The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration

Abstract

Multi-base arithmetic blocks (MAB) are the most frequently used physical materials for teaching about decimal numbers, despite published reservations about their appropriateness. This paper presents an alternative, LAB (linear arithmetic blocks) and compares the two materials on the basis of epistemic fidelity and accessibility for students. Two teaching experiments involving 30 matched students indicated that LAB is considerably more accessible for students, and identify three contributing factors (LAB modeling number with length rather than volume, MAB incorporating an apparent dimensional shift and having prior use). Use of LAB was associated with more active engagement by students and de..