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Cultivating Growth Mindset: Problem-Solving Activities for Students Project & Activity Ideas Simulation Activity Educational Tips Cultivating Growth Mindset: Problem-Solving Activities for Students Educational Tips , Project & Activity Ideas , Simulation Activity Cultivating Growth Mindset: Problem-Solving Activities for Students

• by English Teaching 101

Cultivating Growth Mindset with Problem Solving-Skills

As a teacher, we’ve got a super important mission: to plant and nurture the seeds of a growth mindset in our students. It’s like giving them a magic key that unlocks their potential to tackle challenges head-on, keep going when things get tough, and see hard work as their secret weapon to success. And you know what’s at the heart of this? Yep, you guessed it – problem-solving skills. These aren’t just for acing tests; they’re real-life super skills that help our kids navigate the twists and turns of the world out there. So, let’s roll up our sleeves and dive into some fun, creative strategies and activities. Together, we’ll turn our classrooms into vibrant hubs where problem-solving magic happens every day!”

The Importance of Teaching Problem-Solving Skills to Students

Let’s talk about why problem-solving skills are the real MVP s in our students’ learning toolkit. Picture this: the world’s like a giant, ever-changing puzzle, right? Our students are going to be the puzzle masters of tomorrow! Whether they’re dreaming of being the next Einstein, a business mogul, or an inspiring educator, problem-solving is their golden ticket.

Now, here’s the cool part – as they flex their problem-solving muscles, they’re also giving their critical thinking skills a major workout. It’s like a brain gym where they learn to make smarter life choices. It’s a huge confidence booster! The Institute of Competition Sciences even says it not only helps students build confidence but also improves their achievement across all subjects.

So, let’s sprinkle our K-12 classrooms with some problem-solving magic and watch our students thrive!”

Top Problem-Solving Activities for Students

1. open-ended questions.

Open-ended questions are questions that require more than one word or sentence to answer. They can’t be answered with a standard response and require thoughtful answers. They can be used in a variety of ways, but they’re particularly helpful in promoting problem-solving skills. That’s because they encourage students to think about the problem themselves.

Open-ended questions allow students to think critically and respond in their own words. This helps students develop their understanding and build on what they already know. Open-ended questions also encourage students to think outside the box and apply what they are learning in new situations.

Here are some examples of open-ended questions teachers can use to help students develop their problem-solving skills:

• How might we solve this problem?
• What do you think?
• What do you think is causing this problem?
• Why do you think that happened?
• What would happen if we did this?

2. Working on Chemical Equations

Chemistry is all about problem-solving, and you can use it to inculcate these skills in students. Chemistry equations show how atoms and molecules combine to form compounds and mixtures.

A chemical equation shows how to make a product from reactants. However, it doesn’t tell your students what the products are or how much you should use. That’s where their knowledge comes in, as they have to figure out the amounts of each reactant needed for a reaction to take place. This can make them think and try different ways to solve the problem at hand.

Chemical equations can also be used to determine unknowns, like the concentration of a solution. In fact, the subject itself can be complicated enough to make the students start thinking differently. According to a study in the De Gruyter Journal, chemistry students can develop problem-solving skills through chemical kinetics and equations.

For instance, chemical equations need to be written correctly. According to Proprep, symbols of elements in chemistry should be written appropriately. For instance, the symbol of nitrogen is a capital “N,” and cannot be written as a small “n.”

Hence, students will have to pay close attention when learning equations. These attentive skills are vital to help them develop problem-solving behavior. That’s because to solve any problem, students first need to pay close attention to the problem. Only after understanding the problem clearly, can they find a solution for it.

Additionally, you can also make students find Lewis structures for different chemical equations. Similar to the symbols of elements, creating Lewis dot structures for equations can help flow the creative juices of students’ minds. The reason is that there can be many possible ways to create a dot structure for an equation. However, only one of them can be correct.

Suppose you ask them to write HCN Lewis structure. In that case, all three elements – H, C, and N – have different numbers of electrons. The students will first have to calculate the number of electrons and create a bond accordingly to get the HCN Lewis structure .

You can ask them to try by themselves, and then even allow them to use online resources to find an answer. This will again teach them how they can find solutions to different problems they face.

3. Scavenger Hunts: Learning through Exploration

A scavenger hunt is a fun way to engage students in problem-solving. It also provides an opportunity for students to work together, which can help them develop more positive attitudes toward each other.

Here’s how you can set up your scavenger hunt:

• Divide your class into teams of four or five students each. If you have fewer than 30 students in your class, consider having teams of three instead. This will give everyone more time during the activity and allow them all access to the materials needed for solving each puzzle.
• Give each team a paper copy of its list. You could also create an electronic version that includes links back to various parts of your curriculum. This makes it easier for teachers who aren’t familiar with everything being covered during this exercise. They can just follow along with whatever links lead them to where they need to go next.

Scavenger hunt can be implemented for students of all ages. A study by the International Literacy Association shows that even an ABC scavenger hunt can help students learn new words. Even businesses use scavenger hunts to teach new skills to employees. An article from the Taylor & Francis Online Journal shows that a marketplace scavenger hunt can teach employees about consumer behavior.

4. Solving Puzzles : Exploration Problem Solving Activities

Solving puzzles is a fun way to develop the critical thinking skills of students. It requires them to think outside the box, look at things from different perspectives, and come up with unique solutions. This is an important skill set that will help students in their future careers, whether they choose a STEM or non-STEM field.

Puzzles can be used as part of a lesson on problem solving, or for review and assessment purposes. They can also be used as a warm-up activity before starting work in other subjects, such as math or science.

Here are some ideas for using puzzles in your classroom:

• Use puzzles as a way to introduce new topics or reinforce concepts that have already been taught in class. For example, if you’re teaching about patterns in math class, have your students work on a pattern puzzle before moving on to another lesson. Or if you’re working with fractions in science class, have them solve fraction puzzles before moving on to another topic.
• Solve puzzles as homework assignments or extra credit options at the end of each week’s lessons. This will enable students to practice what they’ve learned while being encouraged to use their critical thinking skills at home.

5. Brainstorming Sessions: Unleashing Creativity

Brainstorming sessions are vital for developing creative problem-solving skills. These sessions encourage students to think out of the box and come up with innovative solutions. Teachers can facilitate these sessions by posing a problem and allowing students to generate as many solutions as possible, without judgment. This free-flowing exchange of ideas fosters a collaborative and creative learning environment.

6. Role-Playing Scenarios: Real-World Problem-Solving Activities

Role-playing activities are an effective way to simulate real-world problems. By assuming different roles, students can explore various perspectives and develop empathy. For instance, a role-play on environmental issues can help students understand the complexities of ecological conservation and brainstorm sustainable solutions.

7. Technology Integration: Digital Problem-Solving Activities

Incorporating technology into problem-solving activities can greatly enhance the learning experience. Digital tools like coding games, simulation software, and interactive quizzes offer students a modern approach to problem-solving. These tools make abstract concepts tangible and accessible, thereby deepening students’ understanding and engagement.

8. Group Projects: Collaborative Problem-Solving Activities

Group projects are excellent for fostering teamwork and collective problem-solving. By working together, students learn to communicate effectively, delegate tasks, and respect different viewpoints. This collaborative approach not only enhances problem-solving skills but also prepares students for teamwork in their future careers.

Cultivating a growth mindset through problem-solving activities is a transformative approach in education. By engaging students in diverse and interactive problem-solving tasks, we equip them with the skills necessary to navigate the complexities of the modern world. These activities not only enhance academic performance but also prepare students for lifelong learning and success. As educators, our role is to guide and inspire our students to become confident, creative problem-solvers, ready to face the challenges of the future.

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Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Teaching problem solving

Strategies for teaching problem solving apply across disciplines and instructional contexts. First, introduce the problem and explain how people in your discipline generally make sense of the given information. Then, explain how to apply these approaches to solve the problem.

Introducing the problem

Explaining how people in your discipline understand and interpret these types of problems can help students develop the skills they need to understand the problem (and find a solution). After introducing how you would go about solving a problem, you could then ask students to:

• frame the problem in their own words
• define key terms and concepts
• determine statements that accurately represent the givens of a problem
• identify analogous problems
• determine what information is needed to solve the problem

Working on solutions

In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to:

• identify the general model or procedure they have in mind for solving the problem
• set sub-goals for solving the problem
• identify necessary operations and steps
• draw conclusions
• carry out necessary operations

You can help students tackle a problem effectively by asking them to:

• systematically explain each step and its rationale
• explain how they would approach solving the problem
• help you solve the problem by posing questions at key points in the process
• work together in small groups (3 to 5 students) to solve the problem and then have the solution presented to the rest of the class (either by you or by a student in the group)

In all cases, the more you get the students to articulate their own understandings of the problem and potential solutions, the more you can help them develop their expertise in approaching problems in your discipline.

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Resource library.

• Establishing Community Agreements and Classroom Norms
• Sample group work rubric
• Problem-Based Learning Clearinghouse of Activities, University of Delaware

Problem-Based Learning

Problem-based learning  (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem. This problem is what drives the motivation and the learning. 

Why Use Problem-Based Learning?

Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to:

• Working in teams.
• Managing projects and holding leadership roles.
• Oral and written communication.
• Self-awareness and evaluation of group processes.
• Working independently.
• Critical thinking and analysis.
• Explaining concepts.
• Self-directed learning.
• Applying course content to real-world examples.
• Researching and information literacy.
• Problem solving across disciplines.

Considerations for Using Problem-Based Learning

Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a whole semester. PBL is often group-oriented, so it is beneficial to set aside classroom time to prepare students to   work in groups  and to allow them to engage in their PBL project.

Students generally must:

• Examine and define the problem.
• Explore what they already know about underlying issues related to it.
• Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
• Evaluate possible ways to solve the problem.
• Solve the problem.
• Report on their findings.

Getting Started with Problem-Based Learning

• Articulate the learning outcomes of the project. What do you want students to know or be able to do as a result of participating in the assignment?
• Create the problem. Ideally, this will be a real-world situation that resembles something students may encounter in their future careers or lives. Cases are often the basis of PBL activities. Previously developed PBL activities can be found online through the University of Delaware’s PBL Clearinghouse of Activities .
• Establish ground rules at the beginning to prepare students to work effectively in groups.
• Introduce students to group processes and do some warm up exercises to allow them to practice assessing both their own work and that of their peers.
• Consider having students take on different roles or divide up the work up amongst themselves. Alternatively, the project might require students to assume various perspectives, such as those of government officials, local business owners, etc.
• Establish how you will evaluate and assess the assignment. Consider making the self and peer assessments a part of the assignment grade.

Nilson, L. B. (2010).  Teaching at its best: A research-based resource for college instructors  (2nd ed.).  San Francisco, CA: Jossey-Bass. 

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Speaking skills: Speaking matters

• 1 Speaking skills: Speaking matters
• 2 Speaking matters: Developing fluency
• 3 Speaking matters: Developing and dealing with accuracy
• 4 Speaking matters: Assessing speaking
• 5 Speaking matters: Personalization
• 6 Speaking matters: Problem-solving
• 7 Speaking matters: Role-play
• 8 Speaking matters: Pairwork

Speaking matters: Problem-solving

By Adrian Tennant

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This article looks at problem-solving activities and what they are like. It covers how to set them up, why it's good to use them, the disadvantages and what you should do after the activity.

Introduction

Students need a reason to speak in the classroom. Many speaking activities seem to have no aim other than to get students to talk to each other, but for what reason? By doing the activity what will they achieve? Some activities, like pairwork activities, try to create a purpose by creating an information gap - i.e. where one student has some of the information and another student the rest and, only by speaking to each other can they complete the task. However, this simple transference of information only replicates a small part of what speaking in real life is used for.

Role-plays are another favourite classroom activity designed to get students speaking, but these often focus on creating scenarios or situations where students practise functional language such as giving directions, asking for information, etc. Although this is realistic, it is still often on a level of one student having information that another student doesn't. In real life, we often speak about something when we both, or all, share a lot of the same information. This can take the form of a discussion or a debate where we have opinions, but it can also take the shape of a discussion based on having to solve a problem. In this article, we'll take a closer look at problem-solving speaking activities.

What are problem-solving activities like?

There are a number of types of problem solving activities. For the sake of simplicity I'll split them into three types:

1. The opinion problem-solving activity.

In this type of activity students are given information to discuss where there is not necessarily one right or wrong answer. This type of activity differs from a normal discussion in that there is a built-in problem within the information.

You and three friends rowed out to a small island in the middle of a lake. When you landed you forgot to tie the boat up properly and it has drifted away. Night is now approaching. It is 3km back to the shore, but one of your friends can't swim. You do not have any food with you and you don't know if anyone knows where you are. What do you do?

Students are then expected to discuss the problem and come up with a solution. To help students you can provide a set of ideas/options for them to choose from. You can also make the activity more complicated by giving each student a 'role card' with an extra piece of information on it (that might be a problem) i.e.

There is no wood on the island so you can't build a fire. At night the temperature drops to freezing .

2. The logical thinking problem-solving activity.

In this type of problem-solving activity there is usually one correct solution. To arrive at the solution the students need to discuss information they are given and logically work out what the solution is. There are two ways in which the information can be given, either split between a number of students so that they don't have the same information and they must share it, or where they all have the same information and simply have to discuss things together. In the later version a set of questions can often help students work out the answer. (See activity 2 in the 'Practical ideas' section below for a logical thinking activity).

3.The information gap problem-solving activity.

How does this differ from a normal information gap (i.e. a pairwork information gap where one student has information that the other student doesn't)? Well, the main difference is that in a normal information gap activity it is simply a matter of transferring the information, i.e. two students have a profile of a person. Student A knows the person's age and nationality, etc. Student B then asks 'How old is he?' and fills in the missing information they obtain in the correct space, etc. In a problem-solving information gap, getting the missing information is not the ultimate aim, but merely a stepping stone on the way to solving a problem.

Why use problem-solving activities?

Apart from the fact that these kinds of activities can be a lot of fun they are also very stimulating. They usually require students to communicate information to each other where the focus is on expressing ideas and opinions and not simply repeating phrases. In many ways, problem-solving activities replicate 'real' speaking in that people have a need to speak. Problem-solving activities can also be an effective way of practising language items that have been taught, i.e. both grammar and vocabulary. They are also a great way of developing students' cognitive abilities helping them to process language in a meaningful way.

Are there any disadvantages to problem-solving activities?

Yes, there are. One of the major problems is that stronger students often dominate the discussions, taking over and giving the less able students little opportunity to contribute. Often, this is due to the need for one person to organize and collate information and ideas. One way around this is to give certain students specific tasks, i.e. someone to 'chair' the discussion, someone to make sure everyone has a turn, etc.

Another disadvantage of this type of activity is that students may become frustrated when trying to solve the problem and, especially if they don't have the language skills in English, will switch to their L1. To avoid this it is important that you, the teacher, consider what language they are likely to need in order to complete the task and to pre-teach any necessary phrases, expressions or vocabulary you think they do not possess. Remember, using a problem-solving activity is not the main focus of your lesson/teaching but simply a way in providing students with a forum for using the language they have learnt.

How do you set up a problem-solving activity?

As with other speaking activities, how you set up the activity will often be the difference between a successful activity and one that doesn't work. The first thing to consider is whether the activity uses the language you want the students to practise. If not, then ask yourself why exactly you are using it. Then, it is important to look at the language that is needed and make sure that you pre-teach any new language before they start the activity. This will help the activity run smoothly with the focus being on solving the problem rather than working out the meaning of any new language. Finally, think about whether you want students to work alone to begin with and then discuss the problem with other students or whether you will start with pair or groupwork. Whenever you decide to use pair or groupwork think about who you get to work together so that there is a balance in each group.

What should I do after the activity?

Just as with roleplays, don't just move onto a different activity. If you move on immediately after the activity and don't at least discuss what happened, then students will often lose interest in problem-solving activities, or at least won't benefit to the full. There needs to be an obvious outcome and a rounding-up of the activity. Opening up the activity to a class discussion where you compare solutions is an obvious follow-up. It is also important that during the activity you note down any mistakes students made with the language and think about how you will tackle these either after the activity or in a subsequent lesson.

Some practical ideas

An opinion problem-solving activity

Here I am going to use the idea I mentioned earlier but give a few variations to show how it can be run in a number of different ways.

Variation 1

Put students in groups of 3-5 and give each group a copy (or copies) of the following handout:

Ask students to talk to each other and make a list of possible solutions. Ask them to also think about what problems they might face/encounter with each solution. i.e. If they stay on the island, where will they sleep and what will they eat? What if there is no food on the island? etc.

Variation 2

Give the students the same handout, but also give them the following options (either as part of the handout or written on the board).

• One of you swims to the shore to get help.
• Try and make a fire on the island to attract attention.
• Find somewhere to sleep for the night and then try and get off in the morning.
• Look for the boat and get one person to try and swim to it and bring it back.
• All swim back to the shore taking it in turns to help the person who can't swim.

Variation 3

Give the students the same handout, but also give each one a role card with extra information. i.e.

  A logical thinking problem-solving activity

A new teacher starts working at school. In her class there are a set of triplets, Ana, Bryan and Carl. Unfortunately, the teacher can't remember which one is which, but she has some notes about the three kids.

She knows that two of the triplets are boys and one is a girl.

Carl, one of the boys, is always calm and patient.

• One of the triplets likes playing football and he has a tattoo on his arm.

One of the triplets has red hair, one brown and one blonde.

• The triplet who doesn't get angry easily has short blonde hair.

The triplet with red hair has an earring and she likes to sing.

The triplet who has a tattoo gets angry easily.

Can she work out who is who?

Students should be able to work out the answer simply with the information provided, but, if you want to help them you could also give them a set of questions to answer. e.g.

• Should the teacher have known which triplet was Ana? Why?
• Which triplet likes to sing? How do you know?
• What colour is Ana's hair?
• What else do you know about Ana?
• What kind of person is Carl?
• Does he have a tattoo?
• How do you know?
• What colour is Carl's hair?
• Does Carl like football?
• Which triplet likes football?

These questions guide students through step-by-step, enabling them to work out the answer.

An information gap problem-solving activity

A simple example of this would be to use the same worksheet as above but cut the information about the triplets into strips, put students in small groups and give each student one or two strips. Tell students they have the information between them but that they must not show their information to the other students in their group.

A new teacher starts working at school. In her class there are a set of triplets, Ana, Bryan and Carl. Unfortunately, the teacher can’t remember which one is which, but she has some notes about the three kids. Can she work out who is who?

One of the triplets likes playing football and he has a tattoo on his arm

The triplet who doesn’t get angry easily has short blonde hair.

• British English

Speaking matters: Developing fluency

Speaking matters: developing and dealing with accuracy, speaking matters: assessing speaking, speaking matters: personalization, speaking matters: role-play.

Speaking matters: Pairwork

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

The Harriet W. Sheridan Center for Teaching and Learning

Teaching problem solving.

• Teaching Resources
• Course Design

The other day, a physicist friend was working in the lab with her summer research students. They were talking about the work they’d been doing that summer and how there was no manual or instructions of any sort for any of it; no textbook, no lab procedure. It was as if they were making it up as they went along. Laughing about this, one of the students said, ‘You know what we need? We need an entire course with nothing but problems. Just give us one problem after another, and we figure out how to do them. Because that’s what real research is.’ The rest of the students laughed. And then all of them nodded.

Employers, college presidents, faculty, and students demonstrate remarkable consensus that problem solving is one of the most important outcomes of a college education (Bok, 2017; Hart Research Associates, 2015; Hora, Benbow, Oleson, 2016; Passow & Passow, 2017). At the time of this newsletter, there were 28 courses offered this year that included the words “problem*” and “solving” in Courses@Brown. Course descriptions ranged from focusing on how to apply techniques or skills, to solving problems, to tackling common problems encountered in the field, and concepts that included “problems” within their title. There are undoubtedly more courses that implicitly and explicitly focus on problem solving across campus. In light of this emphasis, it is important to ask, “What is a problem and what is problem solving?” and “How do I foster problem-solving skills in my course?” and eventually, "How will I be explicit about problem solving in my course and course description?" Although problem solving is often associated with STEM courses, this newsletter offers perspectives and teaching approaches from across the disciplines.

What is a “problem” and problem solving?

Problems and problem solving may be context and discipline specific, but the concept and process have overarching components and similarities across contexts. Jonassen (2000, p. 65) defines a problem as an “unknown entity in some situation (the difference between a goal state and a current state)” such that “finding or solving for the unknown must have some social, cultural, or intellectual value.”  Within courses, students may encounter a wide variety of current (e.g., a problem statement) and goal (e.g., a solution) states with different motivations for solving them. Students will be exposed to “well-structured” problems at one end of the spectrum, which have a typical solution path and solution, and “ill-structured” problems, which are highly context dependent and have no one solution path (Jonassen, 2000).

We bring in common case scenarios for students and try to develop the frameworks they need to approach a problem rather than just finding the answer. To help students think about the process, we scaffold scenarios over the years through self-study modules that students can complete on their own. The scenarios stay the same, but students can come back to them with new information and frameworks they have learned, a deeper toolbox to pull from in different clinical settings. This allows students to be lifelong learners and more flexible and adaptable in the future.

Problem solving is a “goal-oriented” process that includes creating and manipulating problems as mental models (Jonassen, 2000). Brown faculty from a variety of disciplines were interviewed by Sheridan staff and asked, “What skills do students need to problem solve effectively?” They responded that students need to be able to do the following:

• Reason, observe, and recognize patterns
• Use current information to understand the past
• Know how to break complex problems down into smaller, more manageable components
• Make connections between concepts and disciplines
• Creatively think of multiple solution paths

These skills, among others, target the following problem-solving steps (Pretz, Naples, & Sternbergy, 2003):

• Recognize or identify a problem
• Define and represent the problem mentally
• Develop a solution strategy
• Organize your knowledge about the problem
• Allocate mental and physical resources for solving the problem
• Monitor your progress toward the goal
• Evaluate the solution for accuracy

Problem solving is an iterative process, and as such, these steps do not necessarily progress in a linear fashion. When creating homework assignments, projects, exams, etc., it is helpful to identify the specific skills you want students to practice, the strategies they should use, and how you will evaluate the solutions they produce.

How do I foster problem-solving skills in my course?

Instructors can signpost the problem-solving skills students should develop in their courses by adapting existing problem sets to fit recommendations from the  Transparency in Learning and Teaching Project  (TILT). The process of increasing transparency in assignments includes communicating the assignment’s purpose, task, and criteria to students (Winkelmes et al., 2016):

• The purpose usually links to one learning objective for the course, the skills students will develop as a result of completing the assignment, or a real-world application that students might experience outside of your classroom. In this way, the problem you have presented to the student becomes relevant because it has “some social, cultural, or intellectual value” (Jonassen, 2000, p. 65).
• Next, the task states the strategy or strategies students should take to complete the assignment. This includes guiding students through organizing the information available to develop a strategy.
• Finally, the criteria could be a rubric or annotated examples that are given to students  before  the assignment is due, so they are aware of the standards for the assignment.

In one study, researchers found that in courses where at least two assignments had features of transparent assignments, students self reported increases in their academic confidence, sense of belonging, and mastery of skills, such as problem solving (Winkelmes et al., 2016). Below are examples of different skills needed for problem solving with suggestions on how you can foster these skills through adapted or new assignments and in-class exercises.

A key skill for problem solving is knowing how to define and represent the problem and its solutions. This is true for all students, regardless of discipline. For example, Berkenkotter (1982, p. 33) states, “A writer is a problem solver of a particular kind. Writers’ ‘solutions’ will be determined by how they frame their problems, the goals they set for themselves, and the means or plans they adopt for achieving those goals.” To help students understand and connect to research in their field, instructors can assign short articles and guide students through rhetorical practices to make expert thinking more explicit. Provide students multiple opportunities to refine their writing allows them to learn “how to frame their problems.”

The distant past can seem uncomfortably strange to modern observers. As we discuss our class readings, one thing I like to do with my students is to explore what seems weird or even offensive to them about our texts and the societies that produced them. Thinking about the disconnect between ancient and modern attitudes, outlooks, beliefs, and values can be an incredibly productive way to think about cultural difference over space and time. - Professor Jonathan Conant, History and Classics

Critical thinking is the “ability to assess your assumptions, beliefs, and actions” (Merriam & Bierema, 2014, p. 222) with the intent to change your actions in the future and is necessary when solving problems. It is a skill required during all steps of the problem-solving process. Fostering critical thinking in your students is one way to create a more inclusive classroom because you are inherently asking students to challenge their assumptions and biases.

Instructors can use the following conditions to promote critical thinking in your classroom (Merriam & Bierema, 2014):

• Foster critical reflection by examining assumptions (see  Promoting Metacognition  for specific reflective strategies), e.g., ask students to read a research article and identify possible assumptions that are made in the questions asked, methods used, or the interpretation of the results. For example, to foster critical reflection you could ask students to identify the sources of knowledge they value and use when completing homework and write a reflection on what assumptions they made about those sources. What are the identities of the people creating those sources of knowledge? What systems or people are gatekeepers of that knowledge?
• Build a learning community where the expectation is that students can be wholly present, honest, ask questions, and productively fail (Kapur, 2016).
• Practice dialogical conversation by teaching an awareness of power relations in the classroom such as microaggressions or micro-affirmations and how to use active listening (see  Microaggressions and Micro-aggressions  for examples and specific practices).
• Provide students the opportunity to make connections between content and their experiences, e.g., by asking students on homework assignments how they apply concepts to a recent experience or asking students why they took your course and how it relates to their career goals.

Instructors can develop aspects of problem solving by being intentional about team building, connecting students to alternative perspectives, and being explicit about the expectations of teamwork in the field (e.g., as a researcher, industry partner, consultant, etc.). You can create homework assignments using the  TILT framework , which asks students to evaluate both their own and peers’ interactions in teams. There are several models or rubrics for how to assess teamwork, such as the  AAC&U Teamwork Value Rubric , which focuses on students’ behaviors or the  Comprehensive Assessment of Team Member Effectiveness (CATME) , which is a free packaged tool that gathers information from students and groups them into teams.

We use team-based learning exercises and collaborative problem solving. Students are assigned pre-reading to expand their knowledge so they are able to think through different aspects of a scenario before they come to class. In class, the discussion focuses on a team deciding and agreeing on what the next steps in a case will be. The problem-solving skills that this team discussion focuses on are interpersonal communication, being an active listener, and a collaborative team member. It is not high stakes, but together the team will succeed or fail. - Sarita Warrier, Assistant Dean for Medical Education, Alpert Medical School

A  jigsaw  is another collaborative approach to teach students how to break up a problem into smaller components. For example, in a class on Romanticism and Romantic philosophies, three groups of students would each be given the following questions about five poems: “How does the writer view nature?” (Group 1), “How does the writer view society?” (Group 2), “How does the writer view the purpose of poetry?” (Group 3). After discussion, three new groups, with representatives from each of these three clusters, might discuss a broader question, such as, “Using the information gathered in the first groups [...] what are Romanticism’s goals? What’s the agenda of the Romantic poets?” (Handstedt, 2018, pp. 121-122).

Expert researchers, practitioners, and educators incorporate reflection and iteration as part of their practice. Key steps of the problem-solving process include being reflective about the process and what is working or not working towards a goal. In a previous newsletter,  Promoting Metacognition , the Sheridan Center provided a list of several activities and assignments you could use to help students be reflective in your course. These activities range from short  minute papers , to semester-long reflective journals. Think-alouds, or having a student verbally solve a problem with another student, can also help students develop reflective problem-solving skills because it “provides a structure for students to observe both their own and another’s process of learning” (Barkley, 2010, p. 259).

For more strategies on how to engage students in these skills and topics, please see the Sheridan Center’s newsletter,  Inclusive Teaching Through Active Learning . It is important to be explicit in how you approach problem solving and convey that information both through your course description, syllabi, and content.

Opportunities at Sheridan for Development of Problem Solving

Problem solving is a necessary skill in all disciplines and one that the Sheridan Center is focusing on as part of the  Brown Learning Collaborative , which provides students the opportunity to achieve new levels of excellence in six key skills traditionally honed in a liberal arts education ­– critical reading, writing, research, data analysis, oral communication, and problem solving. To help you think through how to integrate opportunities for students to problem solve effectively in your course, the Sheridan Center offers problem solving professional development opportunities for faculty and students in an effort to engage intergenerational, faculty-student teaching teams.

Problem-Solving Course Design Institute

Problem-solving fellows program.

Berkenkotter, C. (1982). Writing and problem solving. In T. Fulwiler & A. Young (Eds.),  Language connections: Writing and reading across the curriculum  (pp. 33-44). Urbana, Illinois: National Council of Teachers of English.

Barkley, E.F. (2010).  Student engagement techniques: A handbook for college faculty . San Francisco, CA: Jossey-Bass.

Bok, D. (2017).  The struggle to reform our colleges.  Princeton, NJ: Princeton University Press.

Hanstedt, P. (2018).  Creating wicked students: Designing courses for a complex world . Sterling, VA: Stylus.

Hart Research Associates. (2015).  Falling short? College learning and career success . Survey carried out for AAC&U. Available: https://www.aacu.org/sites/default/files/files/LEAP/2015employerstudents…

Hora, M.T., Benbow, R. J., & Oleson, A. K.. (2016).  Beyond the skills gap: Preparing college students for life and work . Cambridge, MA: Harvard University Press.

Jonassen, D. H. (2000). Toward a design theory of problem solving.  Educational technology research and development , 48(4), 63-85.

Kapur, M. (2016). Examining productive failure, productive success, unproductive failure, and unproductive success in learning.  Educational Psychologist , 51(2), 289-299.

Merriam, S. B., & Bierema, L. L. (2014).  Adult learning: Linking theory and practice . John Wiley & Sons.

Passow, H.J., & Passow, C.H. (2017). What competencies should undergraduate engineering programs emphasize? A systematic review.  Journal of Engineering Education , 106(3): 475-526.

Pretz, J.E., Naples, A. J., & Sternbergy, R. J. (2003). Recognizing, defining, and representing problems. In J. E. Davidson & R. J. Sternberg (Eds.),  The psychology of problem solving  (pp. 3-30). New York: Cambridge University Press.​

Winkelmes, M.A., Bernacki, M., Butler, J., Zochowski, M., Golanics, J., & Weavil, K. H. (2016). A teaching intervention that increases underserved college students’ success.  Peer Review , 18(1/2), 31–36.

• Education & Teaching
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Teaching and Learning the English Language: A Problem-Solving Approach

Teaching and Learning the English Language is a practical guide for anyone seeking to improve their teaching, whether through formal study or on their own. Richard Badger explores teaching English as a problem-solving activity in which teachers must address three fundamental questions: · what aspect of language do students need to learn; · how might they learn this particular aspect of language; · and how can teachers support their learning. Offering a solid, research-based approach along with sound practical advice, this book equips teachers with skills needed to analyse their own contexts and develop their practice. It covers: · Fundamentals of English language · Psychological and social learning processes · TESOL teaching methods and approaches · Lesson planning and classroom management · Language evaluation and assessment · Teaching pronunciation, spelling, grammar, vocabulary and discourse · Teaching listening, reading, writing and speaking · English teacher professional development Pedagogical features include chapter summaries, activities for students and key readings recommendations, and the book is also supported by online resources: video case studies, additional exercises and multiple choice quizzes. Including numerous international lesson examples and case studies, Teaching and Learning English Language is suitable for both trainee and practising teachers who speak English as a first, second or foreign language.

• ISBN-10 1474290434
• ISBN-13 978-1474290432
• Publisher Bloomsbury Academic
• Publication date April 5, 2018
• Language English
• Dimensions 8 x 0.69 x 10 inches
• Print length 304 pages
• See all details

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About the author, product details.

• Publisher ‏ : ‎ Bloomsbury Academic (April 5, 2018)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 304 pages
• ISBN-10 ‏ : ‎ 1474290434
• ISBN-13 ‏ : ‎ 978-1474290432
• Item Weight ‏ : ‎ 1.84 pounds
• Dimensions ‏ : ‎ 8 x 0.69 x 10 inches

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Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

   develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.  

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

    Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

  Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

    Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a  decline in nontraditional testing methods .

But   many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning. 

Performance-based assessments  measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work?  Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations. 

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

• College and Career Readiness Assessment (CCRA+) for secondary education and
• Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

• Measuring students’ problem-solving skills through a performance-based assessment    
• Using the problem-solving assessment data to inform instruction and tailor interventions
• Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
• Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

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Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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There’s no single way to teach English and, in fact, there have been many popular approaches over the years. These are a few of the top ESL teaching methods, including communicative language teaching (CLT) and total physical response (TPR), used in the classroom today. Learn more about these and other methods and how you can apply them to a real-life classroom in Bridge’s Professional Certificate courses .

Whether you’re new to the different teaching methods or you need a refresher, download this guide to popular ESL methodologies to brush up on the definition and applications of the latest approaches developed by industry experts.

Why learn ESL teaching methods?

There are many reasons why learning a few basic ESL teaching methods is a must for ESL teachers. Here are some ways that learning the most popular methods of teaching ESL can help you as an English teacher:

• Demonstrating knowledge of these ESL teaching methods and strategies makes you more marketable.
• Using TEFL/TESOL buzzwords during an interview can improve your chances of getting hired.
• Using a variety of methods in the ESL classroom makes you a more effective and engaging teacher.
• Understanding pedagogy helps you design better ESL materials and lessons.
• Learning methodology can help you strategically use learning objectives that will benefit your students.

If you’re new to teaching, you’ll want to get initial training and qualification with a TEFL certificate . You can explore our online TEFL courses to get started!

What are some popular ESL teaching methods?

Method #1: direct method.

For the direct method, all teaching is done in the target language. Translations are not allowed in class, and the focus lies heavily on speaking instead of grammar. As a result, the direct method is a very student-centered strategy that has gained popularity in recent years.

Students are supposed to learn the target language naturally and instinctively, which is why the direct method is also called the “natural approach.” Mistakes are corrected as they happen in class, and teachers reinforce the correct usage of the language with praise. This method is frequently used when teaching English online . Many virtual ESL companies require teachers to only speak English during class to encourage an immersive experience.

Get more ideas for correcting students’ mistakes by taking Bridge’s 20-hour Micro-credential course: Error Correction in the EFL Classroom .

Begin your ELT journey or take the next step in your career with

Accredited online tefl/tesol certification, method #2: communicative language teaching (clt).

Communicative language teaching is perhaps the most popular approach among the methods of teaching ESL today. CLT emphasizes the student’s ability to communicate in real-life contexts. As a result, students learn to make requests, accept offers, explain things, and express their feelings and preferences.

Additionally, since CLT focuses on teaching language through real-world assignments and problem-solving, it’s less concerned with grammar accuracy and instead focuses on fluency.

Promote communication and fluency in your classroom with these ESL speaking activities.

Method #3: Task-/project-/inquiry-based learning

This teaching strategy for ESL students can sometimes be considered a part of CLT, but it heavily emphasizes the students’ independence and individuality. Inquiry-based learning is a modern approach that is becoming widely popular in schools all over the world. By asking questions and solving problems, with the teacher as a mere learning facilitator, student motivation and participation in tasks and projects are thought to increase.

Find out more about task-based learning.

Method #4: Total physical response (TPR)

Next is the Total Physical Response (TPR) method. You may have heard of this teaching strategy for ESL before, but what exactly is TPR ? Total Physical Response has become a very popular approach in which students react to the teacher with movement. Some examples include miming, gesturing, or acting out the language.

For example, the teacher and students might make an exaggerated frown and pretend to cry when learning the word “sad.” TPR suggests that students learn the target language best through physical response rather than by analysis.

Additionally, TPR is often used when teaching English online and when teaching young learners, as it not only helps students remember vocabulary but also provides an outlet for their energy and helps them stay focused when sitting for long periods.

If you like TPR, you might also like using drama as an ESL teaching method.

Learn about 8 ESL methodologies and get sample activities with the free guide to

Teaching english learners: popular esl learning methodologies, method #5: an eclectic approach.

Many teachers choose from the collection of humanistic approaches (TPR, for example) and communicative approaches (the direct method and CLT). Often, they incorporate bits and pieces of many other teaching strategies for ESL learners and use what works best for their individual students. Generally speaking, there is no one-size-fits-all methodology. Each group of learners will have varying learning styles and preferences. For that reason, conducting a needs assessment is a great starting place for teachers who aren’t sure which methodology, or methodologies, to apply.

For example, a teacher who uses mostly the direct method may occasionally do a lot of grammar explanation when preparing students for English proficiency exams , such as teaching Pearson Test of English (PTE) test prep , or a CLT advocate may borrow some aspects of the direct method or use TPR.

• Pro Tip: Another great way to combine or develop teaching methods is to frequently reflect on your teaching style by using a journal where you write down comments, note adjustments, and brainstorm how you can change certain methods or procedures if necessary.

The list of ESL teaching styles doesn’t have to end here! You can find your own favorite TEFL/TESOL method from among those listed above, combine several strategies for teaching your ESL students, or develop your own ESL teaching methods and techniques. For a full breakdown of the different methodologies and how to evaluate your students’ needs, download Bridge’s ESL Methodologies Guide .

Delve deeper into these and other ESL teaching methods and techniques with Bridge Professional TEFL/TESOL Certificate courses.

After backpacking Australia on a Working Holiday visa, Bridge graduate Johanna traveled to Japan for a year to teach English. She then moved to New Zealand for another two years before returning to her chosen home country, Japan, where she currently lives. Now, with more than eight years of professional English teaching experience, Johanna enjoys her expat life in Japan teaching teenagers at a private junior and senior high school, where she recently received tenure after only two years. When she’s not teaching, Johanna continues to travel regionally and explore new places.

The Lesson Study Group

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Teaching Through Problem-solving

• TTP in Action

What is Teaching Through Problem-Solving?

In Teaching Through Problem-solving (TTP), students learn new mathematics by solving problems. Students grapple with a novel problem, present and discuss solution strategies, and together build the next concept or procedure in the mathematics curriculum.

Teaching Through Problem-solving is widespread in Japan, where students solve problems before a solution method or procedure is taught. In contrast, U.S. students spend most of their time doing exercises– completing problems for which a solution method has already been taught.

Why Teaching Through Problem-Solving?

As students build their mathematical knowledge, they also:

• Learn to reason mathematically, using prior knowledge to build new ideas
• See the power of their explanations and carefully written work to spark insights for themselves and their classmates
• Expect mathematics to make sense
• Enjoy solving unfamiliar problems
• Experience mathematical discoveries that naturally deepen their perseverance

Phases of a TTP Lesson

Teaching Through Problem-solving flows through four phases as students 1. Grasp the problem, 2. Try to solve the problem independently, 3. Present and discuss their work (selected strategies), and 4. Summarize and reflect.

Click on the arrows below to find out what students and teachers do during each phase and to see video examples.

• 1. Grasp the Problem
• 2. Try to Solve
• 3. Present & Discuss
• 4. Summarize & Reflect
• New Learning

WHAT STUDENTS DO

• Understand the problem and develop interest in solving it.
• Consider what they know that might help them solve the problem.

WHAT TEACHERS DO

• Show several student journal reflections from the prior lesson.
• Pose a problem that students do not yet know how to solve.
• Interest students in the problem and in thinking about their own related knowledge.
• Independently try to solve the problem.
• Do not simply following the teacher’s solution example.
• Allow classmates to provide input after some independent thinking time.
• Circulate, using seating chart to note each student’s solution approach.
• Identify work to be presented and discussed at board.
• Ask individual questions to spark more thinking if some students finish quickly or don’t get started.
• Present and explain solution ideas at the board, are questioned by classmates and teacher. (2-3 students per lesson)
• Actively make sense of the presented work and draw out key mathematical points. (All students)
• Strategically select and sequence student presentations of work at the board, to build the new mathematics. (Incorrect approaches may be included.)
• Monitor student discussion: Are all students noticing the important mathematical ideas?
• Add teacher moves (questions, turn-and-talk, votes) as needed to build important mathematics.
• Consider what they learned and share their thoughts with class, to help formulate class summary of learning. Copy summary into journal.
• Write journal reflection on their own learning from the lesson.
• Write on the board a brief summary of what the class learned during the lesson, using student ideas and words where possible.
• Ask students to write in their journals about what they learned during the lesson.

How Do Teachers Support Problem-solving?

Although students do much of the talking and questioning in a TTP lesson, teachers play a crucial role. The widely-known 5 Practices for Orchestrating Mathematical Discussions were based in part on TTP . Teachers study the curriculum, anticipate student thinking, and select and sequence the student presentations that allow the class to build the new mathematics. Classroom routines for presentation and discussion of student work, board organization, and reflective mathematics journals work together to allow students to do the mathematical heavy lifting. To learn more about journals, board work, and discussion in TTP, as well as see other TTP resources and examples of TTP in action, click on the respective tabs near the top of this page.

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HCF and LCM - Problem Solving Full lesson including Stretch and Challenge and GCSE Questions

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

28 August 2024

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Lesson is designed to guide students through the concepts of Highest Common Factor (HCF) and Least Common Multiple (LCM) with a focus on problem-solving techniques. The lesson includes a step-by-step explanation of finding HCF and LCM, practical examples, and a variety of problem-solving questions, including GCSE-style questions for exam preparation… A worksheet accompanying the lesson provides additional practice with Stretch and Challenge questions, allowing students to apply what they’ve learned in a structured and rigorous way.

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