# More kids more math

February 8, 2016 9:34 PM Subscribe

"You wouldn’t see it in most classrooms, you wouldn’t know it by looking at slumping national test-score averages, but a cadre of American teenagers are reaching world-class heights in math—more of them, more regularly, than ever before." Peg Tyre in

Featuring:

Bridge to Enter Advanced Mathematics, a program for low-income students in New York City;

The International Math Olympiad, which the U.S. team won last summer for the first time in more than 20 years;

Math Circles -- find one near you!

Art of Problem Solving, a popular online math forum for math-loving kids;

Proof School, the brand-new math-emphasis high school in San Francisco;

and too many more to link!

*The Atlantic*covers the new wave of deeper, faster, and hopefully broader math education.Featuring:

Bridge to Enter Advanced Mathematics, a program for low-income students in New York City;

The International Math Olympiad, which the U.S. team won last summer for the first time in more than 20 years;

Math Circles -- find one near you!

Art of Problem Solving, a popular online math forum for math-loving kids;

Proof School, the brand-new math-emphasis high school in San Francisco;

and too many more to link!

Thanks for posting this! At 2, my kid is still a little young for this to be a thing, but it'll happen before I know it. This definitely seems like a more inspiring and empowering alternative to the Kumon classes all my classmates were attending when I was a kid.

posted by town of cats at 9:58 PM on February 8, 2016

posted by town of cats at 9:58 PM on February 8, 2016

It's weird having a mathy kid. Math, like most everything I guess, is something that anyone can do with enough practice, but I was one who was always so slow at it that I hated and avoided it. I finally took algebra in my 30s (pre-rec for nursing school) and while I was excited to find out that I

My kiddo is the opposite. She just

This article created some anxieties for me - she's already halfway through 8th grade, is it too late to give her the math challenges she 'needs'?

Weirdly, the article does talk about the class inequalities in who gets access to math education, but it kind of misses some of the heart of it. It's great to find those "gifted" poor kids, but there are social factors that do influence who is "good" at math, so there will probably never be as many of those "gifted" poor kids as their are privileged kids whose parents send them to these special and oh-so-expensive programs that I'm already worried about having not sent my kid to.

posted by latkes at 10:28 PM on February 8, 2016 [5 favorites]

*could*learn it, I certainly didn't take to it quickly or intuitively.My kiddo is the opposite. She just

*gets*math. Each new concept seems to need explaining only once. Unfortunately, her small school offers only one speed of math progression (which is a plus and a minus of the Common Core model as well). She does Kahn Academy on the side but it's not really enough.This article created some anxieties for me - she's already halfway through 8th grade, is it too late to give her the math challenges she 'needs'?

Weirdly, the article does talk about the class inequalities in who gets access to math education, but it kind of misses some of the heart of it. It's great to find those "gifted" poor kids, but there are social factors that do influence who is "good" at math, so there will probably never be as many of those "gifted" poor kids as their are privileged kids whose parents send them to these special and oh-so-expensive programs that I'm already worried about having not sent my kid to.

posted by latkes at 10:28 PM on February 8, 2016 [5 favorites]

I think the term "advanced-math community" should be for referring to research mathematics. Not so much young people training for Olympiads or industry jobs. It's a nontrivial difference - in terms of motivation, culture, philosophy, even if there is a concrete relationship between the two categories of intellectual labor (as the article briefly lets on, if unconsciously by the author).

posted by polymodus at 10:29 PM on February 8, 2016 [6 favorites]

posted by polymodus at 10:29 PM on February 8, 2016 [6 favorites]

I'm pretty curious about that difference: I guess I sensed that kids who are doing these competitive or workforce-readiness-focused programs are really a different core than those folks who just want to do deep, complicated math when they grow up, but, maybe not? I mean, if I want my kid to get to explore math in a deep and exciting way, but I don't give a crap if she decides to go to/gets into the most prestigious school or gets a high paying tech job, how should I be helping her?

posted by latkes at 10:41 PM on February 8, 2016 [2 favorites]

posted by latkes at 10:41 PM on February 8, 2016 [2 favorites]

Yeah, polymodus, I got through an embarrassing percentage of the article before I realized that these kids were not doing anything I'd recognize as "advanced math". But I guess to most people, including many journalists, exposure to mathematics ends at high school. So for them this is as advanced as it gets.

It sounds like a fun way to build problem solving skills and confidence that doesn't hinder on performing arts or physical activity, though, and I'm all for it. But yeah, the terminology was jarring to me, too.

posted by town of cats at 11:05 PM on February 8, 2016

It sounds like a fun way to build problem solving skills and confidence that doesn't hinder on performing arts or physical activity, though, and I'm all for it. But yeah, the terminology was jarring to me, too.

posted by town of cats at 11:05 PM on February 8, 2016

I recall listening to an IMO silver medalist grouse about not really being able to do research math because he didn't have the patience to read literature in anything but number theory and other competition math things. So he ended up doing neural networks stuff (also because there's a lot more money in it), and he now considers the contest problems a hobby that he wastes too much time on.

You do need to be coached well to be at those levels. The motivation should absolutely not be for monetary gain,

The expense of the programs is... remarkably uncorrelated with the goodness of the programs. How to evaluate? Get a person who likes maths to do it.

There is a sort of feeder system from competition math to research math, but it's filled with various holes, which leak out into tech a little and finance a lot. Much holier nowadays, for obvious reasons.

posted by hleehowon at 11:25 PM on February 8, 2016 [3 favorites]

You do need to be coached well to be at those levels. The motivation should absolutely not be for monetary gain,

*even if the end goal is monetary gain*. That is because it's not possible to sustain such a self-centered goal for the length of time and effort that this sort of thing needs. And in practice, at the highest levels, nobody cares about monetary gain. It's like how the prizes at the best quizbowl tournaments are crappy used books the organizers got for $1 each at the used bookstore.The expense of the programs is... remarkably uncorrelated with the goodness of the programs. How to evaluate? Get a person who likes maths to do it.

There is a sort of feeder system from competition math to research math, but it's filled with various holes, which leak out into tech a little and finance a lot. Much holier nowadays, for obvious reasons.

posted by hleehowon at 11:25 PM on February 8, 2016 [3 favorites]

Math Olympiad kind of stuff seems way closer to research math than industry math to me? But then I never got terribly far in any of these areas, so I could be talking out my ass.

posted by kmz at 11:26 PM on February 8, 2016 [1 favorite]

posted by kmz at 11:26 PM on February 8, 2016 [1 favorite]

kmz: Math Olympiad kind of stuff is indeed closer. It isn't the same thing.

posted by hleehowon at 11:27 PM on February 8, 2016

posted by hleehowon at 11:27 PM on February 8, 2016

Yeah I don’t know if people really realize how much access to the "math world" (which is like so so tiny) is dependent on class and cultural capital. Here’s an indicative data point—of the friends I had in undergrad who went on to a top six math grad school, ~90% of them had at least one parent with an advanced graduate degree, and ~70% of them had at least one parent who was on the faculty of a university. I really hope that these sorts of efforts allow for numbers like these to change.

But idk—I worry that a lot of these sort of things for kids put an undue amount of emphasis on being very quick or very clever, which is a part of mathematical culture that I think is really toxic. (And yeah, I think competition math-- especially competition math in middle school and high school, but also the Putnam--does just as much bad as it does good; in particular, I think competition math serves to keep a ton of people who should be in math

I guess my perspective here is pretty myopic tho in that I'm just talking about how to most effectively create good mathematicians and good mathematical culture. To be clear: I definitely think that the more kids get exposed to math reasoning at a young age, the better--even if those kids never take a class beyond precalc. And a lot of these programs seem really cool! I have a friend who teaches at the Proof School who recently taught her students about projective space and basic algebraic geometry and omg I am so jealous of those kids.

(latkes: don’t worry too much—I did not do special math programs or anything like that in high school and still managed to go pretty deep into math before I started undergrad. If you want concrete suggestions about how to support a mathy 8th grade girl, feel free to message me!)

posted by bergamot and vetiver at 12:55 AM on February 9, 2016 [11 favorites]

But idk—I worry that a lot of these sort of things for kids put an undue amount of emphasis on being very quick or very clever, which is a part of mathematical culture that I think is really toxic. (And yeah, I think competition math-- especially competition math in middle school and high school, but also the Putnam--does just as much bad as it does good; in particular, I think competition math serves to keep a ton of people who should be in math

*out*.)I guess my perspective here is pretty myopic tho in that I'm just talking about how to most effectively create good mathematicians and good mathematical culture. To be clear: I definitely think that the more kids get exposed to math reasoning at a young age, the better--even if those kids never take a class beyond precalc. And a lot of these programs seem really cool! I have a friend who teaches at the Proof School who recently taught her students about projective space and basic algebraic geometry and omg I am so jealous of those kids.

(latkes: don’t worry too much—I did not do special math programs or anything like that in high school and still managed to go pretty deep into math before I started undergrad. If you want concrete suggestions about how to support a mathy 8th grade girl, feel free to message me!)

posted by bergamot and vetiver at 12:55 AM on February 9, 2016 [11 favorites]

I have studied in the British and the American school systems, this is my experience

The math education in the United States system suffers from too much fragmentation of concepts and not enough holistic understanding of Arithmetic (which includes Algebra, and Geometry) and Mathematics (the Mechanics of things, Calculus, Trignometry). The GCE O Levels that I have in Mathematics and Advanced Mathematics taught us all the concepts in one coherent stream. In the American I was in the awkward position of choosing between Trignometry (to which we'd been given the merest introduction in the early lessons of differential calculus) and Advanced Placement Calculus. I failed the class but passed the AP exam because I could study all the material together for the exam but the weekly tests were murder without context.

posted by infini at 1:31 AM on February 9, 2016 [2 favorites]

The math education in the United States system suffers from too much fragmentation of concepts and not enough holistic understanding of Arithmetic (which includes Algebra, and Geometry) and Mathematics (the Mechanics of things, Calculus, Trignometry). The GCE O Levels that I have in Mathematics and Advanced Mathematics taught us all the concepts in one coherent stream. In the American I was in the awkward position of choosing between Trignometry (to which we'd been given the merest introduction in the early lessons of differential calculus) and Advanced Placement Calculus. I failed the class but passed the AP exam because I could study all the material together for the exam but the weekly tests were murder without context.

posted by infini at 1:31 AM on February 9, 2016 [2 favorites]

The British system layers educational depth in its annual curriculum promotion - we studied Acids, Alkalis and Bases in 4 years of secondary school, each year getting more and more complicated topics on top of the basics of salt and water.

posted by infini at 1:35 AM on February 9, 2016

posted by infini at 1:35 AM on February 9, 2016

if you are old enough and have been in "STEM" long enough you will have encountered a few math Olympiad types from the Soviet Union or eastern bloc. it was definitely a type and there was often a kind Olympic malaise ie. like other Olympic athletes they had hit their peak young and now it was all down hill.

I have a PhD in math, but I was not a mathy kid. I didn't learn how to solve a quadratic equation until I was 18 and taught myself how to "complete the square" in my own way. I get easily frustrated with logic puzzles, suck at sorting algorithms, etc. yet, I've contributed in my small way to research mathematics. there are fields in mathematics that attract competitive problem solvers: number theory, algebraic number theory in particular, is definitely one. but math is a land of contrasts...

posted by ennui.bz at 3:08 AM on February 9, 2016 [5 favorites]

I have a PhD in math, but I was not a mathy kid. I didn't learn how to solve a quadratic equation until I was 18 and taught myself how to "complete the square" in my own way. I get easily frustrated with logic puzzles, suck at sorting algorithms, etc. yet, I've contributed in my small way to research mathematics. there are fields in mathematics that attract competitive problem solvers: number theory, algebraic number theory in particular, is definitely one. but math is a land of contrasts...

posted by ennui.bz at 3:08 AM on February 9, 2016 [5 favorites]

MetaFilter: I could be talking out my ass.

posted by oheso at 3:21 AM on February 9, 2016 [3 favorites]

posted by oheso at 3:21 AM on February 9, 2016 [3 favorites]

*But idk—I worry that a lot of these sort of things for kids put an undue amount of emphasis on being very quick or very clever, which is a part of mathematical culture that I think is really toxic. (And yeah, I think competition math-- especially competition math in middle school and high school, but also the Putnam--does just as much bad as it does good; in particular, I think competition math serves to keep a ton of people who should be in math out.)*

I agree with you about it being a double-edged sword. I suspect there are kids that it works really well for. Of course, they're going to be the ones who have some kind of knack for math competitions, even if they're not "good". But it took me an awfully long time to really realise that the fact I'm rubbish at math competitions didn't actually reflect on my mathematical ability. I did math team in high school and was fairly mediocre until senior year, when I did the oral competition, which somehow doesn't require the knack for problem-solving* in quite the same way. It helped that orals was seen as "elite" and I was fairly good at it (and that my friend, who was generally cocky and better at the other competitions than me, was crap). But in undergrad, I'd end up on the AoPS website one way or another and feel bad about myself--these were people worried about the USAMO, when a halfway mediocre score on the AIME was my peak. I guess this is a long way of saying that I ended up as a math major despite competitive math. Math team helped, but really only because of the practices where no one else showed up and Mrs Gibson and I would talk about math, not the problems. (Ironically, I ended up doing a PhD in combinatorics. The math team was almost uniformly terrible at discrete math. It clicked in undergrad.)

*NB: The ability to solve problems in math competitions always gets called "problem-solving". My problem-solving in the usual sense is just fine, thanks.

posted by hoyland at 4:39 AM on February 9, 2016

I guess I have a different perspective on this, just because most of the students I'm dealing with don't aspire to get PhDs in math. Most of them want to do something practical: medical or dental school, maybe computer science or actuarial degrees. And they typically crash and burn out of their chosen major in their first year because they don't have the quantitative skills. I can see how calling this advanced math would be galling to people who really did advanced math, but to me, it sort of seems like a revelation. The way my students have done math is that they're given a list of steps to memorize, and then on the test they're given the exact same problem with the exact same steps and new numbers. They cannot do a problem that takes any application or creativity at all. They think that professors are being unfair when they're given that kind of problem. This sounds amazing:

So basically: I think that Metafilter may be full of people who are too genius-y to benefit from this, and I think the article may have oversold the math aptitude of the kids who come out of this system. They're going to be kids who can do well in college math classes, not kids who are going to make new contributions to our understanding of math. But I can see a huge amount of merit for ordinary kids who want good math skills and to see math as fun and creative.

posted by ArbitraryAndCapricious at 5:06 AM on February 9, 2016 [4 favorites]

The new outside-of-school math programs like the Russian School vary in their curricula and teaching methods, but they have key elements in common. Perhaps the most salient is the emphasis on teaching students to think about math conceptually and then use that conceptual knowledge as a tool to predict, explore, and explain the world around them. There is a dearth of rote learning and not much time spent applying a list of memorized formulas. Computational speed is not a virtue. (“Cram schools,” featuring a mechanistic, test-prep approach to learning math, have become common in some immigrant communities, and plenty of tutors of affluent children use this approach as well, but it is the opposite of what’s taught in this new type of accelerated-learning program.) To keep pace with their classmates, students quickly learn their math facts and formulas, but that is more a by-product than the point.And I also understand how the emphasis on competition could be a bummer, especially if your talents didn't lend themselves to math competitions. But many of my students played sports in high school, and that team experience was huge for them, even if they weren't especially good. They had fun; they worked with other kids towards a goal; competition pushed them to work harder. I think it might be great if they associated that camaraderie with intellectual, rather than athletic pursuits.

So basically: I think that Metafilter may be full of people who are too genius-y to benefit from this, and I think the article may have oversold the math aptitude of the kids who come out of this system. They're going to be kids who can do well in college math classes, not kids who are going to make new contributions to our understanding of math. But I can see a huge amount of merit for ordinary kids who want good math skills and to see math as fun and creative.

posted by ArbitraryAndCapricious at 5:06 AM on February 9, 2016 [4 favorites]

So this is more an Ask Me question, but I think my yield will be better here.

If you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school, what would you recommend to give them opportunities for quantitative problem solving?

posted by leotrotsky at 6:09 AM on February 9, 2016 [3 favorites]

If you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school, what would you recommend to give them opportunities for quantitative problem solving?

posted by leotrotsky at 6:09 AM on February 9, 2016 [3 favorites]

If

the problem is that it really isn't a question of "above and beyond" but, unless they are very lucky to get a math teacher who personally enjoys math, what they are learning to do in school is more like learning to program your vcr (if you can remember what a VCR was) than anything resembling mathematics. back when I taught university math, I always joked about how my students had learned to become artificially intelligent when doing math...

but the problem isnt what but who. it's about putting your kid in contact with people who like solving math problems when they come up, and they can come up in a variety of situations. which is exactly the problem with US education: we believe teachers are education professionals, who can competently teach any curriculum that gets handed to them, rather than people who have learned something well and love it.

posted by ennui.bz at 6:28 AM on February 9, 2016 [1 favorite]

*you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school*the problem is that it really isn't a question of "above and beyond" but, unless they are very lucky to get a math teacher who personally enjoys math, what they are learning to do in school is more like learning to program your vcr (if you can remember what a VCR was) than anything resembling mathematics. back when I taught university math, I always joked about how my students had learned to become artificially intelligent when doing math...

but the problem isnt what but who. it's about putting your kid in contact with people who like solving math problems when they come up, and they can come up in a variety of situations. which is exactly the problem with US education: we believe teachers are education professionals, who can competently teach any curriculum that gets handed to them, rather than people who have learned something well and love it.

posted by ennui.bz at 6:28 AM on February 9, 2016 [1 favorite]

*If you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school, what would you recommend to give them opportunities for quantitative problem solving?*

If it's problem-solving he/she likes, why not try setting him/her up with programming instead? It's a little easier to organically find complex new problems to solve there than it is in traditional math without a school like the Russian school.

Do you live near a large research university? Is there any chance that a professor would let them audit a math course such as introductory calculus? I had friends doing that by early high school.

Statistics is under-taught in American school in my opinion. I like The Drunkard's Walk for one interesting and pretty accessible introduction to our statistical fallacies. It's not really high-level math but it's interesting to explore the intersection of math and psychology.

posted by R a c h e l at 6:39 AM on February 9, 2016

*we believe teachers are education professionals, who can competently teach any curriculum that gets handed to them, rather than people who have learned something well and love it*

There's danger in the opposite perspective, too, especially at the university level: we assume that people who have learned something well make good teachers, when that's very often not the case. My younger brother has had a series of retired math/engineering/CS professionals as high school teachers and even though they are clearly interested in the topic and in teaching, many still struggle to communicate effectively and help students ask good questions.

posted by R a c h e l at 6:44 AM on February 9, 2016 [1 favorite]

*what would you recommend to give them opportunities for quantitative problem solving?*

My kid really liked the online course he took at Art of Problem Solving. But, you know, I had $300 to spend on it, so my kid got to take the course, which is one of the issues the linked article is about. To be fair, AOPS does have a ton of free content; I would suggest your kid check out the problems in the "Alcumus" section.

posted by escabeche at 7:01 AM on February 9, 2016 [1 favorite]

*If you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school, what would you recommend to give them opportunities for quantitative problem solving?*

So I can only speak from the perspective of being that kid but what did it for me was simply having a lot of interesting math and science around the house. Just to give you an example from a few years ago at thanksgiving (We were all adults at the time, but my whole childhood was like this) We all come down for breakfast, and my dad mentions he saw a clever variation on the old brainteaser about coins and a scale. My sister and I abandon our breakfasts to work our way through it with him, while my mother shakes her head and grumbles about breakfast getting cold. This was an everyday occurrence in my house all my life. These puzzles were a fun thing we did together, not for educational enrichment, but for the entertainment and togetherness. (Not to exclude my mother, she introduced me to a lot of cool science too)

Like Bergamot and Vetiver said above, a lot of it was an access thing. Our mother is a biochemist, our father is a theoretical mathematician and computer scientist - my sister and I went on to programming and actuarial science (Well, my degree is in chemical engineering and math, but insurance seemed more interesting). And my dad sometimes admits that if the business world had been an option for him that he would have rather been an applied mathematician, but that wasn't available, so academics it was.

posted by antimony at 7:42 AM on February 9, 2016

*If you have a kid, and they're clever and enthusiastic and you think they would thrive in mathematics above and beyond what they're getting in school, what would you recommend to give them opportunities for quantitative problem solving?*

If they can learn from video instruction, Kahn Academy covers pretty much everything.

posted by Huck500 at 7:44 AM on February 9, 2016 [1 favorite]

Some of that money you spend on AoPS is going to support BEAM, which is something you can feel very good about.

posted by Wolfdog at 8:08 AM on February 9, 2016 [1 favorite]

posted by Wolfdog at 8:08 AM on February 9, 2016 [1 favorite]

Back in the late 90s, I was one of those middle class mathy kids who got to do all the cool programs. I was part of the Boston Math Circle from the second year. I went to HCSSiM (Hampshire College Summre Studies in Mathematics) and before that CTY, where I did math classes.

I'm really glad to see these programs are hitting kids early. The math burnout sets in way too early.

I agree that the emphasis on competition is misplaced. Competition can be fun, but it is also frustrating to the students who lose. I still remember the students from poorer schools not having a chance at MathCounts, presumably because they were from environments where the extra studying and tutoring was not available. The thing I remember the most from the Math Circle I was in (Boston) was when we did a class on i

The article glosses over another big difference that you find in mathematics instruction (at least that I saw before dropping out of my ed program). One school of thought tries to bring the top students up even higher. The other tries to get the struggling students up to a competency level. Both say they are trying to do both, but it seems to me that the technique changes depending on which type of student it is aimed at, at least in the US.

Part of the solution, as always, would be training elementary school teachers in math to the point that they're comfortable. But we all know throwing money into education is a black hole unless it's going to charter schools without unions (preferably ones that have corporate backers).

posted by Hactar at 8:49 AM on February 9, 2016 [1 favorite]

I'm really glad to see these programs are hitting kids early. The math burnout sets in way too early.

I agree that the emphasis on competition is misplaced. Competition can be fun, but it is also frustrating to the students who lose. I still remember the students from poorer schools not having a chance at MathCounts, presumably because they were from environments where the extra studying and tutoring was not available. The thing I remember the most from the Math Circle I was in (Boston) was when we did a class on i

^{i}(it's e^{-π/2}, by the way) and they used rotations to show the difference between sine and cosine. The rest is a bit fuzzy, as I'm going back over 20 years for the memory. This is not something you would do in preparation for a competition. This is something you explore because the idea of raising something to an imaginary exponent is mind blowing. I know we proved the Browler Fixed Point theorem also, although I can't remember the technique. Once again, incredibly cool math (you can't shuffle the points around on a ball without having one stay in the same place unless you do some cutting and pasting), but not useful until my senior year of college when I used it in my undergrad thesis. (I was incredibly excited when I saw it pop up.)The article glosses over another big difference that you find in mathematics instruction (at least that I saw before dropping out of my ed program). One school of thought tries to bring the top students up even higher. The other tries to get the struggling students up to a competency level. Both say they are trying to do both, but it seems to me that the technique changes depending on which type of student it is aimed at, at least in the US.

Part of the solution, as always, would be training elementary school teachers in math to the point that they're comfortable. But we all know throwing money into education is a black hole unless it's going to charter schools without unions (preferably ones that have corporate backers).

posted by Hactar at 8:49 AM on February 9, 2016 [1 favorite]

So these academies are concentrating the teachers who are good at math, good at teaching it, and enthusiastic about it. And all three things are required for good math education for most students.

How do you scale that out to the millions of math classrooms needing teachers? Is it even possible? Or is this destined to remain a luxury good?

posted by clawsoon at 8:53 AM on February 9, 2016

How do you scale that out to the millions of math classrooms needing teachers? Is it even possible? Or is this destined to remain a luxury good?

posted by clawsoon at 8:53 AM on February 9, 2016

It might take a short generation of the academies to produce enough mathophiles to staff all our schools. Nasty damping feedback, though: as nath-tolerance gets less rare the career advantage presumably drops and the parental willingness to pay extra does too? We can hope the feedback is slow.

posted by clew at 12:03 PM on February 9, 2016

posted by clew at 12:03 PM on February 9, 2016

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