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Look at graphs with your 6th grade mind to see your understanding evolve

March 26, 2011

Mark Hammond’s recent post on Leading with Mistakes discusses a wonderful idea of the need to teach students the idea that their own conception of the world is bound to change. To quote Mark:

[Students] should seek out the opportunities to change these conceptions and celebrate the replacement of old concepts with new.

I like this idea so much that I think there might be a scientific habit of mind here—refine incrementally? Evolve knowledge? (Clearly naming these habits is going to be as hard as defining them).

Mark discusses a method that he uses where students explain mistakes they make as their “eight grade science self” taking over in physics class. I do something very similar, but since I teach 9th graders (as opposed to 10th and 11th graders), we refer to our sixth grade mind. Often I ask students “what would your sixth grader say?” to elicit the naive conception of the problem or situation, and this has been pretty successful.

Recently, we did an exercise with looking at a pretty common physics graph where we traced exactly how we refine our understanding with time, and I’m going to try to reproduce that conversation here.

It started with looking at a graph of the force a spring exerts vs the magnitude of the stretch of the spring.

Force vs stretch for a simple spring

So I asked my class how their sixth grade mind would read this graph, and this was the progression we came up with:

  • Sixth Grade: As you stretch the spring more, the force increases.
  • Seventh grade:The slope of this graph is constant, so the force increases at a constant rate.
  • Eighth grade: This is a line, so we can write it in slope intercept from y=mx+b, or y=0.9x
  • Ninth grade: This equation will be more useful if we give use symbols with more meaning. F_s=0.9\frac{\textrm{N}}{\textrm{cm}}\Delta x

I don’t think we need to do this all the time, but I do think it is a very useful exercise to get students to go back and see how they are in a constant process of iteratively refining their understanding of the world, and how that process is one of the hallmarks of scientific understanding.

9 Comments leave one →
  1. March 26, 2011 11:33 am

    Too many of my kids still think with their 6th grade mind. I never had a term for it, though. I just chalked it up to laziness or unsophistication. This is a great exercise to show them my expectations for the level of rigor I’d like to see. Thanks!

  2. Sam Evans permalink
    March 26, 2011 5:30 pm

    I was going to say the same thing…many of my 9th graders are still at the 6th or 7th grade level. Maybe explicitly pointing this out will motivate them to advance and/or see a distinction between their own thinking and what it could progress to.

  3. March 26, 2011 11:56 pm

    I like this term a lot. I’ve been talking to my students about their “past self” and their “future self” but I think it’s too fuzzy. As for the name of this habit… “Change your Mind”!

  4. Brian permalink
    March 27, 2011 5:45 pm

    You write such great posts on growth mindset. This one is so useful because it keeps the focus on the course content rather than diverting to metacognition discussions, which while useful, I think many of my students view as the 21st century equivalent of being told how to study/behave/be a good student.

  5. March 27, 2011 6:23 pm

    Hi, I have been assigned your blog by Dr. Strange as part of edm310 I will be posting my reflections on your posts on my blog.
    This is such a creative idea. Self reflection is so important for students. This is a great way for them to look back while having a specific idea to focus on so that their growth is evident. This also might help them recall the basic principles upon which you are building in your lessons.

    • March 27, 2011 9:09 pm

      Thanks! It really would be neat for students to have some way of tracking their learning over time. This is something I want to work on this summer.

  6. Jim permalink
    March 28, 2011 7:15 am

    This leads to the question, at least for me, of how my students who have documented 3rd and 4th grade math and reading levels see a graph.

    I haven’t yet come up with a way to teach them 4th, 5th, 6th, 7th, and 8th grade math quickly enough that they can get 9th/10th grade physics.


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