Look at graphs with your 6th grade mind to see your understanding evolve
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.
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 , or
- Ninth grade: This equation will be more useful if we give use symbols with more meaning.
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.