We're on Day 11 of the term, and we're still in our introductory unit. The time is a little worrying, because I'd like to be moving on to the unit on constant velocity. On the other hand, we've done 5 labs and 5 discussions, which is way more than I've ever done this early in the course. (Go us!)
Today was really humbling for me. I knew my biggest struggle would be to STOP TALKING and let them talk instead, and it has been. I keep jumping in to instruct. A few days ago, I jumped into a discussion on whether a quadratic fit or a linear fit was more appropriate for our data. I wanted to introduce the idea of the shape of the graph needing to make physical sense, as well as move the consensus to a linear fit, so I asked them to describe what a quadratic graph looks like. My follow up question was whether it would make sense in terms of the physical situation for the graph to curve back up. (You know, completely ignoring the issue of where on the graph it curves back up...) They said no, we moved on and got to analyze the slope and y-intercept and all that good stuff.
Back to today. This lab was supposed to have a quadratic fit. And at least 1 group had tossed their initial quadratic fit and put a linear fit on the whiteboard instead. All because "curving back up" wouldn't make sense, even if the curve back up was in the negative numbers.
And I knew. This was COMPLETELY my fault.
On the bright side, we did get to talk about why we ignore Quadrants 2 and 3. They were discussing whether or not we even consider negative x-values, and another student pointed out that none of our graphs would make sense if we started looking at what those values did.
We also got to fix our ideas of checking shape (I hope!). I asked the question, "What's the difference in how a linear graph increases and how a quadratic graph increases?" We had some good conversation about constant increases vs. changing (increasing) increases and checking it against our data points.
Still, what could have been a 30 minute discussion turned into a 60 minute discussion, all because I had tried to rush them to a conclusion a few days earlier.