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.
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
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
Besides producing more episodes of Aircraft Investigation, I also look forward to future episodes of Massive Engineering Mistakes when bridges and buildings are designed by “mathematix”
Even the Soviets wouldn’t dare commit such heresies.
Thank you for breaking this down.
This is important for Parents of K-12 children:
I came upon this page after receiving a letter on 10/5/2021 from my son’s second grade teacher (private Christian school that states no CRT) regarding important information about building math fact fluency.
It states “Recent research shows the importance of fact fluency as a foundation for more difficult math, and even as a predictor of future math success. For these reason, fact fluency is one important component of our math curriculum this year”, “conceptual understanding of the basic math facts, rather than focusing solely on memorization.”, “This conceptual framework anchors students’ recall in meaning. In other words, students are making meaningful connections (“meaningful connections” are in bold) that make remembering the facts easier.”
I removed my son from Illinois public school because of CRT. He is now enrolled in a private school in Wisconsin and they have sworn up and down that this is not CRT in any way shape or form. I’ve asked multiple times. The organization they are accredited through has partnered with an organization that offers Flourishing School Culture Instrument (FCSI) and involves Dr. Walter Strickland. If you know who Walter Strickland is then you know who James Cone is. Despite bringing this information to the schools attention, I was told that Walter Strickland is in no way affiliated with James Cone.
Mathematics *is* a verb, in so far as it is not strictly the formalisms that are written on pieces of paper. Those formalisms must be understood and comprehended, as such there is a verbed component to Mathematics.
One may suggest that Mathematics as a discipline mirrors a Group, with a set of objects that are the “facts” alongside an operation which is how those facts are oriented.
However, there is no “choice” in mathematics. If you look into the implications of the most infamous mathematical axiom: The Axiom of Choice, it is in fact far better labelled as an Axiom of Closure Under Representation. What we label as something by some symbol, must remain the same if we are to convey any meaning.
There is no “choice” in mathematics.
There is no definition for a stochastic/random process.
At best we may suggest that a stochastic process is formed of a number of deterministic processes, such that there are too many to reasonably compute.
But there is literally zero evidence to suggest that there is such a thing as a fundamental stochastic process.
All stochastic methods are constructed from deterministic procedures without exception.
Quantum Physics for example makes fundamental assumptions about the nature of the underlying fields without comment.
On what basis do we assume we may reasonably consider infinitesimal particles?
What is the definition of infinitesimal?
What is the definition of a limit?
What is the definition of an Open Set, and how does that emerge?
What is the definition of the dense limit of a finite class of algebra?
How do finite sub-algebras emerge differentiated entropic growth functions?
Is it possible to integrate these questions into a framework?
The answer is yes, there are various current lines of research dealing with these questions, from Polynomial Functors to Symmetric Monoidal Categories to the different areas of Path Algebra.
None of which admit any level of real agency into their universal domain.
Every “choice” is simply the sum of prior iterated potential (at the level of human interaction we may consider this time invariant, such that there is a well-defined arrow of time, but in general this is not a strict requirement we can work in non-IBN domains).
That is it.
The mind is a game of “square peg, square hole” that is set up at birth.
A process of learning is just that, a hole that changes shape, but it cannot change its fundamental nature.
There is no human mind without a human body.
There is a human body without a complete human mind. Severe congenital birth defects exist where the “holes” have not properly formed.
To deny simple reality in favour of assertion invites destruction: Entropy waits for no one and selects only for Free Energy.
Everything this idiot is saying is complete and utter garbage.
They need to be ridiculed.
There can be no civil discourse with these kinds of idea.
They will win in that arena because they have mastered the art of manipulation.
Playing the linear selection processes of emotional justification.
It is simply not a requirement for them to make logical sense, and logical arguments are simply too long and take too much time and effort to process to be effective counter-tools.
The liberal dream of live and let live must die in favour of pragmatism.
If we want freedoms we must fight for them aggressively because those who will take them away will not be civil.
God bless your work, John Waters, and thanks for that brilliant summary of the history of knowledge.
I hope you find good people to help you spread your work, and perhaps save many people from these mad activists.
What is the origin of the fetish for insisting that nouns (critical race theory, mathematx) are verbs?
Always remember to thank your dinner for performing cauliflower so pleasingly.
So…mathematics is to be based upon and practiced according to a “plurality of epistemologies”.
That’s Marx’s “polylogism” concealed behind a new euphemism.
Gutiérrez is yet another pretentious intellectual lightweight with delusions of competence in fields she has scant understanding of. Contrary to her likely belief, knowing what a Fibonacci sequence is does not make one a mathematician.
Still, I eagerly await critical social justice theory self-righteously demanding domination of engineering. I want to see how many of these woke-minded zealots will elect to fly in aircraft built according to mathematx and different ways of knowing.
Benefits could include:
(1) Plenty more material for new seasons of ‘Air Crash Investigation’
(2) An increase in the average intelligence of the population.
She seems very certain that we’ve ceased to need actual mathematicians!
Be on the lookout for the Gutiérrez School of Architecture, where nothing can actually be built to code much less to blueprints.
If we follow the course of Western Civilization’s history, and focus on the ideas leading up to mathematical science, we can observe Socrates’ skepticism of verbal meanings, Plato’s Academy’s emphasis on integrating the study of mathematical precision with verbal meanings, Euclid’s ingenious integration of logical accuracy to present mathematics as a logical-deductive system, Archemedes’, Eratosthenes’, and Pythagoras’ direct application of pure mathematics to accurately analyze, characterize, and predict, and trace the history of this natural scientific enterprise through Islamic history, the Renaissance, and the Enlightenment, we observe the dereliction in Western philosophers to reject Plato’s Academy rule of integrating precision speech – mathematics – in future philosophizing. Socrates’ exposure of the weakness in facile and arrogant trust in wordiness was rejected, and the romantics rebelled against natural philosophy, and after than Western philosophy splintered into all manner of “free inquiry” and “freedom to express” so that today academia has further fragmented. In my writings I go into greater detail and propose a testable solution to the present disintegrating and demoralizing situation. If this sounds like an arrogant claim, perhaps such arrogance is a good thing in the light of the arrogance in the present academic system.
Education has failed to teach the fundamental importance of philosophy as a guide to sustainable civilization, and not even highly educated college graduates understand the importance of mathematical thinking. Education needs to be revitalized in accord with Plato’s ingenious integration of wordy thinking with rational mathematical disciplines, plus astute observations of human problem solving methods that complement those problem solving methods that were emphasized when I was going to school. Today’s methods apparently are even less effective.
If anyone one you know is interested in contacting me, just google Foundation for the Advancement of Special Talent. I need a good collaborator’s assistance to make my created works available.
Thank you and have a good day.
Interesting. What does Gutierrez have to say about equity? Sounds like she is focusing on the “re-humanizing” of mathematics. Re-humanizing in how it is being taught, correct? Having said this… the bottom line for her isn’t so much addition, subtraction, multiplication, or division; the issue is teaching is political and, therefore, teaching of math must be re-imagined. Is this correct?