Connecting Whole Number Arithmetic Foundations to Other Parts of Mathematics: Structure and Structuring Activity

Abstract

In this chapter, we attend to presentation/discussion of structure and structuring activities as two key routes through which whole number arithmetic can be connected to other mathematical content areas and to central mathematical processes and products like defining/definitions and generalizing/generalization. In the body of the chapter, we use literature to distinguish between approaches focused more on the presentation of structure and those oriented towards structuring activities, before presenting an overview and discussion of studies geared more towards one or other of these approaches. We incorporate studies that have been directed towards both students’ mathematical learning and mathematical (and pedagogical) teacher learning and conclude with commentary on biases towards structure-based or structuring activity-based approaches across these contexts. Our argument is that both approaches show promise for building towards stronger connections between whole number arithmetic and other mathematical areas, with a number of examples in each category included. Given the evidence of difficulties for so many children in many parts of the world in moving beyond the terrain of whole number, our findings suggest that attention to structure and structuring can provide important routes for bridging this chasm.