Previously: PBL, Part 3: Making it Work
Here are my working definitions of three important math terms:
Math exercise – a short, rote problem that takes no more than a few minutes to solve and that looks identical to one or more nearby
Math problem – a task driven by a perplexing, unfamiliar question, sometimes loosely-defined, that has an opaque path towards a solution
Math project – a big task driven by a perplexing, unfamiliar question, sometimes loosely-defined, that has an opaque path towards a solution
These definitions are far from perfect, but they have served their purpose for now in helping me think about what I value. Notice that what distinguishes a project from a problem – to me – is the size of the task, that is, the amount of minutes expended and/or the size, in pages for instance, of the final product. Yes, good projects also have external audiences, capture student interest, involve collaboration and problem solving, and hit all aspects of the PBL unicorn, but so too can problems.
I’m convinced that students solving perplexing, unfamiliar questions is one of the most valuable uses of time in a math classroom. But what size tasks? And how many? Certainly there is value in doing this with frequency, i.e. quantity. How much does quality suffer if a 3-week task is crammed into a few days?
As a lover of efficiency and economics, I often think about how to maximize the above ratio (courtesy of Dan Meyer). Please weigh in on how you do this in your curriculum. I give more of my thoughts in the next post.