Learning Process Studies in the Field of Fractals

Abstract

Our studies on understanding core ideas of fractals are part of a broader project on educational reconstruction of non-linear systems (Duit, Komorek & Wilbers, 1997). They focus on investigations into whether core ideas of chaos theory and fractals are worth teaching relating to the general aims of science instruction and whether they can be understood by students at the age of 15–17. The notion of fractals has already played a certain role in mathematics instruction in recent years. There are also ideas on how to employ this concept in explaining well known and new phenomena to students in science lessons. Studies on how students may learn and understand the new teaching materials (like experiments) are almost non-existent. The two studies address different core ideas of fractals. The first study lays its focal point on the concept of self-similarity (or self-affinity) and on the insight that very complex structures may evolve from simple rules. The second study focuses on employing the concept of fractals to explain certain phenomena. We investigate how students spontaneously understand the occurrence of dendrite structures in two quite different experiments and how they may be guided towards the science explanation. Both studies are designed as learning process studies. Nine groups of two students each are interviewed by an interviewer using the method of ≫teaching experiment≪ (Steffe & D’Ambrosio, 1996). The interviews last about one hour. In study, one the students were aged 16 and in study two they were aged 18. Data analyses follow category-based qualitative interpretation (Mayring, 1995; Bortz & Döring, 1995).