The current paper presents an introduction to a special issue focusing on mathematical flexibility,flexibility, which is an important aspect of mathematical thinking and a cherished, but capricious... Show moreThe current paper presents an introduction to a special issue focusing on mathematical flexibility,flexibility, which is an important aspect of mathematical thinking and a cherished, but capricious, outcome of mathematics education. Mathematical flexibilityflexibility involves the flexible,flexible, creative, meaningful, and innovative use of mathematical concepts, relations, representations, and strategies. In this introduction we discuss the most relevant theoretical, methodological, and educational considerations related to mathematical flexibility,flexibility, which form the background of the empirical studies presented in the special issue. Collectively, these studies provide a broader understanding of the mathematical flexibility,flexibility, its subcomponents, influences, and malleability. Show less
Hickendorff, M.; Torbeyns, J.; Verschaffel, L. 2019
This chapter provides an overview of the current findings about (the obstacles in) primary school children’s strategy use in the domain of multi-digit arithmetic. This involves addition,... Show moreThis chapter provides an overview of the current findings about (the obstacles in) primary school children’s strategy use in the domain of multi-digit arithmetic. This involves addition, subtraction, multiplication, and division tasks in which at least one of the operands contains two or more digits. For both the additive and multiplicative domains, we provide a comprehensive framework for the classification of strategies, with two dimensions: (1) the operation that underlies the solution process and (2) the way the numbers are dealt with in computing the outcome (manipulating whole numbers or single digits). Empirical findings of children’s strategy use in the additive and multiplicative domain show that children use a variety of number-based strategies efficiently and adaptively before the introduction of the digit-based algorithms. The introduction of the digit-based algorithms seems a critical instructional event: children show a large tendency to use the digit-based algorithms once they are instructed, and they do so rather efficiently. The major obstacles children encounter in developing, selecting, or executing these strategies are their conceptual understanding, procedural fluency, and adaptive/flexible strategy selection. Show less
Hickendorff, M.; Torbeyns, J.; Verschaffel, L. 2018
We aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample... Show moreWe aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample of 119 Dutch and 122 Flemish fourth to sixth graders solved a varied set of multidigit division problems. With latent class analysis, three distinct strategy profiles were identified: children consistently using number‐based strategies, children combining the use of column‐based and number‐based strategies, and children combining the use of digit‐based and number‐based strategies. The relation between children's strategy profiles and their instructional setting (country) and grade were generally in line with instructional differences, but large individual differences remained. Furthermore, Dutch children more frequently made adaptive strategy choices and realistic solutions than their Flemish peers. These results complement and refine previous findings on children's strategy use in relation to mathematics instruction. Show less
Torbeyns, J.; Hickendorff, M.; Verschaffel, L. 2017
