Why johnny can't apply multiplication? revisiting the choice of operations with fractions

Abstract

The inadequate choice of operations and misleading interpretations of operations are major obstacles for students to mathematize and solve word problems successfully. Based on theoretical considerations on conceptual change concerning interpretations, this article reports on an empirical study conducted with 830 students. It extends existing investigations on the issue in three ways: 1. by focusing on fractions rather than on decimals, 2. by using an enriched test design, including several aspects of competence and various models for multiplication, and 3. by a deeper explorative analysis of 197 reasons for choices given in an operation choice item format with open responses. The article extends existing theoretical approaches to the problem by reconstructing four main strategies for choosing operations.