This article researches the causes which lead students to lose enthusiasm for reasoning and thinking. Both of these aspects are basic in the mathematics subject. It is difficult to admit that after 12 years of study the enthusiasm decreases in general. This is why we have chosen 102 high-school students from the last mathematics course (18 years old). The students selected are studying arts (62) and sciences (40) in order to obtain results close to the real society. They have answered three questionnaires (two multiple choice and one open) with 40 questions. The information given by the answers has been dealt from 11 indicators which clarify the reasons for losing the enthusiasm for reasoning. All of these indicators have been classified into three growing categories arranged according to an abstraction criterion: knowledge about differences between an exercise and a problem, usefulness and meaning of mathematics, and feelings caused by difficulties and contradictions coming from reasoning. We have observed that students know the differences and the usefulness of exercises and problems. They know that problems are a tool to exercise the thinking and reasoning of mathematics. But they cannot see extra-academic benefits. In addition to this fact, problem solving causes anxiety, loss of self-confidence and loss of concentration. Moreover, reasoning and thinking are not exciting to them. The mathematics program is not pleasant for them and it is one of the most frightening for them. From the results we would conclude that if we could spend more time in solving problems in groups in an environment which rewards the intervention and does not punish it, we could increase their self-confidence, improve their concentration and raise their implication. So, their reasoning and thinking enthusiasm would increase.
|Keywords:||Problem Solving, Exercises, Motivation, Reasoning, Loss of Concentration, Thinking|
Professor, Department of Mathematics Education, University of Barcelona, Barcelona, Spain, Spain