INTUITIVE RULES IN SCIENCE AND MATHEMATICS - THE CASE OF EVERYTHING-CAN-BE-DIVIDED-BY-2

In the last twenty years, researchers have studied students' mathemati cal and scientific conceptions and reasoning. Most of this research is content-specific. It has been found that students often hold ideas th at are not in line with accepted scientific notions. In our joint work in mathematics and science education, it became apparent that many of these alternative conceptions hail from a small number of intuitive r ules. We have so far identified two such rules: 'The more of A, the mo re of B', and, 'Everything can be divided by two'. The first rule is r eflected in students' responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, v olume, matter, etc.), all tasks related to intensive quantities (densi ty, temperature, concentration, etc.), and tasks related to infinite q uantities. The second rule is observed in responses related to success ive division of material and geometrical objects, and in seriation tas ks. In this paper we describe and discuss the second rule and its rele vance to science and mathematics education. In a previous paper (Stavy and Tirosh 1995, in press) we described and discussed the first rule.