Teach Math Through Problem Solving
January 2, 2018
Society is increasingly technology and information based. Success in this evolving world requires that people that solve problems, think logically, and communicate effectively with others. Problem solving approaches to learning are more important than ever and nowhere is this more true than in math classrooms in schools. Math standards in education have changed to require the increased use of problem solving by students and instructional design is transitioning to lessons and student based activities that include more open-ended problems. Teaching in this new paradigm can be exciting and rewarding, but also challenging.
Research for This Tool
We found several resources related to teaching math through problem solving. One of the most useful is from the Ontario Ministry of Education. It provides research, examples, and resources that should help all teachers as they implement this approach:
Ontario Ministry of Education (Retrieved online December, 2015) A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6. Volume 2: Problem Solving and Communication.
This link will take you to the guide: http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_2.pdf
How to Use This Tool
The guide (pp. 4 & 5) mentioned above includes a discussion of the difference between teaching math problem solving as part of traditional math instruction and teaching math using problem solving as the main strategy. There are several positive experiences for students when they engage in problem solving, including:
- Learning mathematical concepts with understanding
- Reasoning mathematically by exploring mathematical ideas and justifying results
- Reflecting on and monitoring their own thinking
- Making connections among mathematical concepts
- Developing strategies that can be applied to new situations
- Representing mathematical ideas and modeling situations using concrete materials
- Formulating and test their own explanations and communicate and listening to others.
These experiences require a lot of advance planning by teachers who understand the purposes and nature of the problem solving process. For many teachers who have not emphasized problem solving as the main vehicle of teaching and learning, planning and practice will be needed to ensure student success. Here are some key teacher roles suggested in the Ontario guide (p. 26):
- Provide appropriate and challenging problems
- Support and extend student learning
- Encourage and accept students’ own problem solving strategies
- Question and prompt students
- Use think alouds to model how a problem is tackled
- Observe students and assess their work as they solve problems
- Anticipate conceptual stumbling blocks, notice students who encounter these blocks, and help them recognize and address their misconceptions.
Problem solving lessons like those described as examples in the Ontario guide have three key parts:
- Getting Started (Students and the teacher discuss the problem.)
- Working on It (Students select and implement strategies, including using manipulatives that are prepared and available; The teacher guides and monitors.)
- Reflecting and Connecting (Students explain how they solved the problem and listen as others explain; The teacher questions and guides.)
Problem solving strategies like those in the photo can be introduced to students throughout the problem solving process and students can use them as they learn which strategies will help them be more effective and efficient.
We have provided a tool, called Step by Step, that may help students as they begin to choose strategies that work for them. Regardless of the problem solving strategies students use, a key part of the process is the think aloud discussion following students’ work. To use Step by Step, students (either alone, with other students, or with teacher guidance), decide what information they have and need, what operation(s) to use, and whether their answer makes sense. This tool can be used as differentiated support for those students who may be struggling with a completely open ended process.