Math Performances

 I'm teaching a summer algebra course for incoming students. It's our intermediate algebra course stretched to two semesters, my first time teaching it. Part of it uses or parallels Stanford's How to Learn Math course. We work on number flexibility, patterns (a lot of visual patterns), graphing, proportional thinking, and linear functions and systems. It's part of our Oliver Wilson Scholars program, which works on community building, transition to college, and college success strategies, plus a start on math and english coursework. Each course has an assigned tutor who attends class and works with the learners directly for tutoring sessions. Lyndsey is our tutor and they are doing a smashing job.

In general, I love the graphing stories/lessons (web archive) from Dan Meyer. Of late, I've been doing them via Adam Poetzel's Desmos activity, but did find a current site with all the videos. For this class, I wanted something more experiential. Back in the days of TI calculators we had the motion detectors and I loved those walk the graph lessons. (How can we not have a motion detector app for smart phones?) Lyndsey thought of having groups perform for each other. I came up with four scenarios for them to do, and one that I could demonstrate. Distance of the head above the ground, distance from the edge of the whiteboard, distance between two people, and distance between a person and a ball.

Warm up was to try to guess the joke from this comic. They hadn't heard any of the expressions, but were able to use the 2nd and third graphs to guess at them.

I kept the 15 second time frame. I wanted movement that would be traceable at a classroom scale. I asked them to make it repeatable, and had them perform it twice. Once so people could see what was happening, and once for data. Instead of a hard 15 seconds, we had someone in the course count out loud. The most complicated performance was a minute with slow counting, but it didn't seem to bother anyone.

Here's the handout, with a couple questions revised after doing it. The screen for demonstration was pretty viewable. I wrote a script that I followed.

3 seconds pull down slow

Let go 2 seconds

Pull down fast 1 sec

Stay 3 sec

Put up half way 1 sec

Stay 1 sec

Slow up 4 sec

I got a little messed up with the counting, instead of 1 to 15! And there are some surprises trying to do anything in real life, so the practice was different from the data round.

We compared data, graphed the result, and compared the graph to what happened. One notice was that the graph was kind of the opposite of the motion, it went up when the screen came down. This is definitely a challenge with qualitative graphs, wanting the graph to somehow be a picture of what's happening. If you have a chance to have learners graph what happens to height above the ground when climbing and coming down a slide, you'll see what I mean.

Though I was nervous, new lesson, new course, it worked better than I could have imagined or had any right to have it go. They came up with creative movements, and it seemed to really help with an intuitive meaning to the graph because of the connection to the kinesthetic.

Here's the folder with all the videos. 

The sequencing worked out pretty well. I think the head above the ground was the easiest to understand, and the graph parallels the motion in a natural way. Distance from the edge of the whiteboard was easy to understand. Distance between people was fascinating, and I'd love to do that in a college algebra or calculus class to graph both positions and then the difference. The basketball was really surprising! I expected a much slower and varied trasfer, but the rapid passing gave them a lot to notice and made data collection a challenge.

They selected one of their graphs to turn in, answering an additional question about how does the graph show the action. Maybe I need to come up with a better way to ask that, but there were some good responses. A lot of understanding about data to graph, and some good understanding of the graph properties. Some confusion about minimum and maximum, which makes sense to me since there were two sets of data, really, the x and the y. 

The follow up the next day was Four Corners, a game for practicing coordinate graphing. Not a hit, but good practice. A couple pairs got really into it.

I'll definitely try this activity again, so if you have ideas to improve it or just to try... hit me!