RUME 26
2024
Omaha, Nebraska
Developing Personal Representations to Access a Set-Oriented Perspective on Counting
Page: 1002
In some classical semiotic perspectives, signs and sign systems can be viewed as either institutional or personal. This dichotomy can place personal representations as antecedent to institutional ones, sometimes with the explicit goal of transitioning away from the personal ones entirely. In this paper I draw from qualitative data to argue that personal representations are legitimate and sometimes necessary components of developing combinatorial facility, and they play an ongoing role in understanding that is not replaced by institutional representations. I frame this theoretical argument around a discussion of common institutional semiotic systems for combinatorics, which can insufficiently support a set-oriented perspective on counting. I discuss how to incorporate personal representations into analysis that uses a classical semiotic lens. Doing so includes attending to the motivations for creating (or refining) a sign system, the connections between those systems and others, and how the form and nature of the sign systems seem to impact or reflect student reasoning. I also discuss how some differences between combinatorics and other areas of mathematics might affect the personal/institutional dichotomy in semiotic analysis.