Polotskaia, E., & Savard, A. (2021). Some multiplicative structures in elementary education: a view from relational paradigm. Educational Studies in Mathematics, 106, 447–469. https://doi.org/10.1007/s10649-020-09979-8
The multiplicative reasoning that students should develop in elementary school is a key area of research in contemporary mathematics education. Researchers employ various views including multiplication as arithmetic operation, multiplicative structures, and multiplicative relationships. They also propose various classifications of multiplicative structures to support students’ development of multiplicative reasoning and problem solving. Our work contributes to this conversation by focusing on simple multiplicative relationships. Drawing on Davydov’s Theory of Developmental Instruction, we employ the relational view to analyze some multiplicative structures identified by researchers and practitioners. We propose a typology of basic multiplicative relationships as well as their specific graphical representations as a set of mental tools allowing for a holistic flexible understanding of the multiplicative situations, simple and complex, primary school students usually encounter (in grades 1–6). We suggest that the new approach may better support students’ multiplicative and relational reasoning and problem solving.
