Tuesday, July 23, 2019

My Concerns About "Problem of the Week" and Related Systems

It is a common practice in different math classes and curricula to occasionally feature "random" big interesting math problems. IMP realizes this as a "Problem of the Week." Other curricula have "Thinking Problems" where students explore great problems in the middle of an unrelated unit. (I'll refer to these as POWs for the rest of this post.)

  • PROS: Why I think educators do this:
    • Educators want to honor the vastness of math. They know that math is full of wonderful rich problems that students deserve exposure to.
    • Educators want to foster "general problem solving skills." A lot of educators (myself included) believe that these skills can only be developed by tackling a diverse collection of big messy math problems. Educators realize that by introducing these non-curricular problems, they can diversify the kind of math that students do. They also tend to focus more on mathematical reflection and "big picture thinking" in these problems than in a regular math class.
    • Educators want students to have a chance to do new and worthwhile math, even if they are feeling disconnected from the general thread of math they're covering in class. Some days, you read the room as a teacher and KNOW that if you don't do something big and different for at least one day, the students will revolt. That's a super real feeling, and sometimes taking a break from things is a necessary decision.
  • CONS: Why POWs as a system can be problematic:
    • If a student's experience with all the biggest, best, most fun problems in math is only in the context of a POW, it will create a false dichotomy between "fun and interesting POW math" and "not-fun and not-interesting regular math."
    • Many educators are pressured to observe a fairly constrained set of content standards, and with not enough time to do so. As such, POWs are often the first to get cut. Or they are pushed into the realm of homework, where they are given much less value, structure, and support.
  • What we could do instead, (ideally):
    • Best case scenario, we DO center our math courses around big, rich, messy problems. This way we can teach to those "general problem solving skills." But we ALSO make sure that these problems transmit the curriculum that is at the center of our courses. This way the problems are connected to what students are doing every day in class, adding value and depth.
    • This is WAY harder for teachers to do. There is a pretty narrow strand of algebra/geometry content that is commonly considered mainstream secondary math standards. Forcing our POWs to be within this limited context does constrain the kind of problems we can give them. It is then incumbent upon the teacher to push the boundaries of their math class by finding problems that feel different and diverse, but ALSO rigorously include mainstream secondary math standards.
  • What I'm NOT saying:
    • I'm NOT saying that we shouldn't do POWs, or have random days when we do math that is disconnected from the unit/course we're teaching that week. As with every other decision we make as professionals, educators have to weight the pros and cons of each decision in the context of who we and our students are, what our goals are, and what the context is.

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