for the learning of mathematics

an international journal of mathematics education

Martin A. Simon ,  Nicora Placa - Vol. 32 Num. 2 (2012)
 Reasoning about intensive quantities in whole-number multiplication? A possible basis for ratio understanding


One of the challenges of learning ratio concepts is that it involves intensive quantities, a type of quantity that is more conceptually demanding than those that are evaluated by counting or measuring (extensive quantities). In this paper, we engage in an exploration of the possibility of developing reasoning about intensive quantities during the teaching of whole-number multiplication. The investigation is grounded in a measurement-based instructional design attempt that built on the Elkonyn-Davydov curricular approach. We report on this investigation and resulting implications for learning to reason about intensive quantities and understanding ratio concepts.