Analysis of Eye-movements during Functional versus Predicative Problem Solving

The theory of functional / predicative thinking, once developed to describe differences in students’ behaviour while solving programming tasks, is applied to analyse eye-movements while solving tasks of visual pattern completion (QuaDiPF-tasks, Schwank 1998/2000). Predicative thinking requires that in order to meaningfully complete the pattern the subject has to get involved with the logic of the static structure of the pattern, functional thinking requires to get involved in a dynamic reading of the logic of the pattern. The QuaDiPF-tasks proved to be useful in other experiments to predict typical functional or predicative behaviour of the subjects. The eye-movement-study is a second approach after an EEG-study to use not only qualitative methods for the classification of problem solving behaviour, but also quantitative ones. 1. Qualitative investigations of functional/predicative thinking In the very first days of the theory of predicative versus functional thinking (Schwank 1986, 1993-1995) we used the nonverbal intelligence test APM (Advanced Progressive Matrices) from Raven (1965) to balance our different groups of subjects spread over such different countries as Germany, Indonesia and China (Marpaung 1986, Xu 1994). The focus of interest was on differences in students’ behaviour while solving some programming problems using different types of microworlds. The label “predicative” was used to characterize a problem solving behaviour highly orientated at and sensible for features, relations and judgements, whereas the label “functional” was used to characterize a problem solving behaviour highly orientated at and sensible for courses, modes of actions and effects. The experiments were run in the form of constructive teaching experiments (Cobb et al. 1983), hence, qualitative analysis methods were to apply. Although one could have expected strong cultural influences on the cognitive processes involved when solving our programming tasks, the results show, that knowledge about the national relationship cannot help to describe or to predict the individual types of problem solving behaviour of our subjects. Instead, the distinction of functional and predicative thinking was very helpful. The results show, that students tend to have a strong preference for either of the two thinking styles, which shows up most clearly in cases when students are quite intelligent and do reach the limits of their intellectual power when challenged by specific tasks. Paper accepted at the 2 nd Conference of the European Society for Research in Mathematics Education, 24 th 27 th February 2001, Mariánské Lázn , Czech Republic