Comments on: [Confab] Snow Day

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By: Evan Weinberg

Evan Weinberg — Mon, 03 Feb 2014 14:13:53 +0000

Dan and Michael:

To toss my hat into the ring, I’d suggest that a computational tool (e.g a spreadsheet or Python/JavaScript program) would be a nice intermediate step in moving toward the abstraction of algebraic tools.

By: Dan Meyer

Dan Meyer — Mon, 03 Feb 2014 05:44:53 +0000

Michael Pershan:

Here’s what I think is going on in a lot of these problems. We give kids a question that they do have the tools to answer…poorly. Maybe their tools are inefficient, slow. Maybe their tools are inaccurate, sloppy. Either way, the question is immediately doable with their poor methods, and hence potentially interesting.

This harmonizes nicely with Harel's writing on need. It's great if students know it's possible to solve a problem given their weak, small tools but so undesirable they'll be interested in learning about stronger, larger tools. It's a nice way to turn arithmetic into algebra. Sure you could figure out the 2,014th term in the arithmetic sequence 13, 14.5, 16, etc., by adding but it sounds annoying. Anybody got a better tool than arithmetic?

By: Michael Pershan

Michael Pershan — Sun, 02 Feb 2014 03:55:32 +0000

I’m having a hard time actually doing good work on this particular problem, but I have an observation to toss into this discussion.

There’s a sort of apparent paradox to engaging math problems that bursts forth when I think too hard about this stuff.

How is it possible for kids to become engaged in hard problems?

A problem needs to be doable for kids to get interested by it. But if a problem’s doable, then what makes it hard?

(We often cheat by saying that “It’s not too hard or not too easy.” No wishy-washiness here. Can the kid solve the problem, or can she not?)

Here’s what I think is going on in a lot of these problems. We give kids a question that they do have the tools to answer…poorly. Maybe their tools are inefficient, slow. Maybe their tools are inaccurate, sloppy. Either way, the question is immediately doable with their poor methods, and hence potentially interesting. The key is to find problems that pair lousy quick answers with better, tougher ones.

By: Bruce James

Bruce James — Fri, 31 Jan 2014 05:13:11 +0000

re Molly: “I”m not sure calculating the cost would actually be the point!”
Too often, our reflex in math is “what’s the answer? Am I right?”
Calculating the cost is simply the period at the end of the sentence. The glory lies in the sentence, in the construction, in the overcoming of itchy, scratchy puzzlement that happens up to the period that ends the sentence that brings the problem to closure.
The idling bus problem is thick with potential. You can spend lots of time just estimating and defending and revising. Every step of the problem is begging you to critique the reasoning of your peers.
As an ancillary to this you might have a mini lesson called How cold is cold?”(here come integers)
We keep math questions sequestered in discrete chunks of calculations because those are the ones that bring the fastest closure.
I think someone commented on the Magic Octagon, or some other one with, “great, where’s the lesson?” The lesson is in your ability to see and hear and dream up the long and diversified narrative that can spin out of such problems.
What’s kind of shape was that hand holding?, How did you know? Draw an octagon, draw a regular octagon, how many degrees are in an octagon?, Hey, how do you use a protractor, and on and on unto a full problem.

By: Molly

Molly — Fri, 31 Jan 2014 00:55:45 +0000

@Dan, as I learned from you, giving students the exact information they need to solve a problem in the exact format in which they need it is ineffective! The idling buses are a real world situation, but turning it into a real-world formulaic question isn’t an actual improvement over what they do in traditional textbooks. The intriguing part of the idling bus depends on your background and passions; do you care because it might waste money? because of environmental harm it might be causing? It’s a great opportunity to explore the concept of skewed information – the data you collect and the formulas you use might be directly related to the point you are trying to prove, pro or con.

By: Dan Meyer

Dan Meyer — Thu, 30 Jan 2014 23:44:42 +0000

@Molly, thanks for the taking the task head-on. Can you give a brief rationale that I can quote for why one task is ineffective and the other one effective?

By: Jason Dyer

Jason Dyer — Thu, 30 Jan 2014 22:47:03 +0000

I dunno what state Matt is in, but the school district may be also subject to fines.

From the EPA’s webpage on idle reduction of school buses:

http://www.epa.gov/cleanschoolbus/antiidling.htm

see the “Compendium of Idling Regulations (2012)”.

There’s also an idling calculator and other fun things.

By: William Carey

William Carey — Thu, 30 Jan 2014 21:31:08 +0000

An interesting question is this: how do you know whether you’re right? The more interesting question is this: did the *adults* do the math?

Somewhere in the bowels of the the school (county?) office, is there an excel spreadsheet? It takes a few variables – number of busses in the fleet, gallons per hour, cost of diesel, cost of a snow day, and spits out a yes or no.

An intriguing (if high risk?) exercise would be to divide the students into groups. Have them discuss what variables would go into that spreadsheet and why. Have each of the groups write a letter to the district office explaining what factors they think are relevant and why, and asking for a response explaining how the actual *adults* made that decision.

If it turns out that the adults do, in fact use some sort of math, then you can have the students play with it and try to understand why the adults did what they did. If not, maybe have the students propose something?

By: Molly

Molly — Thu, 30 Jan 2014 18:52:48 +0000

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? 2. What conditions in the district, state, national or global economy/environment would make it worthwhile to answer this question?

I’m not sure calculating the cost would actually be the point!