Having argued that Dan Meyer is using technology in ways that are novel in American mathematics classrooms, I want to turn to the problems he is using technology to solve (I refer to problems of teaching, not math problems).
This is the area in which Meyer is most explicit about his work. He gave an online seminar (and while we’re on the topic, can we please agree never to use the term webinar again?) recently in which he described the genesis of the escalator problem. Some of my observations will surely match his.
In the Connected Mathematics Project (CMP), which I have worked with for quite some time, we talk with teachers about a teaching model-Launch, Explore, Summarize. CMP is based on problems which form the basis of most daily lessons. Teachers engage students with the context and the mathematical challenge in the Launch, give them time to work on the problem in the Explore phase and then uses students’ ideas and solution methods to Summarize and help students to meet the lesson’s goals.
Meyer is working hard on engaging students in mathematics lessons. He is developing excellent launches.
When I work with CMP teachers, I emphasize two key aspects of launching problems. (1) Students need to understand the context, and (2) Students need to understand what the mathematical challenge is within that context.
Not every student is going to have experience with even the best chosen contexts. That’s OK, but it means teachers need to pay attention to setting contexts up for students, and in helping students to pay attention to important features of the context.
You don’t need to live on the coast to solve a problem involving the ocean, but the teacher has a responsibility to bring important aspects of the ocean to the students’ attention.
But it’s not enough to get students engaged with the context, teachers also need to make sure students understand the mathematical task embedded in the context. Everyone needs to agree what the question is.
Setting up both of these in a finite amount of time is challenging, and Meyer is upping the ante.
The opening shot in the escalator video (below) establishes the context instantly-escalators at the mall. Is there a teen in America for whom this is not a meaningful context? Love it or hate it; having few or many opportunities to visit it, the mall is part of teen culture.
The next 20 seconds suggest the mathematics embedded in this context. We are going to be looking at rates-how fast Meyer (and by extension the students) can go up and down the stairs and escalators.
And here, in my opinion, is the one weakness in the Launch (and it’s a minor one). The video ends with Meyer getting to the top/bottom of the stairs. I want the video to hammer home the implicit question, How long does it take to go up the down escalator? I want him to turn from the bottom of the stairs, go to the bottom of the down escalator and begin to take his first step, then have the video freeze.
But that’s a mere quibble with a masterfully designed launch. So let’s dig a bit deeper.
If teachers want to engage students, they need to know the target audience. Meyer is a high school teacher and he knows his students well. Consider the following elements of the escalator video:
- He smiles slightly and slyly at the camera in the opening close up. Dig this, he seems to be saying to the viewer. While most high school students won’t know who this guy is, he is no longer some random guy; he is a sympathetic accomplice.
- He puts in his earbuds. Adults may not notice this as significant, but high school students will pick up on it right away. It builds their identification with the context.
- The question. I cannot say enough about the question. How long to go up the down escalator? is brilliant. It’s just transgressive enough to be interesting to high schoolers, and nowhere near the border of inappropriate for school-endorsed investigation. Compare to the original-What is the speed of the canoe in still water?-and it’s no contest.
So Meyer has some novel uses of technology, including to launch problems in high school classrooms. For him, the problems of teaching include, (1) How to engage high school students with meaningful problem situations, and (2) How to focus their work on a common question.
But to what end? What happens once the video is finished? Next post.