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long chains of reasoning-making them real

January 6, 2011

SG posted a comment on my final exam postmortem that has really gotten me thinking.

The trick here, I think, involves a few things, but one is working memory. I think that my “regular” physics students would have about the same issues and successes on both of these problems, and that not all of it is about what or how we teach them. Cognitive ability has a big dependence on working memory, and most of these students that I have always had in these classes simply can’t hold several concepts in their minds at once. They can remember the facts or even apply the concepts to different problems, but only one at a time (or two). Having to juggle competing or complementary concepts and synthesize them is the hardest thing for them, and even though we push (and should push) them towards this, a significant fraction simply can’t hold all of those ideas in their heads at once. Probably as a result of this, I’d answer your question “is this the way that my kids see math?” with a “yes,’ because that’s all of the concept flow that they can really get into their heads at once. The trap that lots of conceptual/regular/intro classes fall into is to remove lots of the symbolic manipulation (good idea) and to replace it with more complex reasoning that’s really dependent on understanding and applying the heart of the math all at once. In lots of ways, that pendulum “graph” is really really hard. Even though it’s elegant and awesome, lots of them can’t appreciate the argument, because they can’t understand the whole thing, but only pieces at a time.

This is awesome, and it makes me want to go and do a bunch of reading about working memory to see how to develop deliberate practice to help students improve working memory.

This also got me thinking about some of my previous musings on long chains of reasoning.

If following long chains of reasoning really is a core skill of science, necessary for understanding everything from the photoelectric effect to global warming, and I think it is, how can I help kids to build this skill?

My idea is that when we next try to make an argument like how the floor knows how hard to push you up, or how we are able to measure the acceleration of a mass spinning around a circle using a stopwatch, students practice writing each step of the argument on a stip of paper and connecting them in a paper chain, like so:

Here’s an idea I had recently. What if we practice building real chains of reasoning out of paper?

Would this help them see how they are linking ideas in physics? I guess the only way to tell is to try it. I’ll let you know.

4 Comments leave one →
  1. January 13, 2011 2:20 pm

    I love the idea!

    I wonder if there is a non-physics example that you could use to show them what you mean by “chain of reasoning.”

    I wonder is you could make them explicity write out their “chain” on a quiz/exam/whiteboard. Perhaps in a separate column along side their mathmatical work (similar to the “Commentary” column that is required from problem sets for certain MIT physics courses).

    As we move through kinematics and dynamics, I usally put up a concept map with a = Fnet/m in the middle. Branching off the “a” we have all the kinematic quantities and relationships. Branching off the “Fnet” we have all the emperical force laws (friction, gravity, spring, etc.)

    Then we use the diagram to solve problems. I’ll ask kids where in the diagram where are the knowns (start) and where are the unknowns (goal). Then we use the diagram to trace the solution path. Some kids might work the problem forwards, others might reason backwards first and then solve it forwards.

    This concept map is similar to your links, but it presents all possibilities at once. I have not made students be explicit about their chains of reasoning, but now I might. To me, that is more important (and what I want to see) than a numerical answer.

    Keep us posted!

    • January 13, 2011 2:49 pm

      Thanks for the suggestions, I’m going to look into finding some real world examples that don’t involve physics. Maybe mapping out an episode of CSI or something like that…

      I love doing concept maps, and my kids love them as well. I need to look up some resources on how to do them a bit better. I see these chains as slightly different, since they are specific to one problem explanation, which makes me think the two ideas in concert could be very powerful.


  1. The NYT on learning: studying notes can be deceiving « Quantum Progress
  2. Long Chain of Reasoning exercise 1: Momentum conservation « Quantum Progress

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