The “Reason” of Equality: The Equal Sign and a Standard of Inscribing Difference

• In Event: Curriculum Studies and Historicizing the Present: The Political and the Impracticality of Practical Knowledge

Abstract

It is currently assumed that teaching algebra to all children will grant access to higher levels of mathematics and improve the child’s academic, social, and economic standing (NCTM, 1998; Choike, 2000; Moses & Cobb, 2001). At the elementary level, this foundation to future success in algebra is focused on understanding the equal sign (Falkner, Levi, & Carpenter, 1999; McNeil & Alibali, 2005). However, this learning of the equal sign is not simply about mathematics. Within this logic, understanding the equal sign is to produce equality, articulated as equal access and opportunities for all students.

At this intersection between seemingly distinct mathematical and social notions of equality, the equal sign is taken for granted as a ‘fact’ and left unquestioned. Yet, the equal sign embodies a comparative logic that orders notions of identity and difference, from which equality is understood. This logic operates within a system of reason that entails the rules and norms that connect the content of the curriculum to practices of inclusion and exclusion (Foucault, 1977). That is, in the elementary math curriculum, the equal sign is related to the standards that organize the ‘reason’ of equality and give sense to the comparisons that organize what (and who) counts as ‘equal’.

This paper takes the comparative logic of equality and the standards that frame its commonsense as its focus. It asks, “What principles of ‘reason’ historically order the logic of equality and make possible what is thought and acted on as algebra for all?” The answer will focus on the Standards Based reform movement in mathematics as an entry point into considering how the equal sign is entangled with discourses about how to see, think about, and manage equivalence and difference. In particular, it will take the inscriptions of the equal sign in the Standards documents and curricula and make visible its relation to cultural narratives about who is/is not the ‘standard’, ‘normal’, and ‘equal’ child.

To situate the equal sign in math education as linked to cultural rules of representations of identity and difference, this paper will discursively analyze the inscriptions of equality in the National Council of Teachers of Mathematics Standards (1989, 2001), the Common Core Standards (2012), and curriculum texts. As the equal sign appears in these documents, it is given meaning in relation to other cultural, historical, and political discourses. The analysis will specifically highlight the intersection of the curriculum and Standards materials with sources drawn from educational psychology and learning sciences. This attends to the relationship that emerged between mathematics education and neuro-psychologies to give meaning to the standards, for a particular kind of ‘memory’ as an example, required for all.

Examining the cultural rules that frame the commonsense of equality in mathematics education is to highlight how the statement of algebra for all is limited by a comparative logic that produces notions of difference. By understanding the limits of this logic and the rules of in/exclusion, alternatives for (re)thinking equality as an objective of the curriculum might be possible.

Author

• Jennifer Diaz, University of Wisconsin - Madison