Too many students are ready to do more mathematics but
- do not know where to do it, and
- do not even know that such opportunities exist or that they should be doing it.
The students don’t know; their parents don’t know; their teachers don’t know. They have no way to discover that their peers, successful math students from other communities, do more than just what they see in school.
It’s not just that they need to be told about it; it needs to be part of their culture. It’s not just that they must know that such programs exist and that successful people do them; they should feel it is expected of them, that lots of people they’ve known and admired do math beyond school.
How can we possibly create this culture and community where it does not already exist?
The Summer Program in Mathematical Problem Solving (SPMPS) is one answer to this question. I believe that it does amazing things for the students who go, and it might provide a new pathway to developing future mathematicians, scientists, and engineers from communities where none might otherwise arise. Nonetheless, it is not cheap. How could we create a real systemic solution?
I don’t have an answer, but over the past two weeks I’ve been visiting low-income schools to do interviews for SPMPS, and I’ve had some opportunities to think on it. Here are two half-baked ideas seeking comments, criticisms, ideas for how to implement them, and ideas for how to find funding.
A Math Opportunities Newsletter
[Idea developed jointly with Japheth.]
One double-sided sheet of paper, sent out each month by e-mail, postal mail, and posted on the web. It lists opportunities across NYC, from math circles to competitions to classes to MoMath events, and possibly some online opportunities as well. It includes up-front information about costs and scholarships, and about the mathematical background and maturity required for each program. It also has a feature story each month, about students in different programs and the successes they’re experiencing, setting a cultural expectation that this is what kids should do.
The newsletter would be mailed to every school in NYC and anyone who signs up for it online, increasing knowledge of good math programs. If the newsletter is really successful, it might strain those programs’ capacities—but such success might provide the impetus for more support to scale successful programs.
Costs would be mild: an editor to compile stories (and keep an eye on the overall tone of the newsletter), a graphic artist to lay it out an in appealing way, printing and mailing costs. Although it could be supported by advertisements, it might be difficult to do so in a way that maintains the positive tone of the newsletter and doesn’t get lost in test prep programs.
Math Club Materials
While I was visiting KIPP STAR, I had a discussion with their math coach. She was telling me how she used to run a math club, but she lacked the time to prepare problems, and she suggested that a ready source of good problems would help her school (and possibly many others) run such clubs.
While there do exist materials for running math clubs, they suffer from a number of shortcomings. They are not widely-known. They often rely on an instructor who is already familiar with sometimes esoteric math, or who has time to learn it. They’re geared towards students who’ve already had substantial enrichment. They’re not completely assembled: you still have to put together the problems you want, decide on difficulty, and so forth.
What I imagine instead is having something teachers can just print out and go with each week: problems prepared, perhaps six questions to be done each week, along with short pointers on how to run an effective math club. Each week would have four different problem compilations: one for “Level 1,” another for “Level 2,” and so forth up through “Level 4.” In this way, it’s easy to try out a set with your students and decide if they are too easy or too hard, and then change levels appropriately. Ideally, there might also be special problem sets designed around specific school topics, so that you can reinforce recently-learned material. We might even sync the problems somewhat with Common Core. This is not my ideal model for a math club—I would rather have one that does interesting mathematics different from school math in addition to contest-style problems—but this is an easily-replicated and highly-engaging model with good payoffs for the students. It works well with a teacher’s limited time.
Naturally, the problems would have to be tested in a wide variety of settings and schools, and the key to success is getting teachers to actually use the problems. In addition to mailing schools, there are a number of schools that participate in math competitions but do not prepare for them; we could contact teachers who bring the teams to the events. Through contacts at schools of education, we could reach out to alumni. We could reach out to Math for America alumni. We could make the materials available at NCTM conferences. As use of the materials becomes more widespread, it becomes easier to bring them into new schools.
Costs would be moderate: the problems must be written/compiled (permission must be gotten for existing problems) and then put into PDF format. A webpage must be created and made easy to navigate. Much active work must be done initially to get teachers using the materials, including advertisements, conference presentations, and so forth. However, after initial adoption, word of mouth might be enough to keep them going.
Closing Notes
These two ideas are clearly geared towards students who already have some success in mathematics. While I could imagine the newsletter expanding to include opportunities for those who are not already on the bandwagon, the much thornier problem of helping those who are having serious mathematical difficulties is not one to be addressed here.
With that said, dear readers, I invite you to join me in my brainstorming. Are these ideas feasible? Worthwhile? Are there other pathways to creating a culture of excellence in mathematics?
Consider Learning 
In re the newsletter: you’re talking information when you need to talk culture.
Mere information dissemination is largely ineffective (will they kick me out of the librarian ranks for saying that)? If the problem were that people were merely *uninformed*, that problem would already be solved; we have Google; it is not hard to acquire information.
A newsletter doesn’t do much to build emotional salience. It doesn’t engage people in communities or habits. It doesn’t engage people WITH people. And it doesn’t effectively compete with the many, many other things vying for attention.
I’d say question 1 is audience: are you trying to target teachers or kids? Both important, but different strategies. (Your second idea, for example — clearly targeted straight at teachers, in hopes they will target the kids as a secondary effect, and much more promising; make it easy for teachers to do stuff, YES. Of course it relies on there being teachers with adequate mathematical knowledge…sigh.)
Anyway, if you’re trying to target *kids*, or you’re trying to build *culture*….build *culture*. Get actual people interacting with other actual people, whether in physical space or online. Be in the spaces that people are already in — churches, Facebook, whatever; pick some and go with them. Work with people who are already in those spaces to find out what translates to local culture.
And then create ways for people to get social and emotional rewards, from people they care about (i.e.: probably not you) for engaging in math. Create ways that they can engage with math content and then share that creatively, with an audience (Vi Hart, anyone?). That might be video or Tumblr (http://fuckyeahmath.tumblr.com/!) or art shows or whatever. (Talk to some good teen librarians. Find out how they do these things. Building community and encouraging young people to interact with creativity and intellect — it’s their job.)
I realize I’m being a bit vague in what I’m saying, and that’s because there’s a tension between doing things at scale, and doing things that sound right in the voices of local communities. And I think the answer to that is start in a diverse handful of communities, and work with people on the ground there — teachers, preachers, librarians, teens, whoever — to craft *engagement* — things people can do with math and get validation for, things people can do together to see firsthand what habits of mathematics look like — and then see, from there, what can be repackaged, put in a box, scaled.
Once you have the community, the information dissemination is easy. To a large extent you don’t even have to do it — they’ll do it themselves. And they’ll care, because it’s in a space that matters to them.
(To say this another way: my alma mater has famously increased the participation of women in its CS major manyfold. They did several things, including entirely overhauling the first-semester CS course — but I think the most important thing they did is fund women to go to the Grace Hopper conference. To see that there are people like them doing CS, and that doing CS can be a thing of social validation and belonging and joy.)
The newsletter was definitely not intended for kids — it’s aimed at teachers. Basically, teachers often don’t know about good math opportunities and looking them up is time-consuming for people who are already ridiculously busy. This could allow them to recommend programs and problems to kids who would be right for them. I agree that each individual newsletter builds very little connection, but right now teachers are just completely uninformed about what’s out there and they don’t even think to Google it.
Also, yes yes and yes: building real connections within the community are critical. See, for example, Mary’s intriguing post below about Guerilla Math Circles. However, getting those connections are really hard when those communities are very disconnected from math achievement.
I have been thinking about this issue for years (decades!) and have finally come up with a concept that I hope can scale and really catch on. I have started blogging a little about it here:
http://albanyareamathcircle.blogspot.com/2012/05/guerrilla-math-circles-brainstorming.html
I think the monthly newsletter is an excellent idea. An informational newsletter probably would not be very helpful in creating the desired culture by itself, but it could play a valuable supporting role as the culture is developing. For example, if a school or teacher has had students attend certain summer programs (or had some other good involvement with extracurricular mathematics), a monthly newsletter with information and good stories could make the different between that school or teacher becoming and active participant/supporter in extracurricular mathematics activities and merely being an observant bystander.
Also, it seems that most schools should have at least one math teacher who would enjoy getting (and hopefully pass on) good information about extracurricular math activities.
How many schools would you send it to, anyway?
How many schools it would go to depends on funding. I’d love to send it to a lot of schools, but if we were limited in number of sends we’d have to target carefully. Who are the teachers who will pay attention to it?
I would rather have one that does interesting mathematics different from school math in addition to contest-style problems
What about Khan-academy-style math club sessions (probably mixed with other things, like the problem sheets you suggest)? I’m thinking of videos kind of like Vi Hart’s stuff, only longer with more depth, maybe designed to work with interaction or discussion of some sort. Some way to get interesting non-school math out there even if the teachers don’t yet have the background themselves. Probably there are already some videos like that out there? I’m not really plugged into what’s available now, just thought I’d share the thought.
Good videos are an interesting possibility. They could work, although people are less engaged in videos than they are in actual presenters, and there wouldn’t be someone who could give students feedback on their own work. However, a collection of videos to present at the end of each week’s math club meeting might be pretty fruitful.
What about doing something around team solving of USAMTS problems? Although there are contest-like aspects to it, it also has features that are unlike contests like the AMCs — there’s more time, it’s open-ended, etc. I went to an inspiring talk by Mary Fay-Zenk a few years ago at MSRI (possibly at the first Math Circle workshop — I think you might have been there too!) where she talked about gathering students to explore USAMTS problems together. Then students who wanted to could write up USAMTS problems to submit (and she encouraged this), but more crucially, she made the exploration of this already-available, already-vetted resource into a shared experience.