On the role of translations between modes of representation - case of fractions

Abstract

We believe that utilization of various modes of representation is important for concept development and deepens understanding. Many didacticians stress that the level of understanding is related to the continuos enrichment of the set of various modes of representation and emphasize the development of student’s capability of translationing between modes of representation. But it is also possible to utilize the work with representations for recognition (diagnosis) of the level of understanding, also for searching for misunderstandings and obstacles in understanding, and further as a tool for re-education. This contribution focuses on the study of student’s formulations of word problems to the given formula. (Pose a word problem which can be solved by the calculation $\frac{2}{3}+\frac{1}{4}$) or to the given visual representation. Our present investigation shows that this way we can get a lot of didactically interesting information. In the contribution some examples of problems formulated by students will be shown. Teacher’s reaction to these problems will be mentioned. I will concentrate especially on those problems that contain the most frequent misunderstandings and I will outline suggestions how to re-educate these misunderstandings.