"I understand that an exemplar project might not be best utilized by being "replicated" because of its uniqueness to the learning community within which it was situated. However, I haven't seen anybody do a project that achieves depth in mathematical thinking. I want to see one so that I know what it COULD look like…not what it SHOULD look like in my class. My initial thoughts are that an emphasis on applied mathematics has skewed project-based learning in a direction that veers away from mathematical thought and more towards an application of formulas. I also think that an emphasis on PRODUCTS (or flashy, sexy art) has overshadowed less exciting products that COULD demonstrate thought transformation. Students have come to expect art and "relevance" (which, to them, often means how it can be used to solve a "real world" problem). Anyways….it needs work. I love working here for the freedom we have but I have actually become an opponent of PBL in the ways I have seen it done.
I have been thinking a lot about unit structure since we talked recently. I love the Interactive Mathematics Program model of perplex --> attempt --> identify what we need --> play out mathematical trajectory --> revisit initial problem. By starting and ending a unit with THE SAME PROBLEM, you can easily see where students "began" and where they "ended" which (aside from grading) helps us give meaningful FEEDBACK about their understandings/misunderstandings and development."
Without a doubt, the journey is maddeningly interesting...