group received the same treatment. Sarkar et al. ( 2014 ) also examined changes in salivary cortisol, mentioned above as a possible physiological measure of anxiety. Anodal and cathodal stimulation were applied to the left and right dlPFC, respectively. In their study, Sarkar et al. ( 2014 ) found that, compared to sham stimulation, real tDCS lowered reaction times in the arithmetic decision task for individuals with high mathematics anxiety. They found the opposite pattern for low mathematics anxiety participants, who were slower in real compared to sham stimulation. The cortisol changes mirrored the behavioral changes. Compared to sham stimulation, high mathematics anxiety participants showed a decline in salivary cortisol concentrations from pre- to post-test during real tDCS. For the low mathematics anxiety group, salivary cortisol concentrations declined from pre-test to post-test only during sham tDCS, but not during real stimulation. This suggests tDCS might be able to alleviate the stress associated with mathematics anxiety, thereby improving mathematical performance in individuals with high mathematics anxiety. It is still necessary to be cautious about this possibility for several reasons. Firstly, as discussed above, the relationship between cortisol secretion and mathematics anxiety may not be totally straightforward. Secondly, the ecological validity of such intervention (e.g., as regards the training design and the practicality of using tDCS outside the laboratory) remains to be improved (Cohen Kadosh, 2014 ; Looi et al., 2016 ). In the context of mathematics anxiety, further research is needed to examine whether tDCS could enhance performance for individuals with high mathematics anxiety in real-life settings and examinations (e.g., high-stakes situations). Given that the arithmetic decision task used by Sarkar et al. ( 2014 ) only required participants to decide whether very basic mathematical equations were true or false (e.g., 8 × 2 = 16, true or false), future studies could adopt more complex, realistic tasks. Thirdly, the improvement on such tasks was to the degree of ~50 ms, significant in a laboratory context but hardly relevant to the types of situations where mathematics anxiety is most relevant. Since behavioral studies mostly observe the influence of mathematics anxiety on difficult maths tasks (see Artemenko et al., 2015 for a recent review) and tES appears to be more effective during difficult tasks (Popescu et al., 2016 ), future studies could investigate whether improvements of individuals with mathematics anxiety would be greater during more difficult tasks. Fourthly, since the dlPFC is involved in many functions, it is as yet unclear exactly which of these functions was crucially affected here: in particular, whether tDCS affected performance by influencing its role in emotional processing, or working memory, or both. Fifthly, the findings suggest that such treatments would need to be targeted to people who are high in mathematics anxiety, and that their indiscriminate application to people with lower mathematics anxiety might actually impair performance. Hence, research that examines the mechanisms of such effects (positive or negative; short- or long-term) is needed (Bestmann et al., 2015 ). Finally, behavioral effects are influenced by the parameters of tDCS. For example, while Sarkar et al. ( 2014 ) showed that tDCS applied during mathematical tasks benefited those with high mathematics anxiety and impaired performance of those with low mathematics anxiety, it remains to be investigated whether changing the parameters of stimulation (e.g., applying stimulation before or after mathematical tasks) would yield different behavioral outcomes (for a review of other factors, see Looi and Cohen Kadosh, 2015 ). Thus, these findings are merely the first, though a promising step in the development of tES as a potential intervention for mathematics anxiety.

So what remains to be understood?

During the last 60 years, we have acquired a much greater understanding of the phenomenon of mathematics anxiety. We have learned more about its correlation with mathematics performance, and for example how working memory may be involved in this. We have learned more about how it changes with age. We have learned more about its relationship to social stereotypes, especially with regard to gender. We have learned something about neural correlates of mathematics anxiety. We have learned something about possible ways to treat mathematics anxiety.

Thus, we have learned a significant amount about many specific aspects of mathematics anxiety. Our biggest need for further learning may involve not so much any specific aspect, as the ways in which the aspects relate to one another. How do the social aspects relate to the neural aspects? How do either or both of these relate to changes with age? How might appropriate treatment be related to age and to the social and cognitive characteristics of the individuals? And of course the perennial “chicken and egg” question: does mathematics anxiety lead to poorer performance, or does poor performance, with its resulting experiences of failure, lead to poorer performance (Carey et al., 2015 )? Many more interdisciplinary, longitudinal and intervention studies will be needed to answer these questions. An ultimate goal of such research is to integrate findings from across the behavioral, cognitive and biological dimensions of this construct in order to produce a fuller description of mathematics anxiety as a trait that varies between individuals.

There are also more specific aspects of mathematics anxiety that need a lot more study. For example, although there has been a great deal of research on social influences on mathematics anxiety, most of this has involved one particular type of influence: gender stereotyping. Other influences also need more investigation. In particular, there needs to be more investigation of the role of pressures by parents and teachers for school achievement. This is especially true in view of the increasing importance of both mathematics as such and of academic qualifications in today's society; and in view of the increasing concern of governments in several countries about raising academic standards. The question arises of whether and at what point an increasing emphasis on mathematical achievement might have the negative and potentially counterproductive effect of increasing mathematics anxiety; and how this might be prevented. In this context, there needs to be more research on exactly how mathematics anxiety is related to motivation, and, in particular, whether there are differences in the relationships of intrinsic and extrinsic motivation to anxiety (Gottfried, 1982 ; Lepper, 1988 ; Ryan and Pintrich, 1997 ).

We hope that long before another 60 years have passed, research will have led to a greater understanding of mathematics anxiety, which will enable us to develop interventions and educational methods that will greatly reduce its incidence.

Author contributions

All authors listed, have made substantial, direct, and intellectual contribution to the work, and approved it for publication.

We thank the Nuffield Foundation for financial support.

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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This paper is in the following e-collection/theme issue:

Published on 12.4.2024 in Vol 26 (2024)

The Effectiveness of a Digital App for Reduction of Clinical Symptoms in Individuals With Panic Disorder: Randomized Controlled Trial

Authors of this article:

Original Paper

• KunJung Kim, MD   ; 
• Hyunchan Hwang, MD, PhD   ; 
• Sujin Bae, PhD   ; 
• Sun Mi Kim, MD, PhD   ; 
• Doug Hyun Han, MD, PhD  

Chung Ang University Hospital, Seoul, Republic of Korea

Corresponding Author:

Doug Hyun Han, MD, PhD

Chung Ang University Hospital

102 Heucsock ro

Seoul, 06973

Republic of Korea

Phone: 82 2 6299 3132

Fax:82 2 6299 3100

Email: [email protected]

Background: Panic disorder is a common and important disease in clinical practice that decreases individual productivity and increases health care use. Treatments comprise medication and cognitive behavioral therapy. However, adverse medication effects and poor treatment compliance mean new therapeutic models are needed.

Objective: We hypothesized that digital therapy for panic disorder may improve panic disorder symptoms and that treatment response would be associated with brain activity changes assessed with functional near-infrared spectroscopy (fNIRS).

Methods: Individuals (n=50) with a history of panic attacks were recruited. Symptoms were assessed before and after the use of an app for panic disorder, which in this study was a smartphone-based app for treating the clinical symptoms of panic disorder, panic symptoms, depressive symptoms, and anxiety. The hemodynamics in the frontal cortex during the resting state were measured via fNIRS. The app had 4 parts: diary, education, quest, and serious games. The study trial was approved by the institutional review board of Chung-Ang University Hospital (1041078-202112-HR-349-01) and written informed consent was obtained from all participants.

Results: The number of participants with improved panic symptoms in the app use group (20/25, 80%) was greater than that in the control group (6/21, 29%; χ 2 1 =12.3; P =.005). During treatment, the improvement in the Panic Disorder Severity Scale (PDSS) score in the app use group was greater than that in the control group ( F 1,44 =7.03; P =.01). In the app use group, the total PDSS score declined by 42.5% (mean score 14.3, SD 6.5 at baseline and mean score 7.2, SD 3.6 after the intervention), whereas the PDSS score declined by 14.6% in the control group (mean score 12.4, SD 5.2 at baseline and mean score 9.8, SD 7.9 after the intervention). There were no significant differences in accumulated oxygenated hemoglobin (accHbO 2 ) at baseline between the app use and control groups. During treatment, the reduction in accHbO 2 in the right ventrolateral prefrontal cortex (VLPFC; F 1,44 =8.22; P =.006) and the right orbitofrontal cortex (OFC; F 1,44 =8.88; P =.005) was greater in the app use than the control group.

Conclusions: Apps for panic disorder should effectively reduce symptoms and VLPFC and OFC brain activity in patients with panic disorder. The improvement of panic disorder symptoms was positively correlated with decreased VLPFC and OFC brain activity in the resting state.

Trial Registration: Clinical Research Information Service KCT0007280; https://cris.nih.go.kr/cris/search/detailSearch.do?seq=21448

Introduction

Panic disorder is a common and important disease in clinical practice that leads to a reduction of individual productivity and increased use of health care [ 1 ]. The lifetime prevalence of panic disorder in the general population is 4.8%, and 22.7% of people experience panic attacks [ 2 ]. The most common symptoms of panic disorder include palpitations, shortness of breath, chest pain, numbness of the hands and feet, and cardiorespiratory-type symptoms, in addition to fear of dying, sweating, tremors, dizziness, nausea, and chills [ 3 ]. The US Food and Drug Administration has currently only approved selective serotonin reuptake inhibitors (SSRIs) for the treatment of panic disorder [ 4 ]. However, it is clinically difficult to expect an improvement in symptoms using SSRIs alone in the acute phase; thus we treat patients with benzodiazepine, which can lead to dependence and withdrawal symptoms [ 5 , 6 ]. The most common side effects of SSRIs reported by patients are reduced sexual function, drowsiness, and weight gain [ 7 ], and clinicians may hesitate to use benzodiazepines due to dependence and withdrawal symptoms [ 8 ]. Cognitive behavioral therapy (CBT) is the most widely used nonpharmaceutical treatment for anxiety disorders [ 9 ]. Additional nonpharmaceutical treatments, such as group therapy and supportive psychotherapy, are also available for patients with panic disorder [ 10 , 11 ]. However, these treatments have the disadvantage of requiring face-to-face contact; therefore, other therapeutic alternatives should be offered to patients during pandemics such as COVID-19.

The definition of a digital therapeutic (DTx) is a therapeutic that delivers evidence-based interventions to prevent, manage, or treat a medical disorder or disease; DTxs are currently used in many areas [ 12 ]. This kind of medical and public health use of smartphones and digital technologies is also known as mobile health (mHealth). DTxs related to mental health medicine are actively used in various psychiatric disorders, such as insomnia, substance abuse, attention-deficit/hyperactivity disorder, and anxiety and depression, among others [ 13 ]. In particular, the use of Freespira, a panic disorder DTx, reduced panic symptoms, avoidance behaviors, and treatment costs in patients with panic disorder [ 14 ].

As brain imaging technology advances, a great deal of functional mapping information on the human brain has been accumulated from positron emission tomography (PET), functional magnetic resonance imaging (fMRI), and functional near-infrared spectroscopy (fNIRS). Among these technologies, fNIRS can measure brain activity in a noninvasive and safe manner through measuring changes in the hemoglobin oxygenation state of the human brain [ 15 ]. Various studies have been conducted using fNIRS and fMRI to reveal correlations between panic disorder and brain regions. For example, patients with panic disorder show increased activity in the inferior frontal cortex, hippocampus, cingulate (both anterior and posterior), and orbitofrontal cortex (OFC) [ 16 ]. Previously, we confirmed that patients with panic disorder during rest periods showed increased activity in the OFC [ 17 ].

In this study, we determined whether an app for panic disorder would improve panic disorder symptoms. In addition, we used fNIRS to confirm the association between changes in panic disorder symptoms and changes in activity in specific brain regions.

Participants

Patients who had experiences of panic attacks were recruited between March 1 and July 30, 2022, through billboard advertisements at our hospital. The inclusion criteria for the study were as follows: (1) age between 20 and 65 years, (2) diagnosis of panic disorder based on the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition and (3) ability to use apps without problems. The exclusion criteria were as follows: (1) a history of other psychiatric disorders, except for anxiety disorder, or substance dependence, except for habitual alcohol and tobacco use; and (2) a history of head trauma and chronic medical conditions. The research clinician assessed whether patients fulfilled the inclusion or exclusion criteria. Written informed consent was acquired from all participants at the first visit. This study has been registered with the Clinical Research Information Service (KCT0007280).

Assessment Scales for Anxiety Symptoms

The severity of panic symptoms was assessed using the Panic Disorder Severity Scale (PDSS). The PDSS was developed by Shear et al [ 18 ] in 1997. It is a 7-item instrument used to rate the overall severity of panic disorder and was validated in Korea by Lim et al [ 19 ] in 2001.

The anxiety symptoms of all participants were assessed using the clinician-based Hamilton Anxiety Scale (HAM-A) questionnaire and the participant-based Generalized Anxiety Disorder-7 (GAD-7) questionnaire. The HAM-A was developed by Hamilton in 1969 [ 20 ]. The 14-item version remains the most used outcome measure in clinical trials of treatments for anxiety disorders and was validated in Korea by Kim [ 21 ] in 2001.

The GAD-7 questionnaire, developed by Spitzer et al [ 22 ], is a 7-item self-report anxiety questionnaire designed to assess the patient’s health status during the previous 2 weeks. The GAD-7 was translated into the Korean language and is freely downloadable on the Patient Health Questionnaire website [ 23 ].

Hemodynamic Response of the Prefrontal Cortex

The hemodynamics in the frontal cortex during the resting state were measured using the fNIRS device (NIRSIT; OBELAB Inc). The NIRSIT has 24 laser diodes (sources) emitting light at 2 wavelengths (780 nm and 850 nm) and 32 photodetectors with a sampling rate of 8.138 Hz [ 24 ]. The distance between the source and photodetector is 15 mm. Based on the suggested suitable sensor-detector separation distance for measuring cortical hemodynamic changes, only 30-mm channels were analyzed in this study [ 25 ].

For our study, we used the 48-channel configuration ( Figure 1 ). The detected light signals in each wavelength were filtered with a band-pass filter (0.00 Hz-0.1 Hz) to reduce the effect of environmental noise–related light and body movements. In addition, channels with low-quality information (signal-to-noise ratio <30 dB) were removed from the hemodynamic analysis. The accumulated oxygenated hemoglobin (accHbO 2 ) values in the resting state represent the activation of the prefrontal cortex. In accordance with the theory that oxygenated hemoglobin has superior sensitivity and signal-to-noise ratio compared to deoxygenated hemoglobin data, only oxygenated hemoglobin were used for this analysis [ 26 - 28 ].

The means and SDs for accHbO 2 were calculated from regions of interest (ROIs) in the right and left dorsolateral prefrontal cortices (DLPFCs), right and left ventrolateral prefrontal cortices (VLPFCs), right and left frontopolar cortices (FPCs), and right and left orbitofrontal cortices (OFCs), based on Brodmann area 46. The right and left DLPFCs comprise channels 1, 2, 3, 5, 6, 11, 17, and 18 and channels 19, 20, 33, 34, 35, 38, 39, and 43, respectively. The right and left VLPFCs comprise channels 4, 9, and 10 and channels 40, 44, and 45, respectively. The right and left FPCs comprise channels 7, 8, 12, 13, 21, 22, 25, and 26 and channels 23, 24, 27, 28, 36, 37, 41, and 42, respectively. The right and left OFCs comprise channels 14, 15, 16, 29, and 30 and channels 31, 32, 46, 47, and 48, respectively ( Figure 1 ).

Digital App for Panic Disorder

The app for panic disorder is a smartphone-based app for treatment of clinical symptoms of panic disorder. The mobile app has 4 categories: diary, education, quest, and serious games. The diary category has three items: (1) assessment of daily psychological status, including mood and anxiety; (2) assessment of panic symptoms, including frequency and severity; and (3) consumption of medication, including regular medication and pro re nata medications. The education category has three items: (1) knowledge about panic disorders, (2) knowledge about medications for panic disorder, and (3) knowledge about panic disorder treatment, including CBT, breathing therapy, and positive thinking therapy. The quests include two treatments: (1) eye movement desensitization and reprocessing therapy and (2) positive thinking therapy. The serious games include two games: (1) a breathing game and (2) an exposure therapy game.

The diary, education, and serious games (ie, the breathing game and exposure therapy game) are important parts of CBT for panic disorder [ 29 - 32 ]. The efficacy of CBT for panic disorder has been examined in various randomized controlled trials [ 33 , 34 ]. Eye movement desensitization and reprocessing therapy are also known to help reduce panic symptoms [ 35 , 36 ]. We confirmed that the replacement of worry with different forms of positive ideation shows beneficial effects [ 37 ], so a similar type of positive thinking therapy can also be expected to show benefits. Multimedia Appendix 1 provides additional information on the app.

Ethical Considerations

The study trial was approved by the institutional review board of Chung-Ang University Hospital (1041078-202112-HR-349-01) and written informed consent was obtained from all participants. Participants received an explanation from the researchers that included an overview of the study and a description of the methodology and purpose before deciding to participate. Additionally, they were informed that participation was voluntary, informed about our confidentiality measures, given the option to withdraw, and informed about potential side effects and compensation. Participants in this study received ₩100,000 (US $75.50) as transportation reimbursement. Additionally, the various scales and fNIRS assessments were offered at no cost to the participants. The participants received the results of the tests in the form of a report via postal mail or email after the conclusion of the study. They also receive an explanatory document and consent form from the researchers that included contact information for any inquiries. If the participant agreed to take part in the study after understanding the consent form, the research proceeded. The participants’ personal information was not collected. Instead, a unique identifier was assigned to the collected data for the sole purpose of research management.

Study Procedure

A randomized and treatment-as-usual–controlled design was applied in this study. After screening, all participants with panic disorder were randomly assigned to the app use group or the control group. The randomization sequence in our design was generated using SPSS (version 24.0; IBM Corp), with a 1:1 allocation between groups. At baseline and after intervention, all patients with panic disorder were assessed with the PDSS for panic symptoms, the HAM-A for objective anxiety symptoms, and the GAD-7 for subjective anxiety symptoms. At baseline and after intervention, the hemodynamic response in all patients with panic disorder was assessed using NIRSIT. The app use group was asked to use the app for panic disorder 20 minutes per day, 5 times per week, for 4 weeks. The control group was asked to read short educational letters that were delivered via a social network service 5 times per week for 4 weeks. The short letters contained information about panic disorder and its treatment.

Demographic and Clinical Characteristics

After recruitment, 56 patients underwent eligibility assessments. A total of 6 individuals were excluded because they did not meet the inclusion criteria. The remaining patients were divided into 2 groups: 25 were assigned to the app use group and 21 to the control group, as 4 patients were excluded; contact was suddenly lost with 1 patient contact and 1 dropped out for personal reasons. In addition, 2 patients in the control group quit the study after reporting poor benefits from the short educational letters. Therefore, 25 people in the app use group and 21 people in the control group were analyzed. Figure 2 shows the Consolidated Standards of Reporting Trials (CONSORT) flowchart for participant flow through the trial.

There were no significant differences in age, sex ratio, years of education, marital status, employment status, or substance habits, including smoking and alcohol use, between the app use group and the control group ( Table 1 ).

b Chi-square.

There were no significant differences in HAM-A score, GAD-7 score, or PDSS score at baseline between the app use group and control group ( Table 1 ).

Comparison of Changes in Clinical Scales Between App Use Group and Control Group

The number of participants with improved panic symptoms in the app use group (20/25, 80%) was greater than in the control group (6/21, 29%; χ 2 1 =12.3; P =.005).

During the treatment period, the app use group showed greater improvement in PDSS score than the control group ( F 1,44 =7.03; P =.01). In the app use group, the PDSS score decreased by 42.5% (mean score 14.3, SD 6.5 at baseline and mean score 7.2, SD 3.6 after the intervention), while the score decreased by 14.6% in the control group (mean score 12.4, SD 5.2 at baseline and mean score 9.8, SD 7.9 after intervention) ( Figure 3 ).

During the treatment period, there were no significant differences in the change in HAM-A scores ( F 1,44 =2.83; P =.09) and GAD-7 scores ( F 1,44 =0.22; P =.64) between the app use group and control group ( Figure 3 ).

Comparison of Changes in accHbO 2 Values Between App Use Group and Control Group

There were no significant differences in accHbO 2 in the right (t 45 =0.84; P =.40) or left (t 45 =0.73; P =.46) DLPFCs, right (t 45 =1.04; P =.31) or left (t 45 =0.88; P =.39) VLPFCs, right (t 45 =-0.18; P =.86) or left (t 45 =1.85; P =.07) FPCs, or right (t 45 =0.33; P =.74) or left (t 45 =1.89; P =.07) OFCs in the app use and control groups at baseline.

During the treatment period, the app use group showed a greater reduction in accHbO 2 in the right VLPFC ( F 1,44 =8.22; P =.006) and right OFC ( F 1,44 =8.88; P =.005) compared to the control group ( Figure 1 ). During the treatment period, there were no significant differences in the change in accHbO 2 in the other ROIs between the app use and control groups.

Correlations Between the Changes in PDSS Scores and the Changes in accHbO 2

In all participants (ie, the app use group plus the control group), there was a positive correlation between the change in PDSS score and the change in accHbO 2 in the right VLPFC ( r =0.44; P =.002). In the app use group, there was a positive correlation between the change in PDSS score and the changes in accHbO 2 in the right VLPFC ( r =0.42; P =.04). However, in the control group, there was no significant correlation between the change in PDSS score and the change in accHbO 2 in the right VLPFC ( r =0.22; P =.16).

In all participants, there was a positive correlation between the change in PDSS score and the change in accHbO 2 in the right OFC ( r =0.44; P =.002). In both the app use group ( r =0.34; P =.09) and control group ( r =0.33; P =.13), there was no significant correlation between the change in PDSS score and the change in accHbO 2 in the right OFC ( Figure 4 ).

Principal Findings

This study showed that a digital app was effective for symptom reduction, as well as decreasing brain activity in the VLPFCs and OFCs, in patients with panic disorder. In addition, the panic disorder symptom improvement was positively correlated with decreased brain activity in the VLPFCs and OFCs in the resting state.

The digital app used in this trial proved to be effective in reducing panic symptoms when compared to the control group, as demonstrated by the reduction in the PDSS score. We believe that this is due to the combined effect of the 4 parts of the program, namely the diary, education, quest, and serious games. The diary component helps identify and correct faulty perceptions and enables cognitive reconstruction. The education component provides information about the nature and physiology of panic disorder. The breathing game helps the participant return to a relaxed condition, while the exposure therapy game allows the participant to experience agoraphobic situations in a safe environment, which helps cognitive restructuring. These are the important parts of CBT for panic disorder and have shown efficacy, as reported earlier [ 29 - 32 ]. The control group also received educational data, including the importance of keeping a diary of one’s panic symptoms and how to do it, as well as self-guided direction on breathing exercises, but failed to show a significant reduction of symptoms compared to the app use group. We think this is due to lack of proper feedback in the control group. The app shows real-time feedback on breathing exercises using breathing sounds, and a message was sent if the user of the program failed to use the program for more than 2 days. We know that the therapeutic effect is better when immediate feedback is provided to patients undergoing CBT treatment [ 38 ]. Therefore, we think that the decrease in PDSS score was smaller because the control group did not receive feedback from the app.

The control group also received educational data on diary recording, panic disorder information, and how to execute breathing therapy and exposure therapy. We measured their reduction in the PDSS score, but we found it was less than in the app use group due to a lack of proper daily management.

However, the app failed to lead to a difference in the reduction in anxiety, as defined by the HAM-A and GAD-7 scales, between the 2 groups. This is most likely due to a lack of power, as the trial was conducted as a pilot study. Other studies using CBT techniques or serious games have demonstrated reductions in anxiety symptoms in patients with panic disorder [ 14 ]. Likewise, this study showed a trend toward a reduction in anxiety symptoms, although this was not statistically significant, and future research with more participants may show that these kinds of programs are also effective in controlling anxiety.

Two major changes in brain activity were noted in the app use group, namely reductions in VLPFC and OFC activation. The functions of the OFC are varied and include control of inappropriate behavior and emotional responses, decision-making, and solving problems [ 39 , 40 ]. Abnormalities in the function of the OFC can cause problems in dealing with anxiety and show that it is deeply involved in the increasing the sense of fear in the fear response [ 17 ]. The results of this study confirm that OFC activity decreases as treatment progresses. This reinforces the results of a previous study, which showed that patients with panic disorder had increased OFC activity and that when the panic disorder was treated, the activity of the OFC was reduced, as indicated by decreased cerebral glucose metabolic rates [ 17 , 41 ].

The VLPFC is known to be associated with the amygdala and to maintain flexible attention and responses to environmental threats [ 42 , 43 ]. The amygdala is the backbone of the fear network, and the VLPFC is also known to be deeply involved in the processing of fear [ 43 - 45 ]. Several studies have shown increased activity in patients with panic disorder in the inferior frontal gyrus, which envelops the VLPFC, and other related regions, including the prefrontal cortex, hippocampus, and OFC [ 16 , 46 , 47 ]. After panic disorder treatment, such as with CBT, decreased amygdala and inferior frontal gyrus activation in fear situations was confirmed [ 48 , 49 ]. Through panic disorder treatment, inferior frontal gyrus activation decreased to a normal level; this happened because the treatment reduced fear cognition related to harm expectancy or attention to threats [ 49 - 51 ]. We consider that VLPFC activation increases to modulate the amygdala and decreases with treatment for panic disorder.

We believe that these reductions of brain activity in the VLPFC and OFC reflect how the app affected the patients. We know that overprediction of fear or panic is an important feature of anxiety disorders [ 52 ]. The app for panic disorder, including diary, education, quest, and serious game components, allowed users to correct their faulty perceptions about fear. As mentioned earlier, the VLPFC and OFC are related to fear management, so we can expect that activity of the VLPFC and OFC will be reduced through repeated app use as users learn how to deal with fear.

Limitations

This study has the following limitations: Most of the patients were effectively treated with alprazolam or other anxiolytics, such as SSRIs. Thus, treatment with antianxiety drugs may have influenced our results. Moreover, this study assessed changes immediately after app use. A long-term follow-up to evaluate the sustainability of the observed improvements would provide valuable insights into the effectiveness of the intervention over time. App use time could be easily tracked for the app use group; however, it was challenging to independently monitor the time the control group spent reading educational materials. Due to the limitations of available research tools, no investigation has been conducted on deep brain structures such as the amygdala, which is most closely related to panic disorders.

Conclusions

We believe that this app for panic disorder effectively reduces symptoms and noticeably impacts brain activity in specific areas. We observed a positive link between improvement in panic symptoms and decreased brain activity in the VLPFCs and OFCs in a resting state. These findings support the use of targeted interventions to determine the brain’s contribution to symptom relief. Further research should explore the duration of these positive effects and make digital therapy accessible to more individuals, thus unlocking its full potential in mental health care.

Data Availability

The data sets generated and analyzed during this study are not publicly available as they contain information that could compromise the privacy and consent of the research participants. However, the transformed data are available upon reasonable request from the authors.

Conflicts of Interest

None declared.

Digital app for panic disorder.

CONSORT-eHEALTH checklist (V 1.6.1).

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Abbreviations

Edited by A Mavragani; submitted 03.08.23; peer-reviewed by M Aksoy; comments to author 01.09.23; revised version received 11.09.23; accepted 08.03.24; published 12.04.24.

©KunJung Kim, Hyunchan Hwang, Sujin Bae, Sun Mi Kim, Doug Hyun Han. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 12.04.2024.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in the Journal of Medical Internet Research, is properly cited. The complete bibliographic information, a link to the original publication on https://www.jmir.org/, as well as this copyright and license information must be included.

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Princeton University

Princeton engineering, grad alum avi wigderson wins turing award for groundbreaking insights in computer science.

By Scott Lyon

April 10, 2024

Avi Wigderson has won the 2023 Turing Award from the Association for Computing Machinery. Photos by Andrea Kane, courtesy of the Institute for Advanced Study

Princeton graduate alumnus Avi Wigderson has won the 2023 A.M. Turing Award from the Association for Computing Machinery (ACM), recognizing his profound contributions to the mathematical underpinnings of computation.

The Turing Award is considered the highest honor in computer science, often called the “Nobel Prize of Computing.”

Wigderson, the Herbert H. Maass Professor in the Institute for Advanced Study ’s School of Mathematics, earned his Ph.D. from Princeton in 1983 in what was then the Department of Electrical Engineering and Computer Science.

In addition to the Turing Award, he is also the recipient of the 2021 Abel Prize , considered the highest honor in mathematics, from the Norwegian Academy of Science and Letters. He is the only person ever to have won both the Abel Prize and the Turing Award.

“Mathematics is foundational to computer science and Wigderson’s work has connected a wide range of mathematical sub-areas to theoretical computer science,” ACM President Yannis Ioannidis said in a statement released by the organization.

“Avi Wigderson is a giant in the field of theoretical computer science, bringing fundamental insights to deep questions about what can — or cannot — be computed efficiently,” said Jennifer Rexford , Princeton’s provost and Gordon Y.S. Wu Professor of Engineering . “He is also a wonderful colleague and a longtime friend of the University.”

Wigderson is best known for his work on computational complexity theory, especially the role of randomness in computation. Namely, in a series of highly influential works from the 1990s, Wigderson and colleagues proved that computation can be efficient without randomness, shaping algorithm design ever since. He has also established important ideas in several other areas, including protocol design and cryptography, which enables much of today’s digital infrastructure.

While his work is primarily mathematical, the notions he is trying to understand through that work are computational, Wigderson said in a video released by the Institute for Advanced Study (IAS). That approach has earned him a reputation as one of the most versatile minds in either discipline.

“He is one of the most central people in theoretical computer science, generally,” said Ran Raz , a professor of computer science at Princeton, who was Wigderson’s graduate student at the Hebrew University in Jerusalem.

Wigderson has influenced countless students and thinkers, having mentored more than 100 postdocs and collaborated with an unusually broad range of scholars. “He is always able to make connections between things,” Raz said.

“He’s an inspiration,” said Pravesh Kothari , an assistant professor of computer science at Princeton and a former postdoctoral advisee of Wigderson’s at IAS. “He’s a role model. If I could become 10 percent of the researcher he is, it would be a fantastic success for my career.” Kothari also said Wigderson implores young researchers to view the entire endeavor as one field. And that approach shows up in all of his work, connecting disparate problems from sub-disciplines that are normally seen as unrelated.

His research has “set the agenda in theoretical computer science” for decades, Google Senior Vice President Jeff Dean said in the ACM press release. His work has also found its way directly into everyday life.

In a series of findings at the intersection of mathematics and computer science, Wigderson cemented what is known as the zero-knowledge proof, critical in cryptography and digital security. The technique has found purchase in modern applications of privacy, compliance, identity verification and blockchain technology.

Raz said he was amazed at how far Wigderson’s ideas had traveled, from the depths of mathematics to the technologies that enable global enterprise to the everyday lives of billions of people. “It’s quite amazing that these things can be made practical,” Raz said.

Szymon Rusinkiewicz , the David M. Siegel ’83 Professor of Computer Science and department chair, added that Wigderson has been a great friend to Princeton’s computer science community, including to students and young scholars. “He has had a great influence throughout the world of computer science, and we especially feel that at Princeton, where he has been a great mentor and collaborator.”

Wigderson is the recipient of numerous other awards, including the 1994 IMU Abacus Medal, the 2009 Gödel Prize and the 2019 Donald E. Knuth Prize. He is currently a Fellow of the ACM, a member of the American Academy of Arts and Sciences and a member of the National Academy of Sciences.

At Princeton, in addition to his Ph.D., he earned an M.S.E. in 1981, an M.A. in 1982, and he later served on Princeton’s computer science faculty from 1990 to 1992. He joined IAS in 1999, where he established the program in Computer Science and Discrete Mathematics.

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