Skills Needed for Mathematical Problem Solving (Part 2)

2. Mathematical Problem Solving as a Process

Mathematical problem solving is a process depending on many phases. There are four main phases in mathematical problem solving [10]:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back

The Linear Model

In solving a problem similar or close to another problem solved in the past, we will usually follow a linear process, as shown in Figure 1. The term linear means that the learner moves from one phase to the next until the problem is solved.

The Practical (Iterative) Model

However, this linear process may not be enough when solving a genuine and challenging problem [11]. It is possible that we carry out the plan but it does not give the right answer, or it does not even work. We therefore need to look back critically at the formulation of the problem as well as the information given in the problem.

A more practical model of the process is shown in Figure 2. The learner needs to understand that, in solving a problem, he or she needs to look back and reexamine the whole problem during the process — and be ready to restart if necessary.

One of the difficulties in problem solving is the fact that several steps are needed to solve a given problem. At each step, students need to use several skills. There are also many factors and skills that determine the outcome of the process.