Do you ever find yourself talking about something, defending something, or promoting something when you suddenly realize you don't have a good definition of that thing?

In one way or another, I've been thinking about equity in math education ever since I was an undergraduate. I remember debating the value of "equality of opportunity" versus "equality of outcomes," and getting a sense for how the NCTM

*Standards*prescribed a type of school mathematics for all students. Here at CU-Boulder, issues of equity and social justice are never far away. But what, exactly, do we mean by

*equity*in math education? And why is it important?

Rochelle Gutiérrez focuses on issues of equity as an associate professor of mathematics education at the University of Illinois at Urbana-Champaign. Even though she's been publishing on issues of equity for well over a decade, in 2007 she wrote a book chapter titled,

*(Re)Defining Equity: The Importance of a Critical Perspective*. In that chapter, she argues why we need a definition of equity that gives teachers and researchers a clear sense of purpose.

When equity is loosely defined, it comes under attack from several directions. First is a belief that not

*all*students can learn, and that mathematical proficiency has more to do with natural ability than with effort. The second threat to equity is a "deficit theory" towards groups of students that haven't had much historical success in mathematics, whether that deficit is seen as biological or cultural. The third threat to equity, says Gutiérrez, comes from within the research community itself: so many issues get covered under the umbrella of "equity" that few of them get the kind of focused attention they need, even while many agree equity is important. As Gutiérrez puts it:

Perhaps the lack of a clear definition is what contributes to a general consensus that equity is worth striving for, everyone having his or her own vision of what it means. However, having a poorly defined target means we are only sure we are moving toward it when, in fact, we are very far away. (p. 38)

Gutiérrez argues that we should leave behind the traditional "excellence versus equity" and "traditional versus reform" debates in favor of a new perspective:

*dominant*versus

*critical*. Instead of teaching mathematics that "reflects the status quo in society, that gets valued in high-stakes testing and credentialing, that privileges a static formalism in mathematics," (p. 39), we should be favoring

*critical*mathematics, that which "squarely acknowledges the positioning of students as members of a society rife with issues of power and domination" (p. 40). This includes using math to examine social and political issues, to highlight perspectives of different cultures, and to challenge the view that mathematics is a static entity. Gutiérrez does not wish to create a dichotomy here -- in fact, she argues the importance of learning dominant mathematics because it can help students better understand and criticize the world.

With that perspective in mind, Gutiérrez defines

*equity*. First, she warns not to confuse it with

*equality*; whereas

*equity*implies "justice" or "fairness,"

*equality*implies "sameness." Gutiérrez is *not* arguing that all students should experience the same instruction using the same materials, or that we should expect all students to have the same outcomes. Gutiérrez fully recognizes that, within any group, experiences and outcomes will vary, and that some students will have interests that lead them away from mathematics. That's okay. Instead, she says equity in mathematics should consist of three main parts:

- "
*Being unable to predict*students' mathematics achievement and participation*based solely upon characteristics such as race, class, ethnicity, gender, beliefs, and proficiency in the dominant language*" (p. 41, emphasis original). To clarify, Gutiérrez says, "I contend that only when there is sufficient variation*within*groups and no clear patterns associated with power or status in society*between*groups can we conclude that this aspect of equity is being addressed" (p. 42, emphasis original). As for measuring achievement, Gutiérrez says we should use standardized tests (but not exclusively), because those are often the tools we use to grant power to individuals. - "
*Being unable to predict students'*ability to analyze, reason about, and especially critique knowledge and events in the world*as a result of mathematical practice, based solely upon characteristics such as race, class, ethnicity, gender, beliefs, and proficiency in the dominant language*" (p. 45, emphasis original). It's this aspect of equity that Gutiérrez uses to stress the critical aspects described above. - "
*An erasure of inequities between people, mathematics, and the globe*" (p. 48, emphasis original). Gutiérrez claims "This aspect of equity addresses the fact that having equal access to cultural capital and critical stances to society are necessary but insufficient conditions for change" (p. 48). While this aspect of equity is by far the most difficult to measure, and may not happen in our lifetimes, it should be the key goal of any long-term reform in mathematics education.

It might be the case that the first two aspects of equity must be addressed before we would see any changes in the third aspect. That is, students who gain both (1) dominant and (2) critical mathematics identities will lead to different kinds of mathematicians in the academy, thereby changing what counts as mathematics as well as how it is evaluated. The important thing to consider in this (admittedly simplistic) model is that neither the first nor the second aspects of equity are sufficient to redress injustices in the world. Students need to be able to do both -- be able to play the game of mathematics that is currently associated with power and intellectual potential, and be able to change the game of mathematics to serve a better society. (p. 49)

References

Gutiérrez, R. (2007). (Re)defining equity: The importance of a critical perspective. In N. S. Nasir & P. Cobb (Eds.),

*Improving access to mathematics: Diversity and equity in the classroom*(pp. 37-50). New York, NY: Teachers College Press.