Adaptive tutoring of arithmetic skills

Abstract

Based on the assumptions that (a) addition and subtraction are rule-based cognitive skills, and (b) that the acquisition of cognitive skills is a result of a developmental process in which stages can be distinguished, a “genetic model” was proposed in which emergence of addition and subtraction skills in the domain of the natural numbers 20–100 is described in six stages. The stages were chosen on theoretical and empirical grounds (several studies on addition and subtraction skills conducted at the State University of Leiden). In a longitudinal experiment, 16 second grade elementary school students were followed during 11 months. A diagnostic computer program was used to collect data on their addition and subtraction performance. The strategies appeared to be employed fairly consistently within a stage of development. The proposed genetic model accounted for most of the performance levels displayed by the students. The conclusion seems warranted that instruction should be adapted to the student’s actual stage of development.