Abstract

Technologies of writing have long played a constitutive role in mathematical practice. Mathematical reasoning is shaped by systems of inscription (i.e., writing mathematics) and notation (i.e., specialized forms of written mathematics), and systems of inscription and notation arise in relation to the expressive qualities of mathematical reasoning. Despite this long history, something new is afoot: Digital technologies offer a significant expansion of the writing space. In this essay, we begin with a view of the developmental origins of the coordination of reasoning and writing, contrasting notational systems to more generic forms of inscription. Then, following in the footsteps of Jim Kaput, we portray dynamic notations as a fundamental alteration to the landscape of writing afforded by digital technology. We suggest how dynamic notations blend the digital character of notation with the analog qualities of inscription, resulting in a hybrid form that is potentially more productive than either form in isolation. We conclude with another proposition spurred by Jim Kaput: Digital technologies afford new forms of mathematics. We illustrate this proposition by describing children’s activities with TinkerPlots ^TM 2.0, a tool designed to help students organize and structure data, and to relate their understandings of chance to these patterns and structures in data.