“What’s your plan?”
The question is a simple one to ask, but often doesn’t have an easy answer.
I find myself in a position this quarter which I haven’t been in for a few years. One which has me spending a lot of time thinking with students about their plans.
This quarter I’m teaching a class to a group of seniors who have one final chance to meet their graduation requirements. At our school, this means they need to write and defend a Performance Based Assessment Task (PBAT). A PBAT in math is a 10-15 page math paper in which students solve a non-routine mathematical problem and convincingly argue that their strategy and solution are valid. (As I’ve written before, our school is a part of the New York Performance Standards Consortium, so students meet the assessment portion of their graduation requirements by earning a passing score on these PBATs instead of standardized tests.)
On the first day of the course a few weeks ago, we read this document describing problem solving techniques developed by George Polya (which he laid out in more detail in his text How to Solve It).
Since then, most students have found a problem they want to solve and executed the first principle, “Understand the Problem,” with relative ease. Yet without exception, the students stumbled as they move into the next phase: Devise a Plan. They have researched analogous problems, drawn diagrams, and defined variables/key terms. They have written pages about the problem they are solving, yet when it came time to articulate a strategy for what they are going to do to solve it, they got stuck. “Why do I have to explain my plan?” the students complained, “Can’t I just solve it and give you the answer?”
The question is so common in completing these kinds of math tasks that earlier in my career I started to question the value of Polya’s Second Principle. For many students, getting an answer to complex a math problem is hard enough, why complicate this further by asking them to think/talk/write about “problem solving strategies” abstractly?
But sitting in a room with a dozen seniors in (hopefully) their last months of high school has reinforced my commitment to the Second Principle. I’ve know these students for four years (five years in a few cases) and I have a pretty deep understanding of some of the challenges they have faced and overcome in getting to the place where they are now, one or two requirements away from a high school diploma. They have overcome economic instability, learning disabilities, violence, and the trials and tribulations of being a teenager.
Yet the stark reality is that — especially in today’s economy — getting their high school diploma alone won’t do much for them.
What are the best options for a young person who scraped by in high school? How does one balance the immediate demands of a life lived in economic instability with desires to invest time/energy/money in a way that will lead to more stable long term outcomes? What do you do if you are 18 and you don’t really know what you want to do “when you grow up?”
I have some ideas about these questions, but the reality is that no one can answer them for any of the young adults in my class. Each individual needs to do what’s best for her or for him given the specific realities of their life.
What I can do is help them think about effective strategies for answering these questions, but this won’t be effective unless such a strategy is
possible. The revolutionary aspect of “Polya’s Second Principle: Devise a Plan” is that it allows us to take back a power which we often give up. We are not required to muddle around in the dark. The outcomes of our life are not dictated completely by chance or external factors. We can have power over the choices we make and — once we’ve made them — we can go back and think about whether or not they were “right” for us and our situation.
It is a complicated world and it feels like it gets more complicated every day. I’d never suggest to a student that I know how to navigate this complexity, but I do believe that there are some etablished principles that can help. One of these is to develop a road map to use to track where you are going and evaluate whether or not you’ve gotten there. Requiring students to devise a plan for a complex problem and discuss that plan in detail in order to graduate high school will help them develop that map for the problems to come.
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