Quantities, Numbers, Number Names and the Real Number Line

Abstract

This paper describes an approach to developing concepts of number using general notions of quantity and their measurement. This approach, most prominently articulated by Davydov and his colleagues, is discussed, and some arguments favouring this approach are offered. First is that it provides a coherent development of both whole numbers and fractions. Second, it makes the geometric number line continuum present from the start of the school curriculum as a useful mathematical object and concept into which real numbers can eventually take up residence. Third, in the Davydov approach, there are some significant opportunities for some early algebraic thinking. I further present an instructional context and approach to place value that simulates a hypothetical invention of a place value system of number representation.