ABSTRACT
Students in the first six years of schooling are routinely expected to understand mathematics that were originally developed over the course of centuries. A challenge for schooling, as well as for development, is to design classroom learning environments where this sociohistoric scale is compressed, but the intellectual accomplishments represented by these forms of mathematics are neither eradicated nor oversimplified. Design involves the intentional transformation of a setting for learning and is based upon conjectures about how the features of the designed setting will support learning and development. Our approach to design begins with envisioning how a particular set of mathematical ideas might be approached, often with an eye toward capitalizing on foundations that are not typically developed in schooling. In this chapter, we describe a hypothetical pathway for developing understanding of rational numbers by situating them as measures of length. We aim to illustrate that, although atypical, grounding rational number development in the development of spatial measure affords a fruitful alternative approach to instruction about mathematical concepts and operations that are often challenging for students to learn.
