How is any of that relevant to whether students can reach their full potential?
Unfortunately, our only access to ideal mathematics is through mathematicians, who are absolutely open to cultural influences and biases, including raising and lowering the perceived cachet of entire fields of mathematics, controlling who gets hired (sexist and racist baggage along for the ride) and therefore which research gets emphasized at particular universities and whole countries, etc. I wish the MAA had expanded on some of these criticisms, like you do, and given explicit examples.
Well, what specifically is it about the MAA quote or my remarks about it that you thought seemed irrelevant? That statement excerpt again, with the immediately following sentence in case you missed it:
I’d summarize the reasoning as follows:
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Mathematics is a human endeavor and thus significantly shaped in content and practice by cultural context (which includes ideas about race, and also gender), rather than having some kind of special status of absolute epistemological purity due to the demonstrably objective nature of its results.
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Mathematics as a scientific field is affected by anti-science political ideologies and by social policies and attitudes involving race, among other things, and these ideologies and policies impact the ability of mathematicians and mathematics students to reach their full potential.
Yeah, I think the statement overall is somewhat clumsily written (I still am not sure exactly what’s meant by the phrase “the pattern of violence against our colleagues that give voice to race and racism”). But I think it’s pretty definitely not advocating any kind of 1984-style “doublethink” about the veracity of specific truth claims in mathematics.
I can see how a university or whatever could be racist or sexist towards students or researchers. But that doesn’t really affect the subject itself. I mean, what are these ‘challenging conversations’ supposed to change exactly? What would be different afterwards?
That sounds to me like the same essentializing grade-school mindset that mathematics just is a predetermined body of objective knowledge that can’t be affected by human prejudices. At the level of professional practice, though, as DPRK noted, such prejudices can have substantial impacts on entire fields of mathematics and entire institutions, not to mention entire countries.
In my own experience, such conversations in mathematics departments lead to more focused thinking about whether, say, a job candidate from a less “prestigious” institution is getting judged partly on “brand associations” that correlate with societal privilege, rather than on research and teaching quality. Are there certain research specializations whose impact gets undervalued because they’re clustered in institutions in developing nations where there are more barriers to international scholarly participation, lack of access to “big-name” journals, etc.? When evaluating students or candidates whose first language is not US English, is our perception of their ability to communicate mathematics affected by whether or not they’re white? Questions like these definitely lead to challenging conversations, but we’d be kidding ourselves if we think we don’t need to have them.
Okay, I think I understand it better now. Do you know of any examples of these research specializations whose impact gets undervalued because they’re clustered in institutions in developing nations? I’m curious what they are.
I wouldn’t dare pronounce on which mathematical subfields are “undervalued”, since different mathematicians will have fiercely different opinions on the relative importance of various fields. Nor would I argue that there are any particular fields of research pursued only in developing nations. More definitely, there are various studies of Journal Impact Factor and similar metrics showing that access to “prestige” journals, conferences, seminars, etc., varies widely by region, with mathematicians in developing and poorer countries having less access. (Anecdotally, Ramanujan is a notable case in point.)
Ramanujam lived over 100 years ago. I hope and expect things have improved since then, even if it’s still not a level playing field in terms of whose ideas are influential and whose are ignored.
Do you support the idea that mathematics is invented rather than discovered?
How are you interpreting the difference between “invented” and “discovered”, exactly?
Once again, I’m not denying—and I don’t know of any mathematicians denying—that demonstrated mathematical facts are objectively true within the axiomatic system in which they’re defined. Does that mean that I think mathematics is “discovered”?
At the same time, all these demonstrated mathematical facts are unquestionably articulated by human beings who decide to assign to them particular names, classification structures and judgements about their significance. Does that mean that I think mathematics is “invented”?
And is this still adequately on-topic for the present critical race theory discussion? I made my original remarks in post #200 to rebut the claims that the MAA’s statement that mathematics “inherently carries human biases” is bullshit or nonsensical or racist. But I’m not sure that a deep dive into the fundamental questions of mathematical epistemology is going to shed any more light on that subject. After all, both discovery and invention are human activities, and as such they can both be influenced by human biases.
Laurie Rubel certainly is.
No we don’t. We need to work to remove the influence of any “human particularity or cultural context” that may be biasing math education so that we can do a better job of teaching and using a neutral collection of objectively true facts for students of all types. The “grade-school mindset,” which from context here seems to be a term you are using for “teaching math instead of teaching why math is racist,” is exactly what is needed in grade school. It’s no surprise that when you replace arithmetic with grievance studies in third grade - only in areas where the politics and demographics demand it - you end up with some populations who can’t do math and then complain about how “biased” math entrance exams to specialized high schools and the college admissions process are.
If people in the sociology department want to study incidents of racism in math education, good for them. If some mathematicians have insight and want to collaborate on that work, that’s fine too. This is something that should go in the appropriate context (university social science work) and not as a replacement for actually teaching grammar school kids how to do multiplication, which seems to be the current thrust of the CRT-driven education destroyers.
This is just bonkers. How do you teach outside of a culture? First, teachers are steeped in the culture they’re steeped in. Second, children are steeped in the culture they’re steeped in.
One simple example: sitting still at a desk and solving problems individually on paper, after a teacher has via lecture explained the standard algorithm, is a culturally-informed pedagogical technique. Working with classmates to solve novel problems using manipulatives and having the teacher work mostly to set up the learning situation, to ask challenging questions, and to model mathematical reasoning, is another culturally-informed pedagogical technique. Learning math facts and algorithms through song, dance, and chants is another culturally-informed pedagogical technique.
A child who’s brought up at home learning through song and movement, and who goes to school where she’s expected to learn quietly and individually, may not access the curriculum. A child who’s brought up at home learning through independent reading, and who at school is expected to sing and dance, may not access the curriculum.
Strong mathematical pedagogy recognizes cultural contexts and responds to studnet needs. Most public schools will have kids with different cultural backgrounds, and so a good teacher will use a variety of approaches, recognizing that different kids have different needs, and that many of these needs are influenced by their culture.
Nonsense, if what you’re referring to is the math ed tweets of Prof. Laurie Rubel of Brooklyn College, along these lines:
Rubel is obviously not claiming that “whether 2+2=4 or not depends on what race you are”. Her point is that many people try to jump from the objective universal truth of the simple mathematical fact that 2+2=4 to the unwarranted conclusion that the entire subject and practice of mathematics must therefore be culturally neutral.
In other words, these people are responding to concerns about cultural bias in the practice and teaching of mathematics by reflexively declaring “But math can’t be culturally biased because 2+2=4 for everyone! Ha ha, dumb wokies!” Rubel is pointing out that their declaration is not as convincing as they imagine.
Claiming that you can teach math by removing its cultural context is kind of like white people in traditionally racist societies proclaiming that they “don’t see color”. In both cases, what you’re talking about is a ubiquitous aspect of life in society that you can’t just eliminate by pretending you’re not affected by it.
We’ve all agreed that 2+2=4 is a universal mathematical fact that is true for everybody (skipping technical nitpicks about different arithmetic moduli and so forth). But that doesn’t mean that everybody does, can or should learn this and other mathematical facts in exactly the same way.
Primary mathematics learning is inextricably linked to literacy, to socialization, to the cultural assumptions implicit in teaching tools like word/story problems, and to systemic-bias effects such as stereotype threat, impostor phenomenon, and so forth. (In many cultures, including much of the English-speaking world, these effects manifest strongly not just among ethnic minorities but among female students, for example.)
This is just the usual right-wing “anti-PC” boilerplate propaganda, and shows a profound lack of engagement or knowledge about the real issues involved in mathematics teaching and research. Manufactured alarmism about imaginary efforts to “replace arithmetic” in elementary curricula isn’t accomplishing anything except to transfer more money from the pockets of gullible conservative readers to conservative pundits, and in the process to hamper the efforts of teachers to make mathematics teaching more effective.
Once again, you cannot actually remove cultural context and cultural biases from mathematics teaching by pretending that they don’t exist, or complaining that they shouldn’t exist.
[ETA: as Left_Hand_of_Dorkness has much more eloquently, and speedily, explained.]
All of these aspects are also seen in varying forms in secondary and higher-ed math teaching as well as in mathematical research, which is what I was focusing on in discussing the subject with DemonTree. I remain unconvinced that this whole digression is actually accomplishing much in the way of answering the OP’s question, though.
Well, gosh!
I’m part of a cohort of teachers trying to figure this stuff out at our school and in our district. Literally in the middle of that sentence my phone chimed at me about our equity leadership meeting in ten minutes. We do things like read Culturally Responsive Teaching and the Brain and try to figure out how we can modify our pedagogy.
I’m not great at doing so, but I’m trying. There are definitely cultures that are more music-and-movement-inclined than mine. I grew up in a culture in which we coudl all sit in the living room reading books for hours without talking and be happy, and I’m raising my kids the same way, and that’s fine; but I have friends who grew up dancing and laughing and singing in their homes constantly, where home was loud, and that’s fine too. If I’m not careful, I default to the quiet classroom, which serves some of my students and not others. I have to work to use a different approach.
And here we have CRT - white oppression and black grievance is such a fundamental fact of the universe that it precedes 2+2 = 4. The fact of perpetual race war cannot be changed as everything we purport to know or experience flows from it - yet, even though it is the axiom of metaphysics, some people are still morally guilty for perpetuating it.
I believe you have answered the question at the start of this thread quite dramatically.
Translation: I refuse to enforce any discipline in my class. The people who want to learn are going to have the environment made impossible by those who were raised with the expectation that dancing instead of paying attention in math class and constantly screaming in the classroom is acceptable, and I’m not going to do a damn thing about it because I’m being judged on “equity” rather than whether my students know how to do math.
? Do you think that systemic white racism isn’t a fundamental fact of the universe for people in traditionally racist white-supremacist societies?
Contrary to your misinterpretation, though, nobody is claiming that systemic white racism actually precedes the mathematical fact 2+2=4. (After all, humans almost certainly knew some form of 2+2=4 many millennia before there even were any white people.)
Rather, what we’re doing—with a rational moderation to which your outraged accusations seem like a major overreaction—is simply acknowledging that systemic white racism is part of the culture in which even elementary mathematical facts like 2+2=4 are learned. You can certainly ignore the existence of that cultural context if you want to, but ignoring it doesn’t make it disappear.
Golly, this is almost a parody of classic knee-jerk from the nascent days of right-wing “anti-PC” consternation back in the nineties. Do you really imagine that elementary school classroom discipline can’t co-exist with dancing and singing, and that dancing and singing necessarily imply “constantly screaming”?
Here’s something that’ll positively splode your harrumphing head: When I attended a small rural elementary school (student and staff population 100% white) in the eastern US about a half-century ago, our elderly second-grade teacher had us memorize elementary arithmetic facts via loud chanting, rhyme singing, and clapping-out games. Dismiss from your mind any notion that we were undisciplined: we were not. And we ended up knowing how to do math, too.
Even back then, a lot of experienced teachers understood that effective learning for primary school students required a much more diverse and flexible approach than mindless Gradgrindian invocations of “paying attention in math class” and “enforcing discipline”.
Oh for fuck’s sake.
I’d be madder about it if it weren’t so stupid a thing to say, so completely divorced from the conversation. Mx. Sandstorm over here has a teacher disagreeing with him, and his “translation” is just flinging shit at me, as if I don’t have 14 years of experience running a classroom, as if I don’t struggle in the opposite direction from maintaining discipline and just posted that that was my struggle, as if I don’t look for ways I can have MORE movement and song in my room to reach kids who especially need that for learning.
It’s hard to remember that when someone’s flinging shit at you, it’s really a commentary on the strength of their own position. Realizing that doesn’t make the smell go away, but at least it reminds you what’s really stinking.
What age kids are you teaching? I assume young if you’re using song and dance. Also, I thought rote mémorisation was frowned on these days?