Emergent Technologies for Developing Mathematical Objects-to-Think-With

This chapter focuses on a cluster of conceptual tools and strategies that are common across topics in school mathematics and are ubiquitous in coding-based contexts. Borrowing from Papert (1980), we propose number lines and mutable grids as objects-to-think-with rather than as objectives of instruction themselves. Through four vignettes, we illustrate how such objects-to-think-with can be leveraged, through technology, to operate explicitly and implicitly as part of sense making in mathematics contexts. Number lines and grids are frequently invoked when learning to code, which led our research team to examine how digital technologies, such as programmable robots, touch-screen tablets, and dynamic geometry environments, extend and expand the power of objects-to-think-with. We argue that these technologies present powerful possibilities for supporting children’s mathematics learning.