Home > Uncategorized > How do we make math enrichment less elitist?

How do we make math enrichment less elitist?

February 9, 2016

There’s a great article in the Atlantic that’s making waves on my Facebook page (granted, my Facebook feed has more than its share of math nerds).

Called The Math Revolution and written by Peg Tyre, the piece describes the recent proliferation of math education programs for young people, which include the old-fashioned things I grew up with like math team and HCSSiM, but also include new stuff I’ve heard about (Russian math circles, Art of Problem Solving) as well as stuff I’ve never heard of (MathPath, AwesomeMath, MathILy, Idea Math, sparc, Math Zoom, and Epsilon Camp).

What I like about this piece is it directly addresses something that has bothered me for years and has, frankly, kept me from devoting myself to creating or running one of these programs. Namely, the extreme elitism involved. From the article:

And since many of the programs are private, they are well out of reach for the poor. (A semester in a math circle can cost about $300, a year at a Russian School up to $3,000, and four weeks in a residential math program perhaps twice that.) National achievement data reflect this access gap in math instruction all too clearly. The ratio of rich math whizzes to poor ones is 3 to 1 in South Korea and 3.7 to 1 in Canada, to take two representative developed countries. In the U.S., it is 8 to 1. And while the proportion of American students scoring at advanced levels in math is rising, those gains are almost entirely limited to the children of the highly educated, and largely exclude the children of the poor. By the end of high school, the percentage of low-income advanced-math learners rounds to zero.

So my question today, dear readers, is how to address this problem, which I assume starts before kindergarten. Do we just expand math enrichment programs so much that they eventually become accessible to more people?

And beyond access, how could we possibly keep costs down, considering that the people who are competent to teach this stuff have other lucrative offers?

It’s clearly a transitioning problem to some extent, since once we have enough people who speak “fun math,” there will be enough people to train the next generation. And the beauty of math is that you really only need a stick in the sand (and time, and a devoted teacher and ready students) to make it happen.

Thoughts appreciated.

Categories: Uncategorized
  1. Priscilla Bremser
    February 9, 2016 at 10:19 am

    Well, there’s this: https://navajomathcircles.org/ (I saw the movie at JMM – really good. http://www.zalafilms.com/navajo/)

    Liked by 1 person

  2. DJ
    February 9, 2016 at 10:29 am

    You should meet up with Dan Zaharopol. He lives in NYC. I can introduce you if you’d like. He runs SMPMS (http://www.artofproblemsolving.org/spmps/about.html), which is a zero-fee summer math enrichment boarding program specifically designed for underserved students and in fact only admits underserved students.

    PROMYS charges only room and board for family incomes under $60k and makes a serious attempt to provide financial aid for those who cannot afford costs.

    Running a non-elitist math enrichment program involves basically spending the entire rest of the year raising funds for the program. It can be done, but not while doing much of any other math.


    • DS
      February 9, 2016 at 11:14 am

      Cathy, you’ve possibly even met Dan before, when you visited Mathcamp in Vancouver 15 years ago. (He’s also left comments on this blog in the past.)

      Canada/USA Mathcamp doesn’t charge at all for family incomes under $60k. I don’t think anyone has any better ideas for how to make this sort of thing happen than finding people (or foundations) with money who want to give money for it, as DJ says.


    • February 9, 2016 at 1:10 pm

      Thanks for the mention!

      BEAM doesn’t spend its full year fundraising (thank goodness), but it does take time. As we’ve built up a bigger organization with more staff, the process has become much easier since when I was just doing it myself all the time!


      • DJ
        February 9, 2016 at 7:22 pm

        You’re welcome! I didn’t make the connection to BEAM because I didn’t realize you had renamed.


        • February 9, 2016 at 10:13 pm

          It was long overdue! Apparently I didn’t spread the word as broadly as I’d intended, however.


  3. February 9, 2016 at 11:06 am

    *conflict of interest declaration: I am currently president of the PROMYS Foundation, a 510(c)(3) that supports the PROMYS program. Also, I am exploring business opportunities related to education enrichment, though, at the time of writing, do not have a financial interest in any education business. All of my comments are my own and not official statements from any organization.*

    A lot to write about here:
    (1) the actual cost for a student to attend one of the summer enrichment programs may be far less than the implied $6k from the article. For example, PROMYS only asks for room and board for families with incomes below $60k and there is further financial aid available. I believe the same is true at many of the existing “sister” programs.

    (2) Most of the programs struggle with outreach to communities that are traditionally under-represented. This is a gap that someone could fill, though smart and motivated people have tried. Which is to say, smarter and more motivated people than me, so it is a hard problem for me.

    (3) Math circles, in my experience, are, generally, pretty informal groups that are run by volunteers (mostly parents) as a labor of love. They are not rationed by direct cost, but rather rationed by (a) limited supply of such volunteers and (b) limited outreach of the volunteers.

    (4) There are tons of amazing and zero-marginal cost resources available on-line. I started blogging about math activities with the hope I could emphasize this point and make it easier for other parents to jump in, since it can be hard to navigate the huge list of choices. I know that I’ve fallen far short of my goal, but can at least offer some references here for where people could get started.

    To be honest, I am not empathetic nor broadly experienced enough to really know what hurdles other people have in accessing and using these resources. I’d be delighted if someone wanted to collaborate with me.

    (5) A lot of the approaches and techniques illustrated in the article are standard parts of the math wars/math reform discussion. Collectively, we do know how to teach excellent lessons, design excellent curriculum, deliver excellent schools, and build excellent educational systems. There is a small inhibiting factor where those involved like to have flame wars about technical details and differences that don’t actually matter.

    The bigger issue…we don’t actually want to do it. This is analogous to your point about infrastructure. We do know how to get potable water to the residents of Flint MI, but we choose not to.

    I think the reason is pretty well explained by The Red Queen: families are competing against each other and the faster the whole pack runs, the harder one has to work to get to the front.

    Finally, just to be cheeky, how does this post square with the other <a href="https://mathbabe.org/2016/02/01/raising-kids-the-right-way/"recent one about no pushing kids?


    • February 9, 2016 at 11:12 am

      Thanks for the resources. And just to answer the last question: I wouldn’t force my kids into the programs I think of starting. They wouldn’t like them and I wouldn’t want them there, or for that matter any kid who doesn’t want to be there. But there should be ways for nerds of all races and financial resources to join something like this if they want to.

      I know something about how this stuff is publicized, and it’s obviously much easier to do among highly educated Tiger parents. So yes, it’s a really difficult problem.


  4. Lara
    February 9, 2016 at 11:13 am

    Make it available, make it free, make it fun, and make damn sure the teacher knows how to teach deeply and engage the kids.

    Long term change:
    I think the “competent to teach this” is a key component often overlooked. We can’t rely on industry professionals coming in. If that’s the only hope it’s too late – it’s a bandaid. We have some great great teachers (lots of teacher in my family so please understand I am not anti teacher), but in the US we have some real structural problems in education (let’s not even get into curriculum, politics or Common Core). We accept people with miserably low skills into the profession. Often elementary teachers barely know the math past where they are teaching, Secondly, we don’t teach classroom management, we aren’t good at helping teachers create exciting real world problems to present, and we often don’t teach things like building lesson plans and units (crazy). Most of our ed instruction in theoretical. So if you want to really address this you have to improve the level of teaching skill and teacher content knowledge. If we staffed public schools with extremely talented teachers we’d already be ahead. 1) Create a superior school for pedagogy; 2) Make certification extremely rigorous to get through; 3) Pay for master’s degrees; 4) Retain only excellent teachers; and then 4) Pay them well. (fantasy?) That would mean that, like Finland, being a teacher is prestigious and means you’re a smarty with a decent income.

    Current reality
    If a school is Title I they get a lot of funds for just such programs. The difficulty is this – why would anyone with those skills do these part time gigs? No matter how well you pay them it’s max 18 hours per week. Any full time work would likely overlap with afterschool, weekend and summer camps. Which brings me back to my long term change – if you have fantastic math teachers in school, THEY can raise the level of understanding during regular hours and THEY can oversee clubs and THEY provide enrichment activities afterschool and in the summer (when they are off) – and get paid even more for their skills.

    So here is the answer – use your nonprofit to reach teachers currently teaching that specific population . Make them absolutely fantastic, provide the structure of the program and curriculum if necessary, pay them for their professional development and afterschool hours, and then let them get to it.

    Liked by 1 person

  5. February 9, 2016 at 12:06 pm

    I share you worry about access to these enrichment programs. The small step that I took to try to do something to help bridge that gap was to start putting fun math projects for kids on line. That way kids (or parents or teachers or anyone) interested in math could see and use for free. My specific goal was to show kids other kids having fun doing math, so most of the projects involve my kids.

    One bit of fun that we’ve had recently has been sharing math ideas that professional mathematicans have shared on line or somehow or other in public. So, not contest math but more like math that mathematicians have found interesting to study. In a couple of “Family Math” nights that I’ve run at my younger son’s school in the last month (which, just to be clear, were free and open to everyone) the kids have absolutely loved playing around with these ideas. This week I’m hoping to share a little bit about the surreal numbers with the 4th and 5th grade students. I wrote up some of those projects here – and most (probably all of them except Laura Taalman’s 3d printing projects) require little more than a paper and pencil.


    Anyway, you don’t have to start a camp or a math circle or anything formal and organized to reach kids – you could just share ideas that you think kids would find interesting right here on your blog (or a k-12 version of the blog). You have such an amazing gift for communicating math ideas that I think anything you did like that would be an incredible success and would reach and inspire way more people that you might expect.


  6. February 9, 2016 at 1:05 pm

    I think there are two big barriers to low-income/underserved students entering these enrichment programs.

    (1) Mathematical preparation. In part, students often don’t have the opportunity to learn foundational school math very well. In part, students don’t have access to mid-level scaffolding experiences (like school “gifted” programs or math circles) to build mathematical reasoning skills.

    (2) Community support/strong desire/finding them. Growing up a math nerd, I did seek out a lot of opportunities. But I also had parents who were able to navigate bureaucracy. I had a dad who was a mathematician, which led me to self-identify as a mathematician. I had science-y books, and crucially, I had parents who were proud of me for reading them. If we could create a supportive environment that supports students’ inclination to seek out these opportunities, that would go a long way.

    I’ve found that the most successful BEAM students have some of these elements in their lives. For example, students might have some kind of extracurricular math that their parents enrolled them in (sacrificing part of their income for their kids’ educations) or they might have an uncle who’s en engineer. BEAM is able to take the kids a lot farther when we’re only filling in some of the gaps, not *all* of the gaps.

    We’d be a lot better off if we started earlier. By when we get the kids just after 7th grade, there’s a lot of ground to make up. We’re moving one year younger this year to bring kids in the summer after 6th grade. Ultimately, doing something before kindergarten would be great. If we could work with kids longitudinally over that period of time, I think we could do something tremendous.


    • February 9, 2016 at 8:20 pm

      Dan, I’m curious about how you see this kind of support scaling. The biggest hurdle I hit in SF was not the demand for math circles (even in schools that BEAM might recruit from), but rather having the time or being able to gather the teachers able to create an experience that pulls students into loving math and feeling confident about learning more.

      Sites like AoPS and Brilliant.org scale much more easily, but are currently missing the kinds of hooks needed to, as you say, find these students and fill in enough gaps that they’re able to take advantage of these resources. Is there a way these sites could be more accessible to students from a wider variety of backgrounds?


      • February 9, 2016 at 10:17 pm

        Right now, the sites are very good at reaching out to white and Asian communities with good educations. By that I mean: they are popular there so they are known there; language usage matches language usage in highly-educated communities; the people and culture are nerdy variations of those communities. I think they could be more accessible with a concentrated effort at diversity that started early in their growth (so that it was “baked in”) and if they made a strong effort at social media usage/advertising that reached those groups.

        FWIW, I think the key limitation to scaling math circles or BEAM is funding. People could be found over time, if there were real jobs there doing it. As a hobby, you can’t scale in any focused way.


        • February 14, 2016 at 12:25 pm

          So, on the one hand, I agree with you: if a site has, at it’s core and from the moment of its founding, the ambition of reaching out to such students, this site is going to be in a better philosophical place to achieve this goal. Unfortunately, this theoretical site might not be in a great practical place to achieve its goal – given that it has to fight for every member added to its audience.

          Therefore, at least for now, and given that the existing sites are open-access but populated largely by the audiences that are more easily gathered, given this: what can these sites do to direct some energy and effort to making their content more accessible to US minorities, to students from poorer socioeconomic backgrounds, and to students who don’t have access to good educations?

          Lastly, wrt scaling BEAM: you’d certainly be the expert, and I hope BEAM gets whatever it needs financially to expand as much as possible.🙂


        • February 17, 2016 at 10:16 pm

          OK, concrete ideas! This is totally off the top of my head and not in any way thought through.

          (1) Have very clear entry points that require little background. In particular, they shouldn’t require strong reading comprehension skills or strong logical reasoning skills at first. That makes it possible for those who haven’t had access before to get into it.

          (2) Think carefully about the cultural impressions being conveyed in the problems. Do the problems refer to situations related to affluence? Are the situations things the kids are familiar with? Are the names representative of diverse communities? Does the language choice reflect particular cultural backgrounds?

          (3) If you have interactive forums, are those forums kind to new visitors? If someone gets several problems wrong and is told so unkindly by other more “senior” forum members, they are likely to disengage.

          (4) Now, if that basis is in place, it’s time to start attracting the students. You could spread the word to organizations that serve low-income kids, encouraging them to send high-performers to the site. Or you could try to grow “organically” – can you make a video that might go viral in the right communities, or something else like it? Something featuring mathematicians of color? Can you get someone with the right kinds of followers to send it out? If Neil deGrasse Tyson sends out your problem, that will reach a more diverse audience, for example.

          Anyway, these are just ideas; I have no real experience in designing a popular website!


  7. February 9, 2016 at 1:17 pm

    Richard Ruzcyk’s “The Art of Problem Solving” costs less than a pair of fancy athletic shoes that inner city school children wear. And I’m talking about both volumes and solutions manuals.

    I am grateful to Richard for having given my daughters complimentary sets.


    • February 9, 2016 at 1:19 pm

      Make that Ruszcyk.


  8. February 9, 2016 at 1:37 pm

    Thanks for the shout out, Math Babe. And for the thoughtful comments. Please feel fee to cross post in the comments section in the Atlantic. (at the end of the story.) Peg Tyre


  9. February 9, 2016 at 2:57 pm

    Max Warshauer’s program is another example of a great math program that (as far as I understand) reaches a more economically varied student body.

    As many people have pointed out above, the main obstacles to poorer students are often not strictly financial (as a kid in a family that was educated but poor by choice who did a lot of this stuff for cheap or free I can directly vouch for that). That said, I think the top programs may be somewhat unusual in terms of the generous financial aid that they’re able to offer. So there’s an added hurdle that you not only need to be able to find out that these kinds of programs exist, you also need to find out which ones can be free, and you need to be able to get into those ones (which are likely to be more competitive than the more expensive programs).


  10. Russell
    February 9, 2016 at 4:39 pm

    Here’s some anecdotage. Back in 2009-2010 I found myself with lots of free time, and begain thinking back on the happiest I’ve ever been, which was teaching mid-level undergraduates at ASU as a math TA. I asked the middle and high school systems around my small town if there was any way I could contribute, gratis, my time and energy on a regular basis. And I got no positive replies at all; it seems degrees in chemical engineering and computational mathematics with professional stints at NASA, Sandia NL, etc., count for nothing.

    Some of the comments allude to a lack of basic proficiency in much of the target population. Since my own daughter went through the system from start to finish, I agree completely. Also, first year freshman at ASU, were, hmm, let’s say prominently bimodel in the distribution of talent, with the larger left mode significantly below basic “C” competency. For instance, I was rather surprised my first semester teaching math at the college level to spend time teaching the advanced concept of least common denominators.

    I think the most effective way to address this at an age when it would be most effective might be an hour or so “office hours” a minimum of three times a week, free, where kids can come with their questions and ask them in a non-confrontational environment. When I was teaching I loved using a collaborative approach. I’d use a question as a puzzle, and gently pull up the implicitly embedded context as a method to get toward a general approach that is easier to apply to many solutions, rather than just memorizing the solution to that particular question. From the responses I received in real-time and the evaluations I received after, it seem to be effective and rewarding for a significant fraction of the students. I didn’t have much problem with full attendance, and I enjoyed the experience immensely.

    I’ve thought about this many times, but I have no idea how to build that environment, where there is no cost to the students. It’s very annoying.


  11. Liz Little
    February 9, 2016 at 5:03 pm

    I found that math enrichment is the best math remediation. My article : http://fablearn.stanford.edu/2015/wp-content/uploads/2015/10/FL2015-EducatorPanel-Little.pdf


  12. February 9, 2016 at 6:58 pm

    Schools are going to catch up too slowly, if at all. I think the two viable and necessary strategies for cutting through the elitism are:

    1) Improving, expanding, and publicizing online resources aimed at students who aren’t getting enough out of their classrooms (aka, Brilliant.org and AoPS)

    2) Scaling up efforts to create more in-person extracurricular programs (aka, Math Circles and summer programs like Mathcamp and BEAM)

    My story: After graduating in Math from MIT in ’13 and teaching at MoMath in Manhattan for about a year, I moved to the Bay and decided to try to teach for math circles full time (at 1-2 different schools every weekday). Additionally, over the summers, I teach for mathcamps and I the past two summers, I have taught for the BEAM program featured in the Atlantic article.

    This niche was not as difficult to set up as I expected it would be. Almost immediately upon moving to CA (I live in Oakland), I found that the idea of creating math circles spread like wildfire. I didn’t have much trouble finding half a dozen math circles to teach with initially since I already knew many members of the community. But the real shock came after getting established in the fall semester of last year: I started to get 2-3 offers per week throughout the spring from schools wanting their own copy of the program.

    So, with only so many hours in the day, the dilemma was that I needed to either to A) recruit more teachers to do as I was doing, or B) find a way to teach in more places at one time myself.

    At the end of last year I got an offer to work at Brilliant.org, which I accepted in part because it’s about as close to option (B) as I could ever get. About 1 million users per month access Brilliant, and some of the challenge sets I work on get attempted by upwards of 10,000, within a week or so of my posting them. I love that we really don’t have an ‘upper bar’ on the difficulty of content on the site — anyone can find problems on Brilliant which challenge them. And I’m glad to say that he site and community are awesome and growing insanely quickly!

    I also still teach one or two math circle classes every week – I just couldn’t give it up. 🙂

    My goal over the next several years is to pull other people into this lifestyle (creating content that can be very widely distributed, and creating in-person experiences for as many students as possible). I hoe to slowly enlarge this niche and draw in, what I believe is actually a very large pool of people who love math and who can also be excellent teachers, but who cringe at the realistic future of any career as a classroom teacher.

    Liked by 1 person

  13. David
    February 9, 2016 at 10:22 pm

    One way you keep cost down is having volunteers teach. You can also make it a non-profit and ask for donations. That’s how it’s done where I teach. It’s about $350 per year but we offer scholarships.


  14. Shikhar Srivastava
    February 9, 2016 at 11:50 pm

    The general issue and error with these article to assume correlation (parental income) to be causation (being good at math). Anyone can learn math, irrespective of income levels of parents. Fortunately, math is still a skill that is learned solely through intellect and not much else. Sure we need textbooks, lectures and all that. Internet has revolutionized access to really high level education for absolutely free. Excellent Textbooks can be bought for 10 cents. so if someone want to learn, and sees value in education, we don’t need any of those expensive “programs”. All that is required is motivation, dedication and willingness to learn.


    • February 10, 2016 at 10:55 am

      “All that is required is motivation, dedication and willingness to learn.” — And time. And a peaceful, non-chaotic place to study. And not having responsibilities for taking care of other family members. And probably not being subject to abuse for doing something weird and unusual. And not having brain damage from lack of food or contaminants in the water. And having someone who can identify what an “excellent textbook” looks like. Etc., etc.


      • February 10, 2016 at 10:57 am

        Yes low lead levels are a prerequisite to higher math. Great point.


      • February 10, 2016 at 11:27 am

        I got my appreciation for math from my uncle on Friday night walks in Williamsburg. As my uncle was Orthodox, Friday nights and Saturdays were family time. No TV. No radio. Just walking outside in the free air. He wasn’t college educated, but he taught himself math and math tricks or formulas while serving in slave labor under the Nazis and then incarceration in Siberia under Communist Russia. He would ask us math teasers and we loved it and learned. No fancy books. No excuses. Oh, and I was raised by a single mom who kept food on the table by working in a sweatshop, and my clothes were all hand-me-downs. And I see the same desire to learn in poor Chinese students today.


  15. Japheth Wood
    February 10, 2016 at 6:26 am

    It’s wonderful to see this much attention to developing math enrichment for multiple audiences. At various Joint Math Meetings each January, I mainly see two groups of mathematicians who are engaged with math education.

    One group is focused on developing the existing math infrastructure, strengthening the math curriculum through defining clear and coherent Common Core State Standards, designing aligned curricula and strengthening math teacher preparation.

    The other group is engaged in promoting Math Circles, Math Summer Programs and the like, groups that support math enrichment usually separate from the school, and not necessarily guided by (but often compatible with) school math.

    Since the discussion in these comments is focused on the second group (that includes me, of course!) I want to point out that a big challenge is our ability to organize the the mathematical community to support math enrichment.

    I encourage everyone here to learn about, support, become part of the following groups:

    (1) The National Association of Math Circles (http://www.mathcircles.org) has become very active recently in networking and supporting math circles around the country.

    (2) The SIGMAA on Math Circles for Students and Teachers (http://sigmaa.maa.org/mcst/). If you are a member of the Math Association of America, please join this group!

    (3) The Math Teachers’ Circle Network (http://www.mathteacherscircle.org/) builds mathematical communities for teachers. It’s a great place for mathematicians and math teachers to interact and share expertise.

    (Am I missing a critical group? There’s also a Math Research Community of the American Mathematical Society, focused on math camps, but it’s been inactive.)

    Liked by 1 person

  16. February 10, 2016 at 11:06 am

    Personally I feel like I’m about to go Geghis Khan on the issue of getting math specialist teachers into all elementary grade levels (K-6). The literature I’ve been reading up on lately seems to make it clear that the teachers at those earliest grades are the weakest at math of all college graduates (I’ve had at least one student myself say that she wanted to teach K-6 *because* she didn’t need to know more math to do it), and this directly contributes to students running off the rails at that level. Granted that, no amount of curricular tinkering can make a difference, because regardless of how you try to design a paint-by-numbers curriculum, if the teacher delivering it is math-phobic, then they can’t answer any questions about what or why they’re doing something, or why students will need it in the future. I don’t see any other solution but to inject well-trained math specialists at those levels (or else train all elementary educators to be highly proficient in math, which currently seems infeasible).

    That would at least bring public-school students closer to being able to engage with math-circle participants. And Lara above makes a great point that these math specialists would be exactly the people who could be a catalyst for developing gifted-and-talented programs, after-school enrichment programs, etc.


  17. Aaron Lercher
    February 10, 2016 at 2:09 pm

    The elitist part about the expense of math enrichment programs is immediately preceded by language setting up the assumption that learning math is a race.
    (Incidentally, this is contrary to the “progressive” educational inclinations in the earlier post, https://mathbabe.org/2016/02/01/raising-kids-the-right-way/ “Progressive” educators often say children should learn at their own pace. Joshua also noticed the mismatch.)

    If the goal is for some kids to become “accelerated” and compete in problem solving contests, then why give children extra instruction, if they aren’t going to contribute to winning?

    In particular, the Atlantic article makes the following common assumptions about learning math:
    “And earlier is better than later: The subject is relentlessly sequential and hierarchical.”

    Is this really true?
    I think it is only partly true.
    The puzzle about colored socks that Zaharopol poses does not require prior understanding of algebra or arithmetic.

    But I’m not a mathematician. I’m not even “good at math.”

    Liked by 1 person

    • February 10, 2016 at 4:05 pm

      But clearly competition and competitive success are what the Atlantic knows will sell on the front page. In fact, almost all of the articles on the front page are about competitions, no? — The Superbowl, Elections, and, last week did you hear about Google’s Go-Game AI?

      “Contests, especially contests modeled on war, feel like objective, decisive assessments of ability.” ~Alan Levinovitz That’s what get’s people’s attention and, even if it’s a bit underhanded, I salute the Atlantic for using whatever tricks they can to draw attention to this greater topic.

      However, our inability as a culture to find non-competitive measures of success compelling is actually a real hurdle relevant to this debate.

      The competitive, ‘race to the top of the ladder attitude’ is a setup for elitism — like a suburban culdesac, it naturally creates an isolated, and inaccessible group of privileged participants. Almost by definition, it makes it difficult for anyone who starts off at a disadvantage (or even just outside of elite, highly-advantaged populations) to ‘catch up’ in the sprint up the ladder.

      And it’s completely unnecessary. There’s a ton of amazing math out there, problem-solving focused math that doesn’t require significant preexisting mathematical training. Take, for example, Dan Zaharopol’s sock puzzle from the article (combinatorics), and then there’s graph theory, game theory, the study of surfaces and knots… (the list is infinite)… All topics which can be used to introduce students to math in a way that’s immediately compelling and accessible to anyone.

      .9999… = 1 was the first big eye-opener for me. But only because I was lucky enough to have a teacher up for the debate. “.9999… just isn’t one, can’t you SEE that?!” was what the ‘rules’ that I knew told me. But “is this really the rule?” is not the right question, the right question is “why does the mathematical community choose to define decimals this way?” The first question makes math into an exercise in memory and following directions. The second question opens math up into a debate and a collaborative exploration of a frontier.

      So, while I’m glad it pulled more attention to the Atlantic article, I hope that we can break away from the competitive mindset which seems to consciously or subconsciously drive so many parts of this debate.

      Competition walls out students who aren’t supported in extracurricular math out of what are considered the most advanced/prestigious arenas and it also pushes away a lot of students who might otherwise be interested in math from the investigatory/puzzling perspective. I fell into the latter category myself. I always loved analytical debates, art, and logical puzzles, but I didn’t connect ANY of these to math until one great teacher, late in high school. Math was about rules and speedy application of mental tricks, and being right all the time — and that attitude made math seem both inaccessible and unappealing to me.


      • February 10, 2016 at 4:07 pm

        I’m 100% with you. The readers that tell me I’m being inconsistent by saying I don’t make my kids do stuff they don’t like but I do like doing fun math with people who want to are completely missing the point of fun math.

        Liked by 1 person

      • February 10, 2016 at 5:04 pm

        “it naturally creates an isolated, and inaccessible group of privileged participants. Almost by definition, it makes it difficult for anyone who starts off at a disadvantage (or even just outside of elite, highly-advantaged populations) to ‘catch up’ in the sprint up the ladder.”

        I’m sorry, but I don’t know how to say this politely, but I need to put on my boots because the pile is so deep. “Privileged participants?” Privileged to work hard to gain insight. Just like shooting 3 pointers requires practice, so does learning math or any endeavor. I never heard anyone refer to kids gifted at basketball as “privileged.” Why refer to gifted math students as “privileged?” They don’t come from one socio-economic stratum.

        Of course math education and math enhancement for all is a wonderful idea.


        • February 13, 2016 at 6:28 pm

          Does my post awaiting moderation get better with age?


        • Shikhar Srivastava
          February 13, 2016 at 7:03 pm

          While this debate is going on, I really wonder if the topic “elitist” is even being discussed in a scientific manner. What is the source of this assertion – that kids attending Math focused programs come from some sort of “privileged” background ? I know some of these kids and most of them seem just normal middle class families. No limos, no butlers or chauffeurs. They go to public schools like all others. Only difference is that they are willing to do Math. They spend hours. They discuss intricate concepts online with other like minded kids. They ask questions. They help others.

          The mathematicians who are blaming some sort of elitism should instead focus on educating whoever shows up at their doors and shows interest in “Mathematics”, and is willing to do the work instead of raising questions that they can’t objectively verify. Interest and motivation are more important than the zip code. No amount of money can actually produce a mathematical mindset and generate curiosity. Where Ramanujan grew up, there was no electricity, no books and no teachers, and still he was able to wonders. Same is true today. Terry Tao probably came from same “elitist” setup, but it was his interest in Math that made him Terry Tao, and not his privilege.

          I grew up with family earning less than 100 bucks a month, and my “interest” (not familial income) in sciences and math did wonders for me. Not any coaching, fancy classes or some magic potion. Just doing math and science was good enough. And no, my parents did not engage in helicopter parenting. and I believe same is true today – kids who want to do stuff find ways to do it. It is much easier today to find right kind of education than it has ever been in history of mankind. So all this “elitist” talk is just that, mere talk.

          Liked by 1 person

        • February 14, 2016 at 2:17 am

          There’s an extent to which I agree with you about the question of privilege – mathematicians come from everywhere. But there’s a huge bias towards higher socio-economic strata in terms of mathematical success, and it’s worthwhile to ask why and to acknowledge the myriad forces at work.

          Now that you point it out, I’m amazed at how accessible basketball remains. Not all sports are like that. Tennis, for example, has high-priced individual coaches that help to build superstars. The same for many other sports. Is it possible to get to high levels without that support? Yes, but it’s much, much harder. Hence, privilege.

          The same in math. Can you easily afford extra tutoring? These days there are private tutors for challenging topics at younger ages. Can you afford extra gifted programs? Summer programs? Do your parents have easy transportation to get you to math circles? Sure, it is possible to go to the library, get a math book, and teach yourself. Or it’s possible that a great math teacher will notice your interest and put in lots of extra time to help you. But without that, each hour put in by someone who has access to tutors and summer programs and whatnot will get them further than each hour you put in.

          Don’t get me wrong. Different people also make different choices about how much effort to put into math. But that’s far from the only force at work here.


        • February 14, 2016 at 12:11 pm

          My claims that most math programs are filled with privileged participants is based on my experience working with about two dozen different extracurricular math programs. I love teaching, and teaching all of these groups is a blast, but the near-homogeneity of many of the groups is obvious. There are definitely exceptions, but most programs certainly don’t reflect the demographics of the areas they’re in. Why?

          Transit and $ are definitely issues as well, but I think they’re less the barrier than “social expectation.” For most extracurricular programs, such as math circles and websites like AoPs and Brilliant.org, I think there simply isn’t broad awareness, across cultural and socioeconomic lines, that these programs exist and that they’re an amazing opportunity for kids, (even if not especially those kids who hate or are board in their school math classes.)

          And the second part of my experience here is perhaps the most relevant: when summer programs and math circles put it to the grind and make a program that’s well attended by minority groups and students from poorer families. When the tremendous effort needed to launch such programs happens – the programs that are created are amazing! They are not filled with kids half-heartedly in the circles because their teachers forced them there; they are filled with kids who are stunned to find that they LOVE this kind of math, and that they’re able to develop their skills faster than they or I thought would be possible. In short, there is every indication that once the connection is made, these students are great matches for math circles, not reluctant guinea pigs forced to be there.

          This was the big eye-opener for me (and, yes, maybe this makes me very naive): that it’s not enough to just have open access to a math circle or website. It’s not even enough to run a math circle at a public school. Instead, it really takes an active hand: such as teacher at that school recognizing that a dozen specific students who would otherwise have just moved with the tides of their environment, might love math if they saw it in an investigatory context. The teacher or councilor then has to reach out to that student and maybe their parents as well, leveraging their reputation as a good teacher who cares about this student to get the student to put aside their other responsibilities and try coming. AND THEN those students have to come to the circle and find that they’re on an even footing with those around them, not ‘behind’ or ‘out of the loop.’ AND THEN those students still have years of fighting against social pressure in front of them, pressure to switch back to a path that their parents and community understand better, AND ALSO simple, internal uncertainty because no one they know and no one like them has taken this road before.


        • February 14, 2016 at 8:40 pm

          The issue of “elitism” is an interesting one and of course depends on one’s definition of elite. CUNY was once an elite school system. Only the best and the brightest could get in, until 1970. It produced a dozen Nobel Laureates. But after Open Admissions was instituted in 1970, not a single Nobel Laureate was a graduate of CUNY.

          “The City University of New York began in 1847 as a free academy for young men of poor and immigrant families who normally did not have access to other universities and colleges in the city.” (Later on it was extended to women.)

          “[…] the Depression era as glory years at City College, when the striving sons of immigrants achieved academic excellence on the road to future success. They were members of an elite group, selected from candidates all over the city.”

          ”’The competition was extreme,” said Dr. Hauptman, whose Austrian immigrant father, Israel Hauptman, had attended City College before him but had to drop out in order to support his family as a printer. ”Only the very best got in, and only the very best survived it.”’

          ‘Dr. Karle spent three hours on the subway each day, traveling between his home in Coney Island and his classes on the campus at 138th Street and Convent Avenue. ”I learned how to study under very odd circumstances,” he said.’

          ‘Dr. Hauptman, a math major, commuted from his family’s apartment in the Bronx. ”City College was the perfect place for a person like me,” he said. ”I was a bookish kind of kid who loved to read a lot, especially math.”

          The basement lunchroom was particularly exciting, a place to exchange ideas and engage in spirited debate. ”In order to conserve space, we ate standing up,” he said. ”There was always a lot of discussion going on.”’


          You didn’t need a lot of money, only the desire to learn.


        • February 15, 2016 at 6:52 am

          Abe, we all get you were an exceptional person from an exceptional family. That’s great. But it’s not the universal narrative. Specifically, we cannot count on parents of interested and budding math nerds to have the time, energy, and temperament to foster their child’s education like you describe. Whether it’s due to the history of slavery in this country, or more recent deep levels of racism and exclusionary policies and practices, not all communities think that mathematics is a real option to them and their children, and they’d be mostly right. The truth is, this question of elitism – or if you wish for a more precise term, exclusion – hits on all sorts of cultural, historical, and interpersonal trust and hostilities. We cannot solve all of them, of course, but we certainly don’t want to pretend they’re not there with specific examples of exceptionalism. That would be unfair and narrowminded.


      • February 11, 2016 at 9:02 am

        I think there are two distinct points: (1) is the content of math a competition? and (2) is math as a subject a competition in the US? I think the answers are no and yes.

        For the first, we can just go back to the article. While others liked the sock question, I was a lot more excited about the kids telling stories about 49 + (18-3). No way to make that competitive (um, see below) and, while it doesn’t illustrate every aspect of math, it shows several that are strongly counter to the common stereotypes.

        For the second point, Zandra Vinegar makes an astute observation that (many) Americans love to make everything a competition and (some?) make everything about competition. Heck, there’s even a competitive form of improv comedy.


  18. February 11, 2016 at 7:50 am

    I have a few thoughts about this topic as it fits between my own research (racial disparities in the U.S. — I’m a quantitative sociologist) and the work experiences of my wife who teaches high school math. This is something that we, too, have discussed.

    One way to recruit students without traditional advantages of wealth and well-funded schools is to provide consistent after-school “care” while the kids still have fun learning. One of the biggest challenges parents face in low-income neighborhoods is finding activities that help keep students safe after school. Parents hoping to keep children from experiencing violence is one very large reason that students from lower incomes and racially segregated neighborhoods have more screen time than other groups.

    The second problem involves transportation. In a city like New York, this problem can be overcome relatively easily. The city has a good public transportation system that allows kids to get where they need to be or parents to pick their children up (though, again, safety matters for the transportation home). But many places do not provide the transportation necessary to make this a possibility. My wife has brought this up as potentially *the* limiting factor that prevents many students from participating.

    Finally, on funding, I believe that one might be able to use the college model of charging students from wealthy families a little bit more to subsidize the costs of less-wealthy families. This price discrimination strategy in colleges essentially allows wealthy students (and parents) to pay for deserving but poorer students at the university. Of course, many private universities that use this price discrimination strategy have endowments that allow them the flexibility to play with their tuition structure, but it might be worth exploring as a potential pricing strategy.


  19. February 11, 2016 at 9:48 am

    You might be interested in learning about the Math Corps, a program started by mathematicians at Wayne State University for Detroit public school students that has been running since the early 90s.

    Their website is here:


    and there is a nice 30-minute documentary about the program here:


    I spent a summer watching the program first-hand. Usually when you see something up close it loses a bit of its luster, but in this case I had the opposite experience. I saw 7th graders learning about partial sums and limits with enthusiasm, and high schoolers studying transfinite set theory. One high school student very calmly walked to the board and put up Cantor’s diagonalization proof, and another stated the Continuum Hypothesis as a question in class one day. And what is amazing is that the math wasn’t even the coolest thing I saw – the social side of the camp was even more amazing. I’ve been involved with a group working to replicate the program in Cleveland


    and I would characterize it as using the pleasure of finding things out as a way to build the beloved community. It is about how we teach math, but even more importantly about how we see our kids.

    There are also groups working to replicate the program in Philadelphia and Utica, and you might consider making a visit to Detroit if you are interested.


  20. Karen Smith
    February 11, 2016 at 12:26 pm

    Offering “free room and board” at programs like Promys does little to nothing to help with this problem. The kids who are benefiting from the proliferation of “elite” math opportunities generally have a highly-educated full-time parent who spends considerable time, energy and money researching all kinds of opportunities, shuttling kids to Kumon and math circles, organizing tutoring, even travelling with them to overnight camps! My son was interested in “Epsilon Camp” where one of his (rich over-achieving over-parented) friends was going. Turns out that if he was to go A PARENT (or some adult I guess) had to go to camp WITH HIM! WTF? I am a single working parent with other kids. This is 100% impossible for my family, and I am highly educated, have a good salary, and considerable control over my schedule. Still: impossible! I can almost afford his tuition there but then plane tickets, my expense, and who takes care of my other kids? What about families in which parent can’t just take off work for 3 weeks? This is just one example….it drives me nuts. The saddest part of all of it is then later, when those kids are 20 and in college majoring in math because “it’s what they’ve always done”: a large percentage are depressed, anxious, and have no joy in it anymore…it’s all about “being elite” and “being smart” and “being ahead.” I have met many of these kids in college and listened to many of their tears. The real answer is to fix the public schools. But this is so huge to contemplate…


    • DJ
      February 11, 2016 at 1:31 pm

      I’m not sure how your Epsilon Camp experience relates to PROMYS. Parents aren’t required (or even allowed) to attend PROMYS with their kids. PROMYS commits to free tuition for low-income kids but in practice is usually able to do better, up to and including zero-fee participation. It’s true that we can do better at reaching out, and we’re always interested in having that discussion. I’ll be the first to say that I don’t see many (or even any) depressed kids at PROMYS. The vast majority of them are having the most fun they’ll ever have in their lives.


  21. Robert
    February 11, 2016 at 3:28 pm

    To be honest, the concept in the article is fundamentally elitist. Only a small fraction of the student population will have the ability to learn mathematics at this level, just as would be true for athletes and musicians.

    I would favor an effort to ensure that public school students as a whole be taught mathematics. While I have lived a full and rewarding life, I know that my youthful fascination with science could have gone much farther if I understood math.


  22. KS
    February 13, 2016 at 5:39 am

    The depression comes later, when the fun based on being a “genius” and prodigy wears out, and they grow up enough to realize there is more to life than showing off or being the best at something, or that the thing they’ve always been pushed to do turns out to be not what they wanted to do. To get to a camp like Promys has always required many years of parental resources and investment before that, and now with the proliferation of “elite” programs for ever younger kids, the divide will only grow. I am not saying I think Promys is a bad thing in general even a bad thing for most kids who are privileged enough to go. I am saying it is most definitely elitist.


    • DJ
      February 13, 2016 at 7:33 am

      I agree that math camps are elitist in their current form. This is exactly the problem that we’re trying to fix. You seem to be saying that there is no way to make these programs non-elitist. My view is that we could do a lot more to identify and reach out to less privileged kids.

      It’s also important to distinguish between socioeconomic background and mathematical ability. As Robert points out, math camps are fundamentally elitist in the sense that they discriminate based on intelligence and mathematical ability. But in the context of this post, “elitist” refers to discrimination based on non-performance related factors such as income, gender, race, and geographic origin. Now you may argue that intelligence as measured by tests is just a proxy for parental income level, and while this may be true to a certain extent, it is obviously not a 100% correlation. So to the extent that we can separate out background from ability we should continue to do so, because the entire purpose of these camps is to serve high-ability students.

      I still think your view of what happens in camp is inaccurate. For the vast majority of camp participants, math camp is the first time in their lives that they’re NOT the best at math. Participating in a math camp forces those geniuses to confront their motivations at a much earlier stage in life than they would otherwise, at a point when they still have time to do something about it if it doesn’t work out. A very very few of the very top students (meaning, a student who is the very best even by camp standards) do experience what you describe, and their cases get publicized widely, but it is not at all representative of the norm.


  23. Paul Boisvert
    February 13, 2016 at 6:22 pm

    A Venn Diagram represents the long-term problem: Our society is elitist, like all capitalist ones. Since education is part of society, and indeed the single most important part of reproducing the fundamental inequity of our political economy, it too is largely elitist, with the function of education for most students being the crushing of critical thinking (and thus, potential for dissent) in favor of rote indoctrination and obedience. Since math education is part of education, and a particularly helpful one in inculcating prowess with creative and logical thinking, it is even more elitist, as any rudimentary use of logic leads to awareness of the fundamental illogic of capitalist exploitation, and a search for creative alternatives. A ruthless capitalist system can’t afford to have too many of its citizens able to think their way out of a paper bag.

    The various “math circle” programs and solutions proposed above, all quite admirable per se, are nonetheless only so as band-aids. There’s nothing wrong with band-aids, which may be helpful in the short run, but there is something wrong with thinking that a minor increase in band-aids will ever solve the fundamental problem. Any solution that says we’ll take the kid out of the ghetto for her math education is doomed to band-aid status–you have to eliminate the ghettos from our society. Just as society needs radical reform of our political economy, all education, day-in and day-out, in every classroom and setting, needs similar types of radical reform–it must be democratic, egalitarian, unindoctrinated, creative, and free, leading to the kind of critical thinking that underlies every child’s ability to explore and realize their full human potential.

    That is, every public school should be using models like Sudbury Valley School and Summerhill (google around for takes on these.) But to do that, people who want those qualities in their education system have to seize power in our society (from those who currently hold it, and who emphatically do NOT want to see that kind of education system.)

    This is just as true for subjects other than math–there is no evidence that math educational results are any worse than those in many other subjects. Americans in general are so woefully ignorant of economics, history, social science, and physical science (particularly, um, climatology) that the future of our society looks quite bleak–and not because there won’t be enough math/science/tech geeks to do the narrow work of building the computerized technology that will be idiotically and futilely relied upon to solve what are fundamentally broadly ideological social problems.

    A commenter above mentions Finland, which has what is often regarded as the world’s best educational system (which may be true, although it undoubtedly has a ways to go as well). So a start is to aim make the US like Finland, a much more egalitarian social democracy. That may not be enough–I personally think only full blown democratic socialism will work–but one step at a time. Organizing labor to oppose capital in the political economy is the only likely source of such change–but the good news is, educators are laborers, and are among the last still (partially) unionized workers in the country. Every ed union in the country ought to be fighting for EVERY math class to become a math circle, from kindergarten on up–and ditto for every other subject as well!


  24. Wes Hansen
    February 15, 2016 at 3:53 pm

    You might wish to send an inquiry to Anthony Yom, a math teacher at Lincoln High School in Boyle Heights, a predominantly Hispanic community with relatively low-income households in East LA. Cedrick Argueta, one of Mr. Yom’s senior math students, recently scored a perfect score on his Calc Ap. Out of 21 students who took the Calc AP, all passed the test and 17 scored a 5. This is the third year in a row that all of Mr. Yom’s students passed the Calc AP. And Lincoln High is NOT a charter school!


    I’m not an educator but, based on my own experience, I think a lot of making math accessible to kids from all walks of life is explaining to them exactly what math is, from the global perspective. When one doesn’t really understand what math is it seems nothing more than rote memorization combined with algebraic manipulation. Mathematics is the study of pattern and therein lies the beauty. Once one understands this then learning new classification schemes utilized for the rigorous study of these patterns and the relations between them becomes a great joy!

    Dave and Joy Morris of Lethbridge University in Lethbridge, Canada, have a really good open-access/Creative Commons textbook, Proofs and Concepts: The Fundamentals of Abstract Mathematics, which is geared towards mathematically inclined high school students and freshman undergraduates; I think it could be easily modified to be accessible for those who are less mathematically inclined and that this would be of great benefit:



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