What is Problem Solving?
"It isn't that they can't see the solution. It is that they can't see the problem." -- G.K. Chesterton
Many teachers recognize problem solving as one of the five process standards prescribed by NCTM as components of successful mathematics teaching. There is so much more to know, however. Problem solving can be a powerful part of classroom instruction, a useful vehicle for engaging students in mathematical thought, a lively way to keep teachers participating as learners in the classroom along with students. Utilizing problem solving appropriately and effectively takes time, effort, and thought. This resource page is meant to help with some of that effort by collecting some favorite teacher resources into a single location.
Participants in the Middle School Mathematics Focus Group (made up of Appalachian State University faculty members and school representatives from the Public School Partnership) collected, discussed, and/or shared these materials during meetings in the 2005-2006 academic year. The members expect the discussions to be ongoing as more ideas related to problem solving emerge and more questions are raised.
Why should I use problem solving in my classroom?
Problem solving is a useful instructional tool that motivates purpose and context for mathematics skills. Problem solving also offers opportunities for students to engage in meaningful mathematical discourse, including analyzing various representations of and justifications for their solutions. For more reading of problem solving, try the folowing:
What the NCTM standards say about Problem Solving
Research on Problem Solving
Summary of Polya's How to Solve It
What more do I need to know?
As a teacher, there are a number of considerations for the use of problem solving in the classroom. These will determine the kinds of problems you use. For instance:
Are you using the problem to launch an idea? To support an idea? To practice an idea? To practice problem solving strategies in general?
Is your purpose the mathematics at hand? A mathematical topic not yet presented? Or the process of problem solving itself?
At what level are your students? Does the problem you are considering offer entry points for all students?
How will you evaluate your students' knowledge during and after the problem solving exercise?
It is hoped that the focus group will continue to look at these questions and to collect resources to answer these questions. More information will be posted here as the questions emerge or are answered.
"No problem can stand the assault of sustained thinking" -- Voltaire