The algorithms take it all? Strategy use by German third graders before and after the introduction of written algorithms

Abstract

Solving addition and subtraction problems efficiently is an important goal of elementary school mathematics education. However, after the introduction of written algorithms, many students exclusively use these procedures to solve arithmetic problems, even if they are inefficient and error-prone. We explore the assumption that the dominance of written algorithms is due to the fact that students already previously had only used a very limited repertoire of strategies, which was then replaced by the written algorithms. We used data from a study of 222 German third graders. Sixty students received a brief training on computational strategies at the start of the school year and showed a broader strategy repertoire than their peers before the introduction of written algorithms. After learning the algorithms, the trained students still used a broader strategy repertoire (including short-cut strategies). We assume that students can succeed in flexibly using a broad strategy repertoire even after the introduction of the algorithms if they are supported in doing so from the beginning.This study was funded by Grants HE 4561/3-3 and LI 1639/1-3 from the Deutsche Forschungsgemeinschaft (DFG – German Research Foundation)