Mathematical Problem Solving: Rationale and Approach for Change

Date of Completion


Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Delores B. Gallo


Problem solving is essential to life today. The traditional high school has been creating mathematics students who do well at computation, but seem to lack the understanding and problem-solving skills that allow for connections to the real world. I believe the development of a mathematical problem-solving course, designed for high school juniors and seniors who have an algebra background, will help to bridge this gap. The public has put forth a cry to integrate problem solving into the mathematics curriculum. In 1989 the National Council Of Teachers of Mathematics developed their "Standards and Evaluation" for mathematics education. ‘Mathematics as problem-solving ‘ was now on the forefront of reform. Problem solving must embrace both critical and creative thinking in order to obtain the desired results. Strategies and skills from both areas may be taught and modeled. A climate that is conducive to problem solving must also be developed. The teacher must not address the physical layout of the classroom. But the atmosphere as well: it must be one where risk-taking can be accomplished in a non-threatening manner. The skills and strategies that may enhance critical thinking include working a problem backwards, developing special cases and identifying sub-problems. The skills that promote creative thinking are described in Parnes’ creative problem-solving model. Parnes’ model includes fact finding, idea finding, solution finding and acceptance finding. Lesson plans have been developed that will address problem-solving objectives, creative thinking objectives, critical thinking objectives as well as mathematical objectives. The different strategies developed will embrace problem solving, critical and creative thinking, as well as mathematical skills. These lessons are to be used as a guide for the development and extension of a mathematical problem-solving course. Through the development of a course in mathematical problem solving, I believe that the students of today will become the problem-solvers of tomorrow. Such a course will not only create a generation of people who are better equipped to deal with problems, but also will begin a ripple effect for generations, as each generation passes problem-solving skills on to the next.


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