At PCMI this summer, the focus of our Reflecting On Practice class is mathematical tasks. What makes a task worthwhile? How can we adapt a task to make it more worthwhile for our classroom? What should we be considering as we implement the task in our classroom?
On the first day we had to answer the question, “What is the last cool thing you did in your classroom, and WHY?” For me, that last cool thing was simply devoting
a full most of a class period to a discussion on “What is a number?” (I had students start the discussion at their table, followed by sharing an idea from each table, followed by a whole class discussion). I’ll follow up some time next week with what my goal was for this task and why I thought it was so cool. I already plan to use the prompt (with perhaps another structure to the discussion) in another class next year, but first I’d love to hear others answer this question. Once we can answer this question, we can answer Paul’s question of “What is a numeric illustration of the fact that a negative number multiplied by a negative number is a positive number?” So, please, fire away in comments or tweets.