We all solve problems on a daily basis. Problem solving is not a skill that one is born with – it’s cultivated over time with practice and experience. Doing math helps us to develop the analytical and critical thinking skills required to be a good problem solver. In the last of our blog series of key learnings from the National Council of Teachers of Mathematics (NCTM) Conference in San Francisco, we explore strategies to help students improve their problem-solving skills.
We attended a session called “Productive Struggle: Difference Between Experienced and Inexperienced Problem Solvers,” moderated by Cindy Bryant, former Director of Missouri K-12 Mathematics, with over 30 years of teaching experience. During the session, we learned that experienced problem solvers have a plan, take risks, and are not afraid to ask questions. Even if they don’t know how to solve the problem, they have a plan of how they would tackle that particular problem. On the other hand, inexperienced problem solvers get stuck. They become overwhelmed by the problem, often don’t know how or where to begin, and have no plan of action. Cindy Bryant summed it up succinctly: “Inexperienced problem solvers don’t know what to do when they don’t know what to do. Experienced problem solvers know what to do when they don’t know what to do.”
How can you help students improve their problem solving skills? Below are tips shared by our Director of Marketing (who honed her problem-solving skills from her years working as a management consultant) as well as tips learned from the session at NCTM.
1. Define the problem. It sounds easy enough, but inexperienced problem solvers often don’t know what they are solving for or what question is being asked. Remind students to read the question carefully and make sure they understand the question.
2. Identify what information is given and what information is missing. This helps students to determine what they need to know in order to solve the problem.
3. Ask questions. Encourage your students to ask questions that will help them fill in the gaps. The focus is to get additional facts and/or be able to make reasonable assumptions that will help to solve the problem. Have students think through how the additional information will help to change initial assumptions or hypotheses.
4. Identify possible solutions. Encourage students to approach the solution in different ways and to talk through their thought process out loud. Often times, the students are able to answer their own question as they talk it out and teachers are able to understand their thought process and redirect as needed. Use props, draw pictures, write it out – use any and all strategies that will help students ideate.
5. Evaluate potential solutions and determine the answer. Encourage students to double check and ensure their solution actually answers the original question. Reality check the answer to make sure it makes sense in the context of the original question.
6. Practice, practice, practice! Having a structured approach to problem solving is important but not sufficient. Going through the process of solving problems will help build student confidence as well as competence. Practice solving different types of problems and choose problems that are engaging, relevant and interesting to your students. Here are some resources to help students practice
- NRich Project, University of Cambridge
- Using Low Threshold High Ceiling Tasks in Ordinary Classrooms, NRich Project
- You Cubed, Stanford University
- Illuminations, NCTM
- Visual Patterns
- Alex Bellos Monday Puzzle
- Brain Den
- Math is Fun
7. Celebrate the journey. Cindy Bryant stressed the need for teachers and students to remember that productive struggle is part of the learning process. Praise effort and encourage students to learn from mistakes so that students become experienced problem solvers, become more comfortable with uncertainty and know how to tackle new problems.
What strategies are you using in the classroom to encourage students to be better problem solvers? Share with us on Twitter, @Knowre.