NCTM Punted Culturally Responsive Mathematics To The Science of Learning Movement
I just turned 60. This article is a gift to myself for self-care and to remain steadfast loyal to mathematics — and not its twisted/contorted form that’s mangled up with politics, policy, and pedagogy(not the good kind).
This article is a 13 minute read. But if you only have one minute, just know the word count of “history” was a jaw-dropping zero in a paper about culturally responsive mathematics. Just to give you some stark contrast, here is the opening paragraph from George Gheverghese Joseph’s Crest of the Peacock.
An interest in history marks us for life…
Culturally Responsive Mathematics should have had the smell of mangos, guava, papaya, lychee, etc. It should have had aromas of ancient markets in Marrakech. It should have had the energy of the ancient port of Bugia, where a young Leonardo of Pisa was serendipitously intercepted by advanced Hindu-Arabic mathematics.
That changed the course of civilization with the eventual publication of the book Liber Abaci in 1202.
With zero mention of “history”, you are loudly broadcasting — intentionally or not — that students(and teachers) will be cut off from the story of mathematics, its thematic development through all races, cultures, and civilizations.
Only a sterilized, neutered version will exist that has no past, no present, and no future.
It will smell medicinal, a prescriptive tonic to be administered for, ironically, a misdiagnosis of the situation — where is the excitement/curiosity? Certainly not from this position
This is my perspective — although it is shared by others.
These responses will be in the vast minority. The vast majority will look like the typical institutional responses to disruption — especially the one on the left.
Education and the institutions that run them generally do not like their own perspectives questioned
They certainly do not like getting their “teeth kicked in”. Few do. Yet, for me, it has been survival in both learning about mathematics and music.
If Bourdain wisdom cannot sit positively in institutions, then those institutions are not progressing as far and fast enough to be aligned to wanting their paradigms smashed into smithereens.
Before you read anymore — especially if you are in a leadership position in mathematics education — answer these questions to yourself.
How often do you specifically talk about mathematics — a problem, idea, conundrum, etc.?
When was the last time you tried a math question for the first time?
If you didn’t find a solution, did you share that with anyone?
What’s the last new mathematical fact you learned?
As mentioned already, this is a long read. I vetted most of what I said here with some kindred math folks — about a dozen or so.
I still would have written everything below, but having a little wind in your sails never hurts. In the end, I needed to write this blog for my own sanity. In the end, I felt a moral obligation to point out the disappearance of mathematics as a main actor — relegated to an understudy in now a mathematical play full of absurdity.
Before the internet, if someone said “NCTM”, my mind immediately thought of the magazine “Mathematics Teacher” and the pot-of-gold mathematics that was inside.
Those “golden” days seem to be gone by the glaring omission of mathematics in its recent position paper. You might ask — should ask — how can that be? Few are actually talking about mathematics anymore in terms of content anymore. Most are using mathematics to push agendas that don’t actually centre mathematics.
It’s a Samuel Beckett play, except we’re not Waiting for Godot, we’re Waiting for Mathematics…
This is my perspective on how math education has lost the plot with mathematics — and relegated it as a footnote to the machinery of pedagogy.
I saw the writing on the wall last year for me in the institutionalized space of mathematics education. The theme at last year’s NCSM Annual Conference was about Storytelling.
Hmmm. Maybe I should apply, after all only my entire career in math education has been about that. Cough.
Before you think the titling of this screenshot was a tad snide, let me give you a brief snapshot of the some of the untold math stories I was going to tell:
Ahmad Ibn Ibrahim(1228, Marrakech)
During this time, this area produced tons of silk. Ibrahim asked a question in that how tassels of 3 colours can be made from 10 colours(the three colours must all be different. Yes, the answer is C(10, 3), but combinatorics was not yet developed yet. His approach/solution — case by case — ended up with a patterning of triangle numbers and uncovering “Pascal’s” triangle.
Pingala/Hemachandra(3rd Century BCE/1150’s, India)
The structure and examination of Sanskrit poetry led to the discovery of “Pascal’s” triangle and “Fibonacci” sequence — obviously earlier.
Pietro Cataldi(16th century/Italy)
What is significant about Cataldi — other than the fact he discovered the 6th and 7th Perfect Numbers — is the fact that he chose to teach in the local dialect of Italian rather than in Latin as was the custom in those days. This enabled many people to benefit from his teaching. Quite equitable of him!
Cataldi showed his benevolence by giving the superiors of various Franciscan monasteries the task of distributing free copies of his ‘Practica aritmetica’ to monasteries, seminaries, and poor children.
You may want to fix your rubric, NCSM.
Or, as supervisors of mathematics, do a better job in being guardians of the subject.
How I eventually took solace with all this is that NCSM isn’t interested in mathematics through a lens of its history(which I went on to describe in my proposal). It was closure for me on an organization which has felt more like a country club where certain members seem to have more access and privilege, some kind of secret handshake. Just look at their program. Some of the same faces keep showing up.
3 of the 14 Major Speakers are the same ones from last year.
Access and privilege. Words that institutions like NCSM trip over themselves to want for students, but hold their own gatekeeping as to who gets to say that.
Who gets to speak? Who gets to speak on mathematics?
As far as the last question, very, very, very few. Mathematics instruction on the other hand is heavily populated.
Pedagogy sells. Content doesn’t. I repeat. Pedagogy sells. Content doesn’t. You can package pedagogy. You can be expert in it. You can enter the competitive market of commoditized solutions.
Content? Jeez. Nobody can be expert. Parlay that with math history, and you’re talking terminal rookie/novice.
That’s me!! Knows a thimble of mathematics, but is still far more interested in learning something new than to get comfortable with that thimble. I think there is word for this.
I am finishing up my music book. Everyone in the music community I am connected to I trust 100%. There’s no ego. There’s no celebrity bullshit. There’s no gatekeeping. I am more than okay in being on the outside in the world of math ed.
I will know 100% now who my math ed friends are. It will go from dozens to a handful.
Thankfully.
What I am not okay with is that mathematics is also on the outside. Mathematics is just a buzzword now, having lost all its humanity, colour, awe, joy, wonder, and magic to heavily codified and overbaked pedagogical language.
Everyone in mathematics education seems drunk on Science of Learning.
I just waited for the other shoe to drop.
And it finally did, last week, when NCTM released its position on Culturally Responsive Mathematics.
On first examination, all those pillars of a recent NCTM position on Culturally Responsive Mathematics look powerful — that’s because they are.
However, closer examination reveals a position that is weighted significantly towards instruction/pedagogy that at best, seems to be negotiating with the Science of Learning movement, immediately weakening the position.
At worst, it seems to have abandoned any focus on mathematics that could be examples — pillars — of what culturally responsive mathematics looks like.
Let me give you an example that should be as subtle as a crossbolt to the forehead.
What if there was something like POC Responsive Rock and Roll. First thing you would expect would be content —and actual examples of such. You wouldn’t want me mired in talking about the need for it. At some point, you would want examples.
Play some fuckin’ music already, Sunil!(warning: my new book has the f-word appear over 150 times).
And then of course, we have the legendary Charles Strachwitz, ethnomusicologist, who founded Arhoolie Records, and went on to produce some of the greatest blues, jazz, zydeco, bluegrass, and soul music of the backyards and kitchens of Americana.
Culture needs Content. End of story.
So then where is the content of culturally responsive mathematics? This should have been an open invitation to the magical doorway to the history of mathematics — with specific examples — but it wasn’t.
Ironically, it was curriculum agnostic. Given that one of the positions that mathematics is not culture neutral, it seems odd to not critique/audit the actual curriculum which is going to have instruction that is culturally responsive.
How can such delivery occur if the focus isn’t on what is actually being delivered? Also, to have culturally responsive mathematics in educational institutions that are colonial by nature, hanging on to dear life with anachronistic ideas of standardized testing and “evidence-based instruction” — which recycles itself every generation with new packaging — is classic square peg meet round hole.
It’s not going to fit, unless you ham fist it through.
I strongly implore you to read the blog below before continuing.
Sometimes invocations of “evidence” or “science” in education are used not to begin a discussion but to end one. My new essay: “The Siren Song of ‘Evidence-Based’ Instruction”
Alfie Kohn
This is where Culturally Responsive Mathematics will go to die — because it chose to align itself with the high-rent language of evidence/efficiency, but offering low-rent content.
Where is the mathematics in such a position?
In the position paper, there were no references to books or people who would be examples of rich content.
If mathematics isn’t dead, it’s at the very least abandoned. The place where that should have never have occurred is in this area. I am not the only one. At this time, anonymity was preferred.
Sunil, I have had the same experience. Every time I attend a talk about equity or cultural responsive teaching in the math class, it’s unfortunately a bunch of talk — no math. I feel bad because I believe in the mission, but I am not enlightened by their talk. Let’s do math and show me what you mean. Demonstrate equity and cultural responsiveness — don’t just talk about it. I attended a great talk on math around the world at OAME and found that this speaker was actually doing the work without advertising it. If we are going to do this, let’s do it and stop with all the talk.There is some sad irony here, as I have been championing culturally responsive mathematics — focused on content — for most of my career.\
Math Teacher(30 years experience), California
I have been enlightened and inspired by the mission my entire teaching career. Sorry to be blunt here, but my journey has been with mathematics. How can there be any other way? Equity shot itself in the foot years ago, when it didn’t expand the lens of its mission to include math history. It not only would have been the pedagogically smart move, but it would have also insulated it from attacks from the right-wing groups claiming that culturally responsive mathematics is weaker mathematics.
That perspective was not altered by the position paper. At all.
Here is just a sampling of some of my blogs and presentations over the last 8 years.
Content. Content. Content.
In 2021, I was honoured with this invitation by US National Commission on Mathematics Instruction to present this.
My personal position on Culturally Mathematics is — has been — a stronger one than the one NCTM just put out.
That should never occur — an important institution should have the most robust, colourful, and up-to-date position statement on Culturally Responsive Mathematics.
It should. The reason why it doesn’t is because NCTM is caught up in the dragnet of the cults of pedagogy and efficiency. So much contortion to fit in with the status quo — at the expense of keeping mathematics human and transcending.
I am a devoted follower of Bertrand Russell here. The guy co-wrote Principia Mathematica. He was simply an academic beast of the 20th century. So then, why aren’t we listening to him in 2024?
Mathematics should be an experience rooted in light-heartedness and play — as that has been the totality of its history. It has transcended every race, culture, civilization, and socio-economic condition(death beds, suicidal ideation, poverty, incarceration, and concentration camps).
As such, the claim that mathematics IS NOT culture neutral is not entirely true. Sometimes it is. Are you telling me that the triangle attributed to Pascal, but was also discovered by Indians, Chinese, Arabs, and Italians before Pascal is related to culture?
Yes…the culture of mathematics. The culture of curiosity — which WE all possess.
No reference of curiosity anywhere in the position. At all. Culturally Responsive Instruction sold out to Science of Bullshit.
Is number theory related to culture? The more accurate position statement would be “Mathematics is sometimes not culture neutral”. Also, I guess we can stop saying mathematics is the language of the universe? Of course not. That’s ridiculous.
Closing the door on math history closes the door to all those stories.
It also, in Shakespearean irony, closes the door on Culturally Responsive Mathematics. But, I have to correct myself. NCTM didn’t actually emphasize that, did they?
They emphasized Culturally Responsive Instruction. Do you know how dangerous it is to neglect content here? For example, the current K to 12 curriculum has negative numbers being taught much later than positive numbers — separating it from them(and zero) is not only pedagogically harmful, but it is historically negligent.
You can’t have less than zero energy or matter in the universe, and yet we confidently say that a value of negative 2 is less than zero. We also have a temperature of absolute zero.
Where is the “mathematics is not culture neutral” here? Not only that, we have adopted a Western view of zero — that it is simply a placeholder.
Promising to deliver Culturally Responsive Mathematics through prioritization of delivery/instruction and compromising — intentionally or not — the quality of what is being delivered, diminishes the potential of that position.
It also diminishes the value of mathematics — to be seen primarily as a transactional tool/necessity and its value/currency only measured by external success.
Last year, I volunteered a whole day at the Osborne Juvenile Detention Center in San Jose. Bernadette Salgarino, current CMC President invited me to do so. Almost all of the students were Latino males between the ages of 15 and 17. Most had gang tattoos. Do you know what kind of math I did them — and left all of them smiling at the end of the day?
Number theory — which is culture neutral, and has always been.
The internal vector for finding the curiosity, joy, wonder, and beauty of mathematics has suffered much from institutional neglect, slowly fading into obscurity.
It’s dead. Mathematics is dead.
Last week, a long article that I wrote with my daughter appeared as the front cover issue of a new Wellness Education Magazine
The internal vector of learning mathematics has helped my daughter have a better relationship with mathematics and an improved mental health.
Culturally Responsive Mathematics instruction without equally important mathematics — the most important being found in the treasure chest of math history — is just simply the Science of Learning movement with equity language.
It’s a sellout, with the tax being the deemphasis on mathematics — as bloody absurd as it sounds. And ironically, it will be the demise of it all. We know the story.
When I went to teacher’s college, my mathematics education professor said you only need two qualities to be a good teacher: honesty and being a mutual learner.
We’ve turned teaching into a rigid science to satisfy the traditionalists — who are mostly white. Everything needs measurement. Everything needs analysis. Everything needs effectiveness.
Mathematics cannot breathe in that environment. It has been painful to watch the suffocation.
Time to stop fighting the existing reality…because I’ve stopped believing in it.
