Using Large-Scale Data to Determine Pupils' Strategies and Errors in Missing Value Number Equations

The goal of this study is to show a novel way of using large-scale data (N = 6203) to identify pupils' strategies when solving missing value number equations. It is based on the assumption that wrong numerical results appearing more frequently than would be the case if they were consequences of random guessing can be expected to be underlain by a pupil's rational, theoretically justifiable, solving procedure. We determined all of the numerical results suggested by the pupils in the study for three problems with the same format and classified them based on their occurrence. Possible solving procedures leading to them were inferred using a priori analysis. Next, we identified pupils' strategies based on the anticipated solving procedures in two problems of the same format and validated them by comparing them to the pupils' results in the third problem and to the pupils' whole test result. We identified six strategies, some of them underlain by clearly identified procedures. Our analysis showed a high predictive power of the identified pupils' strategies for their achievement in the mathematics test written 3 years later and in a more difficult problem of the same format. Our study has implications for test makers and teacher practice.