Competency-Based Grading and Common Core Math: A Perfect Match?
My Uh-Huh Moment
Over the summer I spent the day with my math team as we prepared for the implementation of the Common Core State Standards for Mathematics into our school. We were working on an intense math problem when I had one of those uh-huh moments – the kind I used to describe to my students when I taught high school math in Andover, Massachusetts. The problem was a simple one to understand, but it had many layers of complexity to it for math teachers:Imagine you are a peasant, and your ruler told you that you could have as much land as you could mark off by walking in one day. What is the most amount of land you could reasonably claim? Give your answer in square miles and be prepared to support and defend your work.
Among the questions that came to mind when thinking about how to solve this problem were these: How many hours can a peasant reasonably walk in a day? How fast can a peasant walk? How many breaks will the peasant need to take? Are their hills, mountains, or other physical obstacles that the peasant will encounter? What kind of tools will the peasant have to navigate with (i.e. a compass or a GPS)?
Very quickly, a group of us began to debate these questions and create a list of assumptions that we would use to derive our answer. We debated what type of a shape would produce the biggest area. With some trial and error and use of some mathematical formulas, we agreed that a circle might be the theoretical shape that would yield the biggest area, but the square was the shape that would be