# Linear Algebra and Pedagogy; Academic Fairness and Critical Theory

Academic fairness is crucial in our struggle to broaden participation in mathematics. We will be well served to learn from adjacent disciplines, such as critical theory, as we think carefully about who does mathematics and why. Who is a “minority” mathematician? How does this relate to Linear Algebra, and to pedagogical considerations?

“The most important aspect of teaching is deciding what not to teach.” The origins of this idea must be ancient, but I first heard it phrased as such by Amin Gholampour. I’ve learned this lesson again and again over the years. For example, what should one teach in calculus? One could spend four years teaching calculus topics alone, treating special functions, esoteric trig identities, elementary differential equations, a myriad of applications, calculus and social justice, to say nothing of differential forms, analysis and the foundations of calculus. Choosing the material to be left out defines the course. So how can one systematically or thematically choose what material to include/exclude?

My friend and colleague Michael Orrison attempts to deal with this question in part by finding big ideas around which one can frame a given course. For Linear Algebra, in the past he has used the big idea of changing perspective. This is of course very natural in the context of linear algebra, and the idea pervades much of mathematics. Students can gain a deeper understanding of themselves and the world around them by learning a very technical method of changing perspectives (e.g. invertible linear transformations) and relating it to experiences outside the classroom. In fact, given the pervasiveness these basic ideas in mathematics, mathematicians are experts in changing perspectives, solving problems by attacking from different angles, and studying objects that have subtle characteristics which are only manifest when viewed correctly. We can (and should) apply these lines of thought to our discipline itself, as well as the content within our discipline.

The notion of perspective is central to gender inequity and underrepresentation in mathematics. Who is “minority”? The problem lies within the term itself.  “Minority” is manifestly relative. Are you a minority? The answer depends on context: within your family? your friends? your school? your department? your neighborhood? No one is inherently minority. No one is birthed “a minority”. It would be far more accurate and fair to use terminology that is sufficiently flexible to allow for this change in perspective.

We need not reinvent the wheel, as theorists have solved the problem for us. The term “minority” has been problematized and replaced in education theory, and critical theory more generally. Individuals are not “minorities”, but each of us may be minoritized. A quick search shows how well this term is used in education theory literature. I myself learned this term from Shaun Harper’s article Race Without Racism in The Review of Higher Education, which Darryl Yong hipped me to.

The term minoritized highlights the extrinsic nature of finding oneself in the minority of a given group. It also emphasizes, to paraphrase Legier Biederman, that minoritizing is a process, not an object.

As a practical matter, within mathematics we should eschew the use of “minority” as a class of people, and instead consider who is minoritized within mathematics, as well as how and why this process takes place.

For those of us who have felt within a minority in mathematics, either because of race, class, ethnicity, orientation, or any other reason, it is comforting to consider that minority is not inherent. The processes by which individuals are minoritized may be changed. We can learn from our colleagues in other departments, especially those who think professionally about issues surrounding power structures and social inequities; it will be to our benefit as we work to make the process of becoming a mathematician increasingly fair.

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