Everyday in our lives we are faced with problems which can be big or small. Problem that we will discuss here is problem in Mathematics. Our focus is on teaching mathematical topics through problem-solving contexts and enquiry-oriented environments which are characterised by the teacher ‘helping students construct a deep understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring, testing, and verifying’ (Lester et al., 1994, p.154).
It cannot be denied that we always find problem in Mathematics and we should understand it then solve it. The next question is what characteristics of a good reasoners and problem solvers.
Good reasoners and problem solvers show similar traits. There are certain common characteristics exhibited by those who perform well on such task. For instance, having desire to solve problems. They are interested to any kind of problems and feel that they get challenges. They enjoy persuing the solution to a logical conclusion. Their thoughts go beyond the obvious to the “why” of the answer.
Good reasoners and problem solvers are extremely persevering when solving problems. They refuse to quit. Then, they are not easily discouraged. They go back and try new approaches again and again. They are reluctant to give up on a problem.
These people are not afraid to speculate, to conjecture, or to guess. They are risk-takers, not afraid of being wrong or unsuccessful when they face the problem. They will show an ability to skip some of the steps in the solution process. They make connection quickly, notice irrelevant detail, and often require only a few examples to generalize. They are the students who hold conversation with themselves. They know what type of question to ask themselves to help solving the problem,
To sum up, good reasoners and problem solvers are people who can focus on the task at hand. They know the direction they have to satisfy the requirements of the faced condition.
Krulik, Stephen. Rudnick, Jesse A. 1993. Reasoning and Problem Solving: A Handbook for Elementary School Teacher. A Division of Simon & Schuster Inc.