Paper presented (Dr A Dendane) at the 10th Annual Research Conference - UAE University - 13th -16th April, 2009
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 the fact that many skills are needed for a learner to be an effective problem solver. Also, these factors and skills make the teaching of problem solving one of the most complex topic to teach. This paper will discuss 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.
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 . 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 the computer technology, it has helped in making social, economical and technological advances that few decades ago would have been unthinkable.
Learning mathematical facts and contents 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 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 . If well facilitated, mathematical problem solving may help students
develop and improve the generic ability to solve real life problems, 
develop critical thinking skills and reasoning, 
gain deep understanding of concepts, [8 ]
work in groups, interact with and help each other.
Most of the mathematics textbooks suggest few types of problems as examples with detailed solutions and then suggest similar problems as exercises. Studentsí learning is limited if only routine problems are solved. The problems used to create genuine learning opportunities should be of the challenging type and 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 therefore makes it challenging both to learn and to teach. If the instructorís 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 am addressing issues and concerns related to mathematical problem solving. However, much of what is said in this paper may be applied to any problem solving of the quantitative type such as those encountered in physics, chemistry, Business and Engineering. Our students, at the UAE University, have difficulties in 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 studentsí 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.