Solving problems is a key component of many science, math, and engineering classes. If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems. Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.
How do I decide which problems to cover in section or class?
In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.
You have given your students a problem to solve in class. What are some strategies to work through it?
- Try to give your students a chance to grapple with the problems as much as possible. Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
- When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems. This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
- Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question). Ask students to start solving the problem, either independently or in small groups. As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion. After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
- It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
- If you have ample board space, have students work in small groups at the board while solving the problem. That way you can monitor their progress by standing back and watching what they put up on the board.
- If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.
When do you want students to work in groups to solve problems?
- Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
- Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
- Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others. This ensures that every student engages with the problem and is ready to contribute to a discussion.
What are some benefits of having students work in groups?
- Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
- In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
- Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.
What are some strategies for helping students to form groups?
- Instruct students to work with the person (or people) sitting next to them.
- Count off. (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
- Hand out playing cards; students need to find the person with the same number card. (There are many variants to this. For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
- Based on what you know about the students, assign groups in advance. List the groups on the board.
- Note: Always have students take the time to introduce themselves to each other in a new group.
What should you do while your students are working on problems?
- Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
- If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.
After students work on a problem during class, what are strategies to have them share their answers and their thinking?
- Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
- Use online polling software for students to respond to a multiple-choice question anonymously.
- If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
- Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
- Have students write an answer on a notecard that they turn in to you. If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.
If you had assigned different groups to work on different problems, you can:
- Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems. Students now are responsible for teaching the other students in their new group how to solve their problem.
- Have a representative from each group explain their problem to the class.
- Have a representative from each group draw or write the answer on the board.
What happens if a student gives a wrong answer?
- Ask for their reasoning so that you can understand where they went wrong.
- Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
- Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
- Do make sure that you clarify what the correct answer is before moving on.
- Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.
How can you make your classroom inclusive?
- The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
- See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity.
A few final notes…
- Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
- Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.