(So I have started getting in the weird habit of going on runs to process big events and also to train for the Boston half marathon this fall. Not quite this fast, but just to allow hard-to-process ideas to come into focus a little more. TMC 13 required a 14-miler, which worked out well since I missed my long run while in Philly.)
I decided to sign up for Twitter Math Camp when I was in a talk by Sam Shah about the MathTwitterBlogosphere almost exactly a year ago. The number of ways that hour changed my life and first year of teaching would be hard to enumerate exactly. All I know is that I could not wait for Twitter Math Camp.
The session that got me thinking most about my classroom was Dan Goldner’s session on structuring a problem-based curriculum. While that phrase means all sorts of things that can be hard to pin down, Chris put it best:
One of the best things about Dan’s session was that he ran it in a “problem-based” way. From the materials here, he generated an incredibly rich discussion, all while talking less than 10% of the time to the entire group (and not much more to smaller groups), simultaneously being super approachable.
The gist of the exercise was to take a selection of problem-based courses, map certain decisions to values, and then use that to map our own values back to concrete decisions about how we structure our classrooms. This is easier said than done, but I think we made a good start, and it generated a TON of questions that I need to answer (or at least start working on). Some of them are more general and perhaps obvious, some are specific to my teaching situation. Here they are:
- Where do I get problems from? How do the sources/types of problems I use reflect my ideas about what is important? For example, classrooms run on Exeter problems versus Park Math problems send very different messages to students about your ideas of how mathematics is held together, even though both of those curricula are very similar media-wise. If I believe in the personal nature of mathematics, should I be writing a lot of the problems myself, and should I decide on problems way ahead of time or should I pick problems in response to my students’ learning?
- How does this tie into assessment? Last year I ran a Dan Meyeresque 4-point SBG scale on approximately 20 standards per semester, using maxima for grade calculations and with 1-3 summative exams per semester which also counted for standards. Due to being a newbie, being lazy/pressed for time, and the culture of my school, all formal assessment on standards was in a traditional, individual, timed setting (but with extra time always offered at lunch). Does a problem done alone deserve a higher level of mastery? Maybe, but that would disincentivize collaboration, not a value I want to stifle.
- (How) can I hybridize problem-based curriculum ideas into my current teaching situation, if internal or external factors don’t allow for a switch to a completely problem-based curriculum? My school is not run like a traditional high school, but more like a traditional small college. Most English classes are seminar style, most science classes are lecture plus lab, and many math classes are (to be fair: well-run, thoughtful, interactive) lecture with some work time thrown in at the younger grades. I also believe that there are important mathematical ideas that don’t necessarily lend themselves to solving problems and mathematical activity that does not fall under the problem-solving header. For example: discussions of infinity, making mathematical art, coming up with conjectures. I also believe there is a (quite small) place for lecture, just like any music student should spend most of their time playing music, but benefits from listening to performances.
- How do I adapt PBC ideas to match the pace asked of me at my school? As a Texas native, my first exposure to proof-based mathematics was a Moore method Calculus course at a summer program, in which the entire course consists of students working through a list of theorems (called the script) with minimal help, class time dedicated almost completely to presentation and critique. In addition to not being for the faint of heart, it moves very slowly content-wise.
- How do I help students transitioning from a very traditional math classroom to a problem-based learning classroom? My school has an application process that involves a test, an application, and an interview, so we get a student body who are mostly very good at school in the big scheme of things. That said, there’s a wide range of study skills, prior training, parental support, and ideas of what school looks like in our incoming freshman class, especially since we have ninth graders who come from literally dozens of high schools. This means that I am not only tasked with helping students adjust to a class structure that will be new to (almost) all of them, they will be coming from vastly different start points, in terms of how much responsibility and genuine mathematical work was expected of them. How do I help them transition to my classroom (and implicitly) my values while respecting their prior experiences, which may have been good or not so good?
Perhaps these are all obvious questions to the non-newbie, but this list is what I want at the front of my mind as I start picking problems and designing expectations for the fall.
I’m teaching the two sections of honors 9th grade math at my school next year, and since we want to allow students to flow between the honors and non-honors sections at the end of any semester in the first two years, I think adopting some of these problem based learning structures would be a good way to challenge my group by pushing them in weird and interesting directions instead of just pushing them “ahead.”
There were numerous other completely awesome things that happened at TMC, but this is the one I had to write down/write about immediatiely. There’s already a Global Math Department session coming up on September 10, dealing with Problem Based Course design and run by Dan Goldner, which I’m looking forward to, but in the mean time, I want to think about how I can implement some of these ideas going into this year.
Any advice, resources, or further questions to add to this list are most welcome in the comments! And if anyone is interested in thinking through these questions together (especially anyone with freshman experience, eep!) hit me up @compactspaces or dprice at bhsec dot bard dot edu.