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Lesson progression: discovering THE equation

October 21, 2010
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So, for intro physics terms, this equation is the first moment when kids take a big gulp and wonder what they’ve signed up for. Here it is:

\Delta x= v_0t+\frac{1}{2}at^2

Yep, that’s the constant acceleration kinematic equation. I mean this looks like a killer—2 parameters, 2 variables, subscripts and superscripts? Egads.

For years I’ve tried to find better and better ways to teach this. One attempt was just using a better text. Here’s a great one written my a former colleague, Mark Hammond.

A custom physics text I used to use, written by Mark Hammond.

Literally, whether or not kids could understand this page was one of the best indicators of student success in my previous courses.

Hoping to help kids along that path, I’ve tried all sorts of things. Including making a movie of me reading this page of the text. Kids loved it. I don’t think it really moved the understanding needle (you really can’t watch physics—gotta do it).

So how has this lesson progressed now that I’m embracing modeling more fully, and trying to get kids to take control of their own learning?

Well, it starts with this graph.

One graph to challenge them all.

And I ask this question

  1. Find an equation for v in terms of a,v_0 and t.
  2. Find an equation for \Delta x in terms of a, v_0 and t.

And then I just let them work together to figure it out. Kids were trying all sorts of things. Asking tons of questions—to which I most often replied, “I don’t know—why do you say that?” or “what does this mean?”, or “did you check units?”

Then one kid got it and, and another and another, and they started helping each other, without giving away the answer. And some came up with totally awesome different approaches like:

\Delta x=\left(\frac{v_i+v_f}{2}\right)\Delta t

Next, the bell rang, and no one moved. They kept working—almost every single kid. “Can we do this for homework?” one asked.

Can you, on your own, take ownership of this idea and discover it for yourself? Heck yes! Do it.

So what’s the lesson from this lesson progression? Do I need a the perfect powerpoint or smartboard ‘activity’? Nope. Do less. Challenge the kids with something interesting, and let them run.

5 Comments leave one →
  1. October 21, 2010 3:26 am

    Very nice! I know it can be hard to turn it over to the kids because (1) it’ll take longer (2) it’s easier for you if you do it (3) kids might complain they can’t do it. I have to take more of those risks.

    2 observations: (1) You’re a southpaw just like me! Well, I have mixed dominance. I only write and eat lefty but do everything else righty. (Using a knife righty but eating lefty means I don’t have to put down utensils and switch. I love it.)
    (2) I didn’t know Mark wrote his own text. It looks similar to the PSSC text.

    • October 21, 2010 3:35 am

      You know, I think in the end, this approach is going to take LESS time. All of the kids will have discovered it themselves, and really practiced it, which will save a lot of those “well, i wasn’t really paying attention when you explained it, can you explain it again” moments that happen when I decide to show my algebraic brilliance on the board.

      Lefties rule! I’m amazed you watched the video. I want to try to do more of these, but I keep forgetting to bring my tripod home from school.

      Mark really adapted the text from PSSC. We originally used PSSC, then a teacher condensed that into bullet point notes, and then mark re expanded it into a nice LaTeX textbook. But kids never learned to read it, so it wasn’t helpful. Thought now is to put small readings in packet, a la modeling.

      • October 21, 2010 3:49 am

        I agree with you about it taking less time in the end. But when you’re confronted with that deafening silence and the blindingly blank stares, it can be hard to wait it out and gamble for a delayed payoff.

  2. October 23, 2010 12:20 am

    This is cool. I have found this to be true as well. I love this modeling stuff! How much did you discuss acceleration before giving this challenge? I mean how did you introduce ‘a’? I intro’d the idea this week with them rolling batteries down the whiteboards with the metronome blaring in the background. I have motion sensors, but I wanted them to really get a feel for the process before the ‘magic’ of the sensors. As of this moment Mr. Battaglia knows nothing of this ‘acceleration’ word the kids keep bringing up. (I haven’t read that chapter yet.😉 )

    • October 23, 2010 1:54 am

      We’re near the end of our 3rd unit, which is the constant acceleration model. Kids have been graphing velocity vs time graphs, and they realized very quickly the slope was the acceleration (They all had this in 8th grade, though they miss finer points like the meaning of negative acceleration, etc). Our paradigm lab was to produce motion where the “velocity changed at a constant rate.” Soon I’m going to write up how we extended this stuff with kinematics equations today—it was awesome. Now we’re working to engineer a “photo finish” between a constant velocity cart and a bearing rolling down a ramp.

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