Transformation as a fundamental concept in arithmetical competence modelling: An example of informatical educational science

Abstract

This chapter is an unusual approach to arithmetical competence. The starting point is the idea that students often produce their own strategies, which might differ from how their teacher teaches them, to solve prescribed exercises. To cope with these different strategies, the teacher has to make a great effort in understanding and solving them. Differences in strategy, in the use of facts and automatisms in subsolutions, in speed and number of steps can be observed by an experienced teacher; but in a group of 25 children, these observations cannot be systematically used in noticing, giving support and planning new exercises. The given volume of data cannot be handled within the constraints of working in the classroom. It would then be a good idea to provide a computer program for the teacher, which can then assist in such assessments.