Abstract:

The challenge for mathematics teachers in nowadays, at all levels, is to develop the process of mathematical thinking alongside the mathematical knowledge.
In this framework, helping students to develop skills on problem solving is an important requirement of teaching mathematics.
This paper is focused on the impact that problem solving has to the students mathematical development and on teaching techniques that enable teachers to develop that valuable skill at students.
Through problem solving, teachers develop students' confidence in their own ability to think mathematically; create opportunities for students to enrich their mathematical vocabulary and to use the mathematical language in a meaningful way; help students to interact with each other and with teacher; ask insightful questions and promote sharing of ideas between students; encourage students to learn how to make generalizations about rules and concepts.
Problem solving is a skill which enhance logical reasoning. While teaching mathematical problem solving to students, teachers should explain them that learning how to solve problems in mathematics is knowing what to look for.
Mathematical problems often require established procedures and knowing what and when to apply them. To identify procedures, it is necessary to be familiar with the problem situation and be able to collect the appropriate information, to identify a strategy or strategies and to use the strategy in the appropriate way.
Students should be aware that there are some steps they have to pass in the process of solving a problem:
- they have to read the problem carefully, to understand what facts are given, how they are related and what they need to find out;
- they need to discuss on the data and define a strategy to solve the problem;
- they have to use the strategy and to solve the problem;
- another important step for them is to look over their solution and to discuss if it seem probable, and if it answers to the question.
Based on the fact that creating mathematical skills on problem solving requires practice, teachers should engage students in the process instead of solving problems for them.
The best way teachers can make this happen is through arousing the curiosity of students. Curiosity can lead students to explore new ideas in mathematics. Teachers can realize this by:
- introducing mathematics through daily life activities, making classroom mathematics relevant in real-life;
- modifying their teaching techniques, creating a reasonable rate between written and oral tasks, guiding students in making questions, posing open-ended tasks, finding time for discussions and interpretation of solutions;
and
- creating at themselves the belief that problem solving should be developed as a valuable skill in itself, as a way of thinking, rather than just as a mean of finding the correct answer.

Keywords:

problem solving, mathematics, teaching techniques.