Twenty-six of our strongest sophomores from last year have been given to me as juniors, to take algebra 2 and pre-calculus in one year. About twenty are serious and ready to work. About six are boisterous and unable to hold their attention on listening to one person for more than about 90 seconds—but they do quality work when they work. All twenty-six would clearly (to me) be bored in our regular algebra 2 class. The knee-jerk reaction: the ones who know how to stay focused can stay, the other six have to go. But that’s the reaction that has put thousands of students, primarily low-income students of color, in courses below their ability level for decades. So the right thing to do is keep them all, and work explicitly on classroom behavior skills. And the only time that doesn’t feel good is when the first twenty students keep telling me they can’t concentrate, that the six don’t belong there, that I should get rid of them.

And there you have it: the single most influential tension in the US education system. It’s why we have private schools and charter schools and parochial schools and good schools and bad schools.

Announcing a Global Math Department webinar on Problem-Based Course Design, Tuesday, 10 September, 9pm Eastern.

Following up on a #TMC13 session, we’ll have an open discussion on ideas and questions people have about designing their own problem-based courses. All are welcome – if you didn’t catch the TMC13 session, you can catch up by looking over the materials. Questions or comments? Leave them here or #PBCmap on twitter. See you then!

We had a super session at #TMC13 on designing problem-based courses. Materials and notes are posted for those interested.

At #TMC13, my session is about designing problem-based courses. But all math courses involve solving math problems; most do little else.

So what makes a course “problem-based”? R.A.C.S.V.P. (Répondez aux commentaires, s’il vous plaît.)

I’d love to get this fleshed out before we all get to Philadelphia!


Guess what? Poverty really sucks. It’s incredibly hard. All the lifespan studies going back to the 1920s show that poverty in youth is a very hard force. We need to build fault-tolerant schools and systems if we’re actually going to address equity. —Uri Treisman, Iris M. Carl Equity Address, NCTM 2013, at 35min, 10sec.

Every year at my school we try to improve the math program, and I think the quotation above captures what we’ve been going for. Our challenges:

Students in the wrong course

We do our best to place incoming freshmen from the information we have, but we’re finding that middle school grades don’t really communicate what students are able to do. So next year we’re hoping to up our game on intake, placing them from our own assessment within a week of their arrival. This also means offering, for freshmen, not only Algebra 1, but also an accelerated pre-algebra-plus-Algebra-1 course, as well as an Algebra 2.

Students below grade level

Next year we also hope to offer a couple options for kids to double up on their mathematics so they can catch up to a level that would allow them to take AP Stats, AP Calc or Pre-Calc before they graduate, even if they’ve previously gotten behind.

Intermittent attendance

This one is harder. Most of our courses are still structured around the expectation that every kid is there every day. That is a legitimate expectation to which to hold most of our students, but we don’t want their prospects to end if they miss some school. We’re all working on how to create structures to provide more individualized instruction to help fill gaps. A few of us have also been kicking around the idea of a master standards list spanning all four years (or at least three years), so students wouldn’t necessarily be tied to learning a particular blob of material in a particular 9-week term, but it’s unclear how to make this work without a lower student-faculty ratio.

Repeat repeaters

Fewer and fewer students are failing a course repeatedly. This is clearly a case where prevention is the best cure (see items above). Still, as long as the number of these students is more than zero, we need to find some way in that works for them.

Speeding up students’ applying new concepts

Throughout the program we’re increasing the amount of time that students spend solving problems alone and in groups, and articulating their solutions verbally and in writing. I’ve seen students’ abilities to think, write, speak, and critique improve dramatically. In my room, though, when students solve problems they tend to rely on concepts they are fluent in (like adding) and avoid concepts that are new to them (like exponentiation, or modeling with equations). Helping them master particular skills and provide copious opportunities for them to practice applying them in a meaningful context is an ongoing challenge.

The overall goal

We want to make sure that each student has a clear path to get from his or her current level of ability to, at a minimum, success in college coursework, and for most students, an AP or similar college-prep experience prior to graduation. We’re working to build a system where a student isn’t permanently derailed if something goes wrong for a while.


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