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

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 deeper discussion. Epistemic fidelity is critical to facilitate teaching with the models, but we attribute the enhanced classroom environment to the greater accessibility of the LAB material. Further research is warranted, so that teaching of mathematics with physical materials can be improved. This revised version was published online in July 2006 with corrections to the Cover Date.