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.
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?