Introduction

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Introduction

Over the past few years we have been bombarded by the media for the need to teach our children problem solving skills in order for America to retain its technological edge. Creative problem solving skills are needed in a technological society in order to generate innovative ideas. Furthermore, research has shown that a favorite subject among elementary students is mathematics, but at the middle school level mathematics is reduced to being the least favorite subject. It isn’t too difficult to determine why middle school students learn to loathe mathematics. The middle school curriculum is concerned with teaching students basic addition, subtraction, multiplication, and division. Consequently the students are tested more on their rote memorization skills and their ability, or lack of ability, to crunch numbers for hours on end. Very little in the line of creative problem solving is introduced to the student at the middle school level. It is therefore no wonder that these students suffer from math burnout.

Since I am a teacher of mathematics, I decided to write this report on problem solving in an effort to help my students retain their love of mathematics. It should be noted that most of the procedures explained in this paper will be incorporated in my teaching strategies and classroom experiences. I strove to draw upon information from the diverse fields of mathematics, biology, cognitive science, artificial intelligence, education, and business. Problem solving is used in all areas of endeavor and so its applicability in a variety of subjects should be investigated.
Looking at problem solving philosophically, it is likely that by teaching our children problem solving skills, or what some circles refer to as critical thinking skills, we will in essence be teaching our children to assume responsibility for their actions. Hence they will be better equipped to predict the consequences of their actions, and hopefully respond in a manner that is acceptable and/or productive to our society.

What you are about to read is an abbreviated version of a lengthier paper. The original paper contained considerably more information and exercises on the practical aspects of problem solving, but I have retained what I deem to be the most effective of the practical exercises. Chapter One defines problem solving, the structure of problems, and the steps and stages utilized in problem solving strategies. Chapter Two delves into human information processing systems, defines several of its different components, and discusses the processing of information. Chapter Three defines the problem space (where the actual problem solving process takes place), and goals (where we want to go). Chapter Four then discusses different techniques that are used in searching the problem space in an effort to attain a goal state. Since human problem solving takes place in the brain, Chapter Five deals with the biological components of problem solving. Highlighted in Chapter Six are the developmental factors instrumental in a child’s acquisition of problem solving skills. Chapter Seven next discusses the effects of attitudes on problem solving and provides methods for bringing about attitudinal change. Chapter Eight concentrates on Polya’s problem solving strategy. Closely allied with problem solving is the writing process, which is covered in Chapter Nine. Chapter Ten then defines creativity, discusses the various blocks to creativity, and proposes various methods for overcoming such blocks. And finally, Chapter Eleven highlights the importance of memory in the problem solving process and provides various memory tools.

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