Skills Needed for Mathematical Problem Solving (Part 1)

Abstract

Mathematical problem solving is one of the most important topics to learn and also one of the most complex to teach. The main goal in teaching mathematical problem solving is that students develop a generic ability to solve real-life problems and apply mathematics in real-life situations. Problem solving can also be used, as a teaching method, for a deeper understanding of concepts.

Successful mathematical problem solving depends upon many factors and skills with different characteristics. In fact, one of the main difficulties in learning problem solving is that many skills are needed for a learner to be an effective problem solver. These factors and skills also make the teaching of problem solving one of the most complex topics to teach. This paper discusses the idea that problem solving is a process that needs to be understood by instructors so that they can develop better and more effective classroom activities and tasks. The necessary skills for problem solving as well as the methods and strategies to teach or facilitate them are discussed.

1. Introduction

Mathematical problem solving related to counting and daily transactions of commerce has been present from the earliest days of human experience. Geometry was also widely used in land measurement [1]. Mathematics is now used to quantify numerically and spatially natural as well as man-made situations. It is used to solve problems and, with the advent of computer technology, it has helped make social, economic, and technological advances that a few decades ago would have been unthinkable.

Learning mathematical facts and content is important but is not enough. Students should learn how to use these facts to develop their thinking skills and solve problems. Mathematics educators have accepted the idea that the development of problem solving ability deserves special attention [2] and that one of the most important components in any mathematics curriculum or program is genuine mathematical problem solving [3][4][5]. If well facilitated, mathematical problem solving may help students:

• Develop and improve the generic ability to solve real-life problems [6].
• Develop critical thinking skills and reasoning [7].
• Gain a deep understanding of concepts [8][9].
• Work in groups, interact with, and help each other.

Most mathematics textbooks suggest a few types of problems as examples with detailed solutions and then suggest similar problems as exercises. Students' learning is limited if only routine problems are solved. The problems used to create genuine learning opportunities should be of the challenging type, not only those similar to ones already solved in the past.

Mathematical problem solving is a process that involves a set of factors and tasks to achieve a defined goal. It depends on many skills and factors, which makes it challenging both to learn and to teach. If the instructor's understanding of the process is limited, difficulties in teaching mathematical problem solving will arise. Hence the great need to understand these factors and skills if we want to help our students acquire this important process.

In this paper, I address issues and concerns related to mathematical problem solving. However, much of what is said here may be applied to any problem solving of the quantitative type, such as those encountered in Physics, Chemistry, Business, and Engineering. Our students at UAE University have difficulties with mathematical problem solving and we need to be aware of it. I believe that we need to address this issue and discuss it if we want to improve the teaching of quantitative problem solving, which will greatly improve our students' thinking skills and problem-solving abilities in general. My purpose here is to present some of these issues in order to stimulate discussions. Suggestions on how to facilitate certain aspects of mathematical problem solving, as I apply them in my classes, are also presented.