Modelling Activities In Kinematics Understanding quantitative relations with the contribution of qualitative reasoning

摘要

In Greek traditional teaching a lot of significant concepts are introduced with a sequence that does not provide the students with all the necessary information required to comprehend. We consider that understanding concepts and the relations among them is greatly facilitated by the use of modelling tools, taking into account that the modelling process forces students to change their vague, imprecise ideas into explicit causal relationships. It is not uncommon to find students who are able to solve problems by using complicated relations without getting a qualitative and in-depth grip on them. Researchers have already shown that students often have a formal mathematical and physical knowledge without a qualitative understanding of basic concepts and relations". The aim of this communication is to present some of the results of our investigation into modelling activities related to kinematical concepts. For this purpose, we have used ModellingSpace, an environment that was especially designed to allow students from eleven to seventeen years old to express their ideas and gradually develop them. The ModellingSpace enables students to build their own models and offers the choice of observing directly simulations of real objects and/or all the other alternative forms of representations (tables of values, graphic representations and bar-charts). The students -in order to answer the questions- formulate hypotheses, they create models, they compare their hypotheses with the representations of their models and they modify or create other models when their hypotheses did not agree with the representations. In traditional ways of teaching, students are educated to utilize formulas as the most important strategy. Several times the students recall formulas in order to utilize them, without getting an in-depth understanding on them. Students commonly use the quantitative type of reasoning, since it is primarily used in teaching, although it may not be fully understood by them. By modeling activities,we tried to achieve the development of qualitative and semi-quantitave premise and then express magnitude relationships in a quantitative manner. It was observed that students practise semi-quantitative relations, easily can create models and make use of semi-quantitative reasoning in an accessible and comprehensible way. They developed a strategy to simplify the situation, by creating simple models containing few relationships contrarily to their original custom to create complex patterns without having fully understood their function.