The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration.
Abstract: Because of a lack of strong alternatives, MAB (multi-base arithmetic blocks) 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 transparency for students. Two teaching experiments demonstrate that LAB is considerably more transparent for students, and identify three contributing factors. In both experiments, 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 transparency of the LAB material. Further research is warranted, so that teaching of mathematics with physical materials can be improved.
Stacey, K., Helme, S., Archer, S., & Condon, C. (2001). The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration. Educational Studies in Mathematics. 47, 199-221.