Month: August 2010

Total 15 Posts


Deborah Loewenberg Ball, on being less helpful:

In other words, we need to help teachers know how, when you help too much, you’ve actually made the problem into a different problem. But how do you help enough so that the problem is do-able? It’s sort of the interaction between the task and learning how to question and being aware of what your questions are doing to the task. I think we’ve all had the experience of giving so much structure and help that the problem becomes a simple routine problem when it wasn’t originally.

DLB On Real-World Context

Deborah Loewenberg Ball, the full quote, so solid, knocking me back into line a bit:

It’s interesting because these problems — speaking of context — aren’t really contextualized. We’re not making them into fake cakes or breads or anything. They really are just shaded rectangles. And the kids are finding them very challenging and interesting. So I do think, on the question of context, it’s worth remembering that mathematics itself is a context and that puzzle-like problems are often both very engaging for kids and good equalizers because kids looking at those diagrams aren’t shaped by some of those same inequities about kids’ experiences. There are certainly differences in their experiences but they’re not the same as problems about how cakes get shared or other kinds of real-world things.

Unnatural Currents

This is basically perfect, a single panel that goes 80% of the way to explain a) why your students roll their eyes when you assert the value of math, and b) the uncreative state of curriculum development in 2010.

In the second hour of my St. Louis workshop last Saturday I assigned an application problem to each group and asked them to locate the problem’s “hook,” which is to say, the point of the problem. Invariably, we found the hook in the middle or at the end of the problem, buried beneath all kinds of exposition and set-up. This is something like pressing the gas for ten minutes and then turning the key in the ignition.

One teacher said, “My students do all this work and they don’t know why they’re doing it. They’re doing it because the textbook is telling them to do it but when they get the last answer, they forget how they got it, they don’t know what it means, and they don’t care.”

We also noticed that the publisher sometimes chose an unnatural hook for the problem. For instance:

Let me put a situation to you: a high-rise is on fire. It is surrounded by marshy grass and shrubbery. Everyone has evacuated except for a man and his son who are waving and coughing from a window on the eighth floor. A firetruck speeds up to the building and parks as close as it can, some twenty feet away. The rescue ladder starts extending …

… and is anybody wondering anything besides “will the ladder reach?!

That is the natural current of this evocative situation. The unnatural current is to ask, “how high is the top of the ladder above the ground?” or, to reduce the example to absurdity, “what is the circumference of the firetruck’s tires?”

This leads me to three recommendations:

  1. Don’t force it. I’m not saying that the only math that matters is math that applies to some real-world context. Like Deborah Loewenberg Ball said, “On the question of context, it’s worth remembering that mathematics itself is a context.” I’m saying that if you can’t find a natural current for the Pythagorean theorem, don’t wrap a neckerchief around a dog and tell your students that the natural current is to apply the Pythagorean theorem. That is an unnatural current. Unnatural currents posit mathematical investigation as an unnatural act, which hurts all of us.
  2. Stop using clip art and stock photography. Clip art and stock photography are still water. They lack current of any kind, which is their whole point. They exist so that as many interested parties can purchase them and apply them to as many different purposes as possible. On the upside, still water can lead you anywhere you want, to any question or content standard. On the downside, you and your paddle are doing all the work, and your students will notice that you’re sweating when you assert the value of math.
  3. Find the natural current in some evocative photography or video. Paddle with that current. The boat in the river video is effective because, at its conclusion, no one is wondering anything but, “how long will it take him to go up the down escalator?” I found the natural current of the video and paddled with it. If that current doesn’t lead to the skill you hoped, try remixing the problem.

    This is difficult. A good example is this video from commenter Scott Haluck. He put a lot of care and craft into it.

    I asked him what question he’d ask and he replied:

    • “if everyone started at the same time, how far apart were they when they started?”
    • “what time will each person be passed by the fastest racer?”
    • “how long is the race?”

    And I’ll suggest here that there is a strong natural current to a video that shows four people racing across a screen. That video begs one very specific question, especially if you pause the video in the middle of the race. Ask a different question and you might hit more or different content standards, but you are pushing your students along an unnatural current and they will notice.

Just Checking

If teachers catch wind of (let’s say) these wiki things and want to know a) “are they really a big deal?” and b) “how can I get my students started?” I’m assuming there’s some kind of website registered (let’s say where they can find:

  1. a video interview / case study of a telegenic teacher who set some ambitious goals and used wikis to achieve them.
  2. a step-by-step guide for deploying that technology in the classroom
  3. a list of people who have volunteered to serve as tech support representatives over e-mail.

I mean, that’s out there, right? Given the edublogosphere’s abundant hectoring and cajoling, I figure that has to be out there. If it isn’t, that begs the question, have you done enough to help the people who chose to do something?