Don’t Worry About Finishing – Just Show Me Good Math!
Last Thursday, I tweeted out a preview for my Geometry students’ alternative to a regular test:
A couple of my students came in murmuring, “I think the test is about Star Wars or something!” Yes, they were as excited as I was. Hopefully they’d still be excited when the class was over. Hopefully I didn’t ruin Star Wars for them!
I started the class by saying “I don’t expect you to finish. I just want to see evidence of good math.” This was going to be a very subjective assessment, I knew. That was less important than my goal to make it meaningful. I wanted students to be more invested than they would be in a typical test on geometric solids: “Here’s a bunch of pyramids, prisms, cylinders, and spheres. Find their volumes or lateral areas or surface areas because I said someday you may need to know this.”
Instead, I told them that I was offering them a dream job – to get to work on the models for the next Star Wars movie. I gave them two pictures, one of Starkiller Base, and one of the Millennium Falcon, and told them that I wanted scale models built for each of them, but need to know how much material to buy and how much paint to buy. They had to use whatever math tools they knew (and had full access to their notes) to make these calculations. Since I didn’t give them any numbers, they had to ask for information through Google Hangouts. Some information I gave was exact, some was an estimate, and some was LMGTFY (for unit conversions, etc.).
I reminded them again that I did not expect them to complete all the work and get the right answers in the time they had. What I graded them on was:
- Using tools that we have learned (25%)
- Determining what information you need (20%)
- Thinking creatively (25%)
- Correct Calculations and Estimates (15%)
- Explaining Errors (15%)
Unless they spent the whole time not doing the assignment (which did happen for a couple of students), they were going to get credit for a whole lot of noticing, wondering, evaluating their work, making plans, estimating, justifying their choices, and doing those things that mathematicians do.
What I found was that almost all of my students, when given the chance, can do some great math and have become more comfortable with embracing and explaining their mistakes, going in one direction and then changing their mind and going in a different direction, and starting problems by estimating. I also found that they need more help structuring their time, planning their problem solving, and solidifying their estimation skills and number sense. (More regular Estimation 180 activities are on the agenda for next year’s Geometry classes).
There were a lot of things that I really liked about this assignment, but it definitely needs some work. Most students were on board with not having a finished problem when I explained it at the beginning of class, but some students really felt a need to finish . I designed the task with the idea that there’s always more one can do to be more exact, to help reinforce the idea that a model just needs to be good enough, and that time constraints are real. There were also more than a few students who said that they would have preferred a plain old test. How much of this was because it was new, and how much was because it is less predictable? The open ended tasks that we’ve been doing definitely have helped, but maybe a few more of these projects with more possible closure would be helpful.
I did have a few students note that they weren’t big Star Wars fans, so maybe I need some less dated pop culture references in the future. On the other hand, one student is a bigger fan than I, and pointed out the different estimates on some of the measurements that I gave, and which ones were more reliable.
Overall, I really liked this attempt at something new, and hope that I can develop it some more and help students find more success in showing what they know and how they can apply it.