Earlier this week, Matt Reinhold tweeted:
Fearing our buses wouldn't start due to cold, our district let them idle overnight. The first student question this morning: "How much did that cost?"
- That's kind of amazing.
- There's a local, personally relevant, real-world math problem somewhere in there for students to work on and learn from. But one of my theses with fake-world math is that relevance and the "real world" aren't necessary or sufficient. They don't guarantee interest and they don't guarantee learning.
So tell me about an effective treatment of this situation in math class. (Draw on research on curiosity, abstraction, and the CCSS modeling framework if they're helpful.) Also tell me about an ineffective treatment of this situation in math class.
BTW. "Curriculum Confab" will be a recurring feature around here, similar to our early "What Can You Do With This?" days only with more design and theory attached.
2014 Feb 02. Molly helps out enormously with this confab:
Ineffective: If gas costs 3.38 per gallon, and the bus burns 1.1 gallons per hour idling, what is the cost of the fuel burned by 32 buses over a period of 13 hours?
Effective: 1. What questions do we need to ask in order to answer this question?
The first treatment offers no "information gap" of the kind that's generative of student curiosity. Moreover, curious or incurious, the first treatment doesn't have students doing modeling of the sort promoted by the CCSS, where students set themselves to " identifying variables in the situation and selecting those that represent essential features."
I'd only add one question to Molly's effective treatment: "How much would you guess it cost the district to keep the buses idling overnight?"