Eye-movements as trace for predicative or funtional thinking [Augenbewegungen als spuren prädikativen oder funktionalen denkens]

Abstract

We are going to report about methods and results of a study in which pupils of grades 10 and 11 of two grammar schools have been tested in individual examinations using problems of the QuaDiPF-test. The main focus of this investigation was to detect a correspondence between predicative versus functional explanations and patterns of typical eye-movements. While working on the test-problems, the eye-movements of the subjects were recorded. After having worked on a problem, the subjects were asked to explain their procedure and to give reasons for their results. When evaluating these explanations, they were classified according to characteristics of predicative or functional thinking. Moreover, an algorithm was developed that was used to analyse the recorded eye-movements. Both methods of classification of a predicative versus functional cognitive structure showed a very clear correspondence. This study is part of a research project about the importance of individual differences in the preferencefor predicative versus functional thinking and has been conducted for several years now at the Institute of Cognitive Mathematics. The results of this basic research are especially used to explain the pupils' understanding of mathematical concepts and their problem solving behaviour in regular mathematics lessons.