The teacher put up this photo at the start of class and asked her students, "Where's the maths in this picture?" She asked them to discuss the question in their groups while she took attendance. After four minutes, she pulled them back together and asked a student from each group to tell her where they found the maths in Wembley Stadium.
"The amount of seats," one student said.
"Area and perimeter," said another student.
"The number of seats," said a third student.
"We already have the number of seats," said the teacher.
The student tried again. "The, uh, perimeter … of the lines."
The teacher pressed a little — what lines? what perimeter? — and then accepted it.
After two more groups, a girl named Sarah said something I can't quite make out on the video, but the teacher was visibly floored.
"Have you read my lesson plan?!" she said. "Because that is very, very spooky. Because what we're actually going to look at today is based on what Sarah just said. I'm a little bit … that's very odd … but good stuff."
- If you give students some photo of their world and tell them, "We're definitely applying math to this — you figure out how," you're confusing the master and the servant in the relationship between math and their world.
- If a majority of your students are interested in a single question (eg. the number of seats) then use it. That's a gift. Can math help your students resolve that curiosity?
- Conversely, if you are shocked when your students' questions zero in on the point of your lesson, you're designing your curriculum for the only person in the room you shouldn't care about.
2011 May 24. Bowen Kerins picks up some of my slack:
There's a big fault with this sort of question that you didn't mention: students start skipping the mathematics altogether and try to determine what it is the teacher wants them to say. It's the equivalent of the teacher asking "What number am I thinking of?" then waiting for a bunch of answers. It's a totally different game, decidedly not math, and not even close to good inquiry-based teaching. Such questions should either be clarified or just not asked in the first place.