The What Works Clearinghouse produces reports showing evidence of effectiveness in education research.

According to The What Works Clearinghouse report on improving problem solving in grades 4-8, the following practices are recommended:

1. Prepare problems and use them in whole-class instruction.

2. Assist students in monitoring and reflecting on the problem-solving process.

3. Teach students how to use visual representations.

4. Expose students to multiple problem-solving strategies.

5. Help students recognize and articulate mathematical concepts and notation.

The recommendations that showed consistently strong evidence of improving student outcomes for a wide population of students were #2 and #3. Let’s take a closer look at these two:

2. Assist students in monitoring and reflecting on the problem-solving process.

This recommendation underscores the importance of thinking through or reflecting on the problem solving process. Prompt students to think through the answers to such questions as “What is the problem asking me to find?”, “Which information in the problem is relevant?”, “In what way is this problem similar to problems I have solved previously?”, “Is my approach working? If I am stuck, is there another way I can think about solving this problem?”, and “Does the solution make sense? How can I verify the solution?”  Model for students how to monitor and reflect while solving a problem by using the prompts – say aloud not only the response to each prompt, but also the reasons why each step was taken.  Make sure to use a prompt at each stage in the problem solving process, for example, when first reading the problem, when attempting a strategy to solve, and after solving to check the reasonableness of the solution. Use guided questioning to help students clarify and refine their own thinking .

3. Teach students how to use visual representations.

Six studies with middle school students consistently found that using visual representations improved achievement with both general education students and students with learning disabilities. Visual representations include tables, graphs, pictures, number lines, and bar diagrams.  Promote discussions by asking students guiding questions as they practice representing problems visually. Help students ensure that their representations capture the important actions and relationships and any other relevant details from the problem. Then show students how to convert the visually represented information into mathematical notation.