Is it possible to confine the application of the intuitive rule: ‘Subdivision processes can always be repeated'?

Abstract

This paper studies the effect of various interventions on students’ ability to confine the use of the intuitive rule ‘subdivision processes can always be repeated’ to mathematical tasks only. Seventh and eleventh grade students who had formal instruction about the particulate nature of matter were asked to respond to six successive division tasks related to mathematical and material objects. Students in each grade level were randomly distributed into four intervention groups and each group was provided with a different intervention test. The interventions touched upon formal, relevant knowledge in science and mathematics and differed in their level of explicitness. It was found that the most explicit intervention increased the percentages of correct responses to all tasks in both grade levels. However, the effect of the other three interventions was minor. These results are discussed and suggestions for further research are made.