Yesterday I wanted students to reason through this question:
if you have a belt snug around the earth at the equator, and then you lengthen it 6 feet and have it kind of "hover" over the earth, what can now fit between the earth and the belt? An amoeba? A cat? A horse? ... I find the answer (a cat) surprising. I think trying to articulate why that is so surprising, and then trying to figure out to make sense of the answer, a really interesting thing to do. The math, it seems to me, is simple enough that getting the answer isn't too hard. Articulating why it's surprising is a little harder - and a fun and useful thing to do in class. Since this is a class about knowing and learning, I thought this exercise - where we think about being able to do the math, and how that does not mean we understand the problem - would be a great start.
But it totally fell flat. Most students plugged into a formula, came up with "cat" and were like "yeah, huh. I might have guessed amoeba, but it's not...". And I didn't recover well. I spent a lot of time trying to convince them they should be surprised, and then trying to get them to articulate why they were surprised. Ugh.
Then today I had half the class to discuss this more (I had anticipated using today to talk through the 'how do we make sense of this?' and instead did more of a worksheet approach... it still didn't go so well...); I tried to use an example of how math that doesn't seem sensible (imaginary numbers) can be seen to make sense (terrible idea). And the last half of the class I wanted to set up the use of stop-motion animation. The prompt for stop motion was for all groups to create a video of something moving at constant speed -- slow and fast.
I didn't think about this needing more of a prompt, but clearly it did. Some people wrote out "hello" at constant speed, or drew a balloon at constant speed. Some took a video of something moving. Some used a string to simulate a snake. Some had a spinning pen. Another group had a coin zig-zagging - slowing and speeding up. One group used a ruler and a pen to have constant motion. I had anticipated videos being uploaded and us thinking through how "speed" gets represented here - but that was not to be. Again I just felt dumbstruck and unsure of where to go next.
I'm co-teaching and feeling just so sheepish about how it's going. How unprepared I feel and how it looks like I've just never met a preservice teacher. When I think of why teachers are nervous about teaching by inquiry, this is why.
