How a child math prodigy sees numbers as shapes

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There’s a real important nugget near the end where he essentially says that there’s no one right way to do math. Keep this in mind the next time your weird uncle posts some “new math common core is bullshit” thing on Facebook. It’s not how you should solve a problem, it’s how you could.


I typically think of numbers as letters in a very short alphabet.

Maybe this is why I’m so bad at math.

Quick! What’s MCMXII divided by V?


child math whiz…

For a moment I thought this was the speaker in the video, who sports a rather luxurious beard for a child. They grow up so fast these days!

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I agree whole-heartedly. Curriculum developers are often well-versed in creative thinking, learning styles and child development. Unfortunately the very simple equation of (New Math + Standardized testing) / Gutting of public education transforms all this good will into something rather different.


To be fair, Jake Barnett isn’t a child either. But when he was a child, he was a math prodigy. As an 18 year old, he’s a physics PhD student, which is still really damned impressive.


How do you tell the difference between 1642 and 1646?

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It’s two 821-gons versus two 823-gons, obviously.


Look at whether King Charles still has an army?


Here, just for kicks, are two overlapping 821-gons and two overlapping 823-gons.


I’m never that much of a fan of these kinds of stories because I think that too often they feed an unhealthy obsession with genius, and perpetuate the myth that you need to be a “genius” to use math or develop the field. Don’t get me wrong, good on Barnett for having an interesting perspective, and it is interesting. But anyone can develop good math skills, and think about numbers and logic in new and interesting ways. I find most simply lack motivation for one reason or another.


I really like the idea of looking at numbers as shapes, and lovely little fractal-like shapes at that. Of course, my Pythagorean-Illuminati leanings would dictate that I would like this.


Whenever someone says they’re “not a math person”, they usually mean that they can’t stand math the way it’s taught in schools. Although I am a math person, I can still sympathize with that statement.


Do you have kids? I ask because that’s not been my experience of common core (or whatever the pedagogy of the day is).

My kids are pretty good at math (not too unexpected, considering there are two physics degrees and one math degree in the Ambiguous household), but they have no end of frustration in school math, owing to the fact that they always have to “show there work,” which is to demonstrate that they are thinking about the problem in the way that they are supposed to be thinking about it. At the elementary and middle school level there is always one, approved way of doing things. And it changes every few years.

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I’m not saying this to be confrontational, but I can’t say that I sympathize as much as you. I used to think like that, but the older I get the less I do. A little algebra, statistical awareness at the level of Darrell Huff’s famous book, and some basic problem solving skills is what I want the bulk of the population to have. Beyond that? I don’t know that it matters that people be “math people.” I’m not a “geography person” but we don’t have this weird expectation that everyone love geography and if the majority of humanity doesn’t like geography it’s being taught wrong. All my life I’ve been told math is taught wrong, but I find that most people don’t have a clear idea of what “right” looks like.

There’s a lot to unpack about math education that I’m frankly not qualified to. Most people aren’t. I find it interesting that teachers go to school to be teachers but everyone and their brother knows what’s wrong with schools from personal experience. But, I’m not impressed with most ideas about “teaching differently” that I hear from laypeople. Teachers do work, constantly, using evidence-based study to improve pedagogy. The way we teach math has changed in my lifetime but no one notices.


Cool video… if you like this prime number decomposition, check out this blog post on my favorite way to write numbers.


Perhaps, but it’s kind of irrelevant in any practical way. In the same way that I think we need evidence-based policies on a societal level, we need evidence-based pedagogy, and I don’t see where we have that.

As a first example, I think my son (who is getting ready to graduate high-school) has been through four total swap-outs of curriculum and pedagogy in his academic career. It kind of begs the question that if each of these were good enough to justify the downsides of swapping, how come after only a few years its no longer good enough? And where is the evidence that such trashing doesn’t make things worse for the kids? If each of these changes really was superior enough to justify the time and expense of retooling the schools and bumping the kids around, by now he should be in some kind of educational nirvana. He’s not.

As a second example these understandings of “learning styles” seem to totally ignore neurological studies and research when hey conflict with the fads of the day. Recent studies, for example, have suggested that the “old way of doing things” – things like rote memorization and cursive writing – actually help to lay down important neurological pathways for learning (cursive, for example, requires the student to manipulate symbols on a higher level than printing, owing to the fact that the letter change depending upon their context (surrounding letters)). And other studies suggest that rote memorization actually does help students learn how to think. But this conflicts with the “common sense” of the curriculum designers, so it is largely ignored.


I can say that this is not taught in education schools and is specifically debunked in most Psychology of Learning and
Psychometrics classes taught to teachers.

I think you’re conflating two unrelated things, the political and economic motivations that alter curricula and the development of new or better curricula. If schools have to “teach the test” in order to retain funding, as is the current model in many areas, the curriculum will shift to reflect that reality, and since parents are constantly unhappy with these tests and since there’s a metric fuckton of money in creating these tests for a company like Pearson, there’s a lot of cruft that gets thrown in the mix that means the decisions that get made are democratic in the purest sense: They give everyone a stomachache, except for private enterprise. This is why everything tends to shift a lot.

Now charter schools are the new fad. Never mind that they drain money from public schools and have yet to really demonstrate a significant advantage over our current crappy way of funding schools. Meanwhile your kids are taught by people. Those people are qualified, trained, and licensed to teach effectively and they’re the first to be treated like corrupt garbage in public discourse about education in the past ten years. The effect of trying to unify curricula and disempower teacher’s unions means that a lot of times teachers have to go along with bad curricula or teaching to the test (which I have yet to see a teacher think this is the best idea.) People think it’s because teachers don’t like having their salaries tied to the performance of people they cannot control. And they’re right, but it also means teachers have less time to take certain diversion and use the full range of their skills to teach more effectively.

All of these factors make for a delicious turd soup that makes people consider home-schooling.


These sounds like management and implementation problems, not problems with curriculum or standards. Perhaps education standards are a problem, if time has shown they can’t be implemented in a helpful way. What is for sure is that we are now carrying this discussion on in the wrong thread…


A lot of people don’t even have that. I’m not advocating that everybody is supposed to know Partial DiffEq or Modern Algebra or anything like that, just a basic understanding of probability/statistics and algebra. I’ve known so many people who tell me that they loved math until that damn X got thrown in there, and I’ve known a shocking number of adults who thought 1/3 is bigger than 1/2 or 0.05 cents is the same as $0.05. There’s a difference between being not interested or able to do higher maths (beyond Linear Algebra and DiffEq) and being numerically illiterate.

Geography is taught wrong, as are most subjects. I was taught geography like “here’s a list of rivers in Asia, come back when you’ve memorized them”. We were never taught why it matters, why geography and natural resources shape cultures, etc. The same is true for math, and pretty much every other subject. The emphasis is on rote memorization, or at least it was for me. Teaching to the test increases this emphasis on memorizing random crap, which is a shame, because discovering how things fit together is magical for me.

As far as insisting people love or even like a subject, that’s just something I can’t do and don’t want to do. All I expect is a little understanding of how things work and what they mean. Like, understanding that there’s an X percent chance of Y happening doesn’t mean OMG TEH SKY IS FALLING111!1!! and understanding that politics in Venezuela is different than politics in New Jersey.

Teach the how and why instead of just the what. The same goes for all subjects. It will encourage less spoon-feeding and more critical thinking.

I understand that. I’m sure a lot of the problems I’ve had with public primary education have been fixed by now, and I didn’t notice the changes because they were after my time. Maybe they were changing before or during my time as well, but only in the rich-kid school districts or in the more progressive private schools. Stopping teaching to the test is hardly an unpopular opinion even in education, and it’s hardly revolutionary, and it’s about to get better soon.