Mathematx

Social Justice Usage

Source: Gutiérrez, Rochelle. “Living Mathematx: Towards a Vision for the Future.” Philosophy of Mathematics Education Journal 32, 2017.

This paper offers specific implications for teaching and learning and brings into conversation ideas from ethnomathematics (including Western mathematics), postcolonial theory, aesthetics, biology, and Indigenous knowledge in order to propose a new vision for practicing mathematics, what I call mathematx. I build upon the work of sustainability in mathematics education and suggest we need to think not only about more ethical ways of applying mathematics in teaching and learning but question the very nature of mathematics, who does it, and how we are affected by that practice.

New Discourses Commentary

Mathematx (pronounced “math-e-ma-tesh”) is the brain-child of the critical mathematics education activist Rochelle Gutiérrez, who holds no degrees in mathematics (see also, critical pedagogy). She describes it as “a living mathematx” and recommends it as a new, revolutionary approach to teaching and doing mathematics (see also, ethnomathematics). It is billed by the author as a means to “reconsider our definitions of mathematics in light of our current state of global crises.”

Even with a detailed reading of Gutiérrez’s paper, it is difficult to ascertain what “mathematx” is meant to represent. It is clearly an attempt to reimagine mathematics and mathematics education in accordance with the “insights” from ethnomathematics, among other things, but it also indicates that mathematics and mathematics education should be reformulated by incorporating unexpected “knowledges,” as the author has it. On the one hand, there is the argument to include “Indigenous knowledge,” meaning some of the various ideas about mathematics had and used by indigenous peoples (though it seems to escape Gutiérrez that this is anthropology of mathematics, not mathematics or mathematical pedagogy). On the other hand, she advocates directly that we learn mathematics from “other-than-human persons,” including plants. (“I underscore with examples from biology the potential limitations of current forms of mathematics for understanding/interacting with our world and the potential benefits of considering other-than-human persons as having different knowledges to contribute.”) She also advocates getting away from the problem-solving orientation of mathematics in favor of “play” and “joy.”

Mathematx must be thought of, then, as an extension on the broader ethnomathematics project of dismantling methodologically sound and established mathematics and mathematics pedagogy in favor of something that Critical Social Justice activists would have greater advantage in, namely the sociology of an academic discipline and critical (as in Critical Theory) presentations of the subject’s anthropology. The focus on the usual conflict theory-oriented “domination” and “oppression” is plainly central to Gutiérrez’s project:

Not only must we: a) be conscious of the ways mathematics can dominate and b) constantly question what counts as mathematics and who decides, we must also c) think about how we, as living beings, practice mathematics as we interact with others and ourselves. As we begin to reimagine mathematics, we have the opportunity to reimagine the mathematician—who is considered a mathematician as well as how are mathematicians influenced by the mathematics they do?

Much of Gutiérrez’s presentation of mathematx focuses on “centering indigenous knowledges.” The paper that first introduces this idea, when comprehensible, is significantly dedicated to the mathematical cultural anthropology of a small number of Native American tribes. This is, no doubt, an interesting subject in its own right, but Gutiérrez uses this (and claims that those “knowledges” are unfairly marginalized and excluded by white, Western approaches to doing mathematics—see also, white mathematics) to call for a complete “reimagining” of mathematics as a subject and as a subject to be taught (see also, critical pedagogy). It is best to encounter this conceptual leap in her own words:

Combining the views of In Lak’ech, reciprocity, and Nepantla allows us to raise new questions about a vision of practicing mathematics that might move past previous notions of Western versus other mathematics, past an idea of mathematics as either oppressing or liberating, beyond a mathematics that is either discovered or invented, towards an idea that allows us to deal with today’s complexity and uncertainties. Towards that end, I am calling for a radical reimagination of mathematics, a version that embraces the body, emotions, and harmony.

The descriptions of what mathematx is supposed to be and do remain elusive, however. For example, Gutiérrez instructs us that “Mathematx is a way of seeking, acknowledging, and creating patterns for the purpose of solving problems (e.g., survival) and experiencing joy.” From there, she embarks on a long report about aesthetics in mathematics, which she problematizes by writing,

Current versions of what count as “beautiful” in mathematics tend not to reflect the diversity in our world. Instead, they tend to relate to truth, implying universals rather than uniqueness/expression that would align with performance or a plurality of epistemologies. If we can recognize that cultural theses of modes of living are aesthetic choices and some aesthetics are not superior to others, then the means for controlling or dominating is lessened.

In this regard, it is clear that the focus on truth in mathematics—finding mathematical truths and establishing them through (sometimes elegant) proofs—is a strike against mathematicians and mathematics as it is currently conceived because it highlights ideas like universalism and objectivity. These are framed as aesthetic choices that can be put up against other aesthetic choices in one of the more creative applications of cultural relativism in the Critical Social Justice literature. Mathematx is clearly meant to favor a “plurality of epistemologies” and knowledges in mathematics and to take the focus off finding proofs or right answers in calculations.

Gutiérrez then cites noted queer Theorist Judith Butler on the concept of gender performativity implying that there is a kind of mathematical performativity, in order to make the case that mathematx is a verb—specifically one that isn’t particularly interested in the end product of the process (of doing mathematical work):

Second, whereas mathematics tends to be thought of as a noun (e.g., a body of knowledge, a science of patterns, a universal language), mathematx is performance and, therefore, a verb. Just as identity is not something that you are, but rather something you do (Butler 1999), mathematx emphasizes the guiding principles and the process as opposed to the product.

This would classify mathematx not just as critical in orientation (see also, Critical Theory and critical pedagogy), but also postmodernist, or at least poststructuralist (in the Butlerian sense). Butlerian “poststructuralism” (which is its own diversion from the real, mostly Derridean, thing), centers primarily on the concept of parody (see also, politics of parody), by which the absurdity of some existing phenomenon or institution is deconstructed by deliberately making a kind of parodic joke of it—for political ends. How this is supposed to help anyone get better at mathematics is beyond any reasonable person to ascertain, but, as Gutiérrez fairly notes, it might make “doing” (in the Butlerian, i.e., screwing-around, sense) mathematics more fun, “joyful,” and “living.” The starting point for this is indicated as embracing joy and emotions in mathematics and taking on more indigenous perspectives. The result is a “living mathematx” that is best read as described by the author herself:

Living mathematx means moving through the world with other living beings, acknowledging, appreciating, and reciprocating the patterns produced. If we look to animals and plants for some insight, we see that Brassica oleracea (Romanesco cauliflower) performs itself in both utilitarian (compact) and non-utilitarian (pleasing) ways that may get us to pay attention to its form and to continue to cultivate it. On the one hand, Romanesco cauliflower performs a version of the “Fibonacci” sequence that maps onto Western mathematics, and the elegance of the pattern brings joy while at the same time solves problems of space. Yet, like all persons, every brassica oleracea, performs itself in a way, and over its lifetime, that shows variance and suggests a departure from a pre-determined set of possible outcomes programmed by genomes.

If you read that as Gutiérrez suggesting that a head of a certain varietal of cauliflower performs mathematics and that we should learn math from the cauliflower’s performance, you will have read that correctly. This will achieve a “living mathematx” that is intended to install a “living mathematics” that will replace the usual mathematics, as the author understands these subjects.

As virtually nothing in this paper makes any sense, it’s difficult to tell for sure what Gutiérrez intends with her “living mathematx” except that, per her other works, she intends it to be the basis for a “revolution” in mathematics and mathematics education that is needed because “equity isn’t enough.” That is, it is another attempt by Critical Social Justice activists to replace sense with nonsense, which ultimately empowers them as the purveyors of the only authenticated nonsense.

It is of some note that while one would be forever forgiven for believing that Rochelle Gutiérrez and “mathematx” are fringe topics included here only for humorous intent and to highlight the profound confusion of the activist Critical Social Justice canon, that is unfortunately not the case. Gutiérrez’s work is routinely cited by major education activists and institutions, including MIT, and is incorporated as a Theoretical basis for “ethnomathematics” curricula in states including Washington and Oregon, possibly among others by the time of your reading.

See also, ethnomathematics and white mathematics.

Related Terms

Butlerian; Centering; Conflict theory; Critical; Critical pedagogy; Critical Theory; Cultural relativism; Deconstruction; Derridean; Dismantle; Domination; Equity; Ethnomathematics; Exclusion; Gender performativity; Indigeneity; Knowledge(s); Marginalization; Objectivity; Oppression; Performativity; Play; Politics of parody; Postcolonial Theory; Postmodernism; Poststructuralism; Problematize; Queer Theory; Radical; Reimagining; Revolution; Social Justice; Theory; Truth; Universalism; Western; White; White mathematics

Additional Examples

Source: Gutiérrez, Rochelle. “Living Mathematx: Towards a Vision for the Future.” Philosophy of Mathematics Education Journal 32, 2017.

Mathematx is a way of seeking, acknowledging, and creating patterns for the purpose of solving problems (e.g., survival) and experiencing joy. Beginning with the principles of recognizing self and/in others, responsibility towards others, and valuing tensions, several things stand out as different from the typical way Western mathematics is conducted or experienced by students in school. First, although some mathematicians experience pleasure as a result of solving previously unsolved problems, that aspect of joy is often a very small percentage of the time and almost always absent from the “mathematical product” (e.g., new theorem, new proof) that is valued by the community. Yet, mathematics education researchers who study aesthetics highlight this domain as essential to human meaning making and to the insights that mathematicians develop. … Although much of this intuitive/aesthetic work remains at the subconscious level for many mathematicians, mathematx is intricately tied to what is pleasing and rewarding in a connected way, not just a utilitarian or “problem solving” manner. This perspective is consistent with Boylan’s call for putting passion and pleasure at the heart of mathematics education. For me, “pleasing” includes not just the playful way in which many “purexi” mathematicians invent new workspaces by beginning with different axioms, (e.g., 8-dimensional space) but also how other persons perform mathematx for/with us. This version of play deviates from Bishop’s definition surrounding games because play does not necessarily involve an organized game, but includes a kind of frivolous activity with value perhaps only for the one performing it.

Revision date: 4/1/21

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James Lindsay