Leading with mistakes
There has been some internet-based discussion recently amongst math and science teachers about the usefulness of Khan Academy videos in particular, and lecture videos in general. Derek Muller at Veritasium.com has created a short video about his research findings into the efficacy of using videos to teach introductory physics concepts. If you watch that quick video, you’ll get a snapshot of one thread of the recent discussion. The upshot of Derek’s argument is that videos which contain student misconceptions and show real people working with and through their misconceptions lead to more successful learning by the observer of the video than does a straightforward exposition of the proper concept.
A recent blog post by John Burk at quantumprogress discusses the idea of using video examples of problem solutions that include common student mistakes and/or misconceptions. The idea is for the students to identify the mistakes made, thereby potentially learning more than if they simply ceded control to the expert on the screen solving the problem. We’ve all seen the effect of students watching an expert solve a problem for them. The students watch the solution unfold before them, usually failing to notice the subtle (albeit clearly presented) steps that cite fundamental principles and call out the broad models or chunks of knowledge that lead the expert to appropriately set up the problem (they just see the problem set itself up). Then they are bewildered at the prospect of starting a problem themselves.
In the comments to John’s blog post, there are some fantastic observations. One is from Jim Doherty who mentions the possibility of giving a correct and incorrect solution to the problem, having the students select the correct one and explain the mistake in the incorrect one. He also mentions a device used by a colleague, whereby a troubled student (“Careless Carl”) appears in problems, making common mistakes. Joss Ives wonders in the comments whether such devices might lead to student frustration on a level that leads them to give up. I’d like to address 1) how I use Careless Carl and 2) how I avoid the “oh crap, I just agreed with this idiot, which means I’m an idiot, too, so I quit” syndrome.
Careless Carl makes appearances in my class all the time, as John Burk knows. He went by the name Bobo (what a clown) when John and I taught together, but now Kelly O’Shea has given him the name Throckmorton (apologies to the Throckmortons of Fort Worth/Dallas, Texas). Throcky (who is your cousin) is a bit more advanced than Bobo… what he says is often ALMOST correct, containing lots of good reasoning with some crucial boneheaded blunder buried deep inside. Sometimes students reluctantly agree with Throcky, dropping their head, wincing, knowing that they are in less than stellar company. But they generally don’t “throw their hands up in the air in defeat,” as Joss worries.
Here’s why: My students have a very strong conception of their scientific self as something that is fluid and ever-changing. They have this conception because we talk about it! Not for long periods of time, but it comes up at least once a week. They have heard again and again that what they know to be true about the world now will, undoubtedly, change as they become wiser, more skilled, more observant and more careful. In this way, they are just like established, expert, working scientists. Scientists expect their view of the world to change and evolve as they understand more about it.
Many of my students, when faced with their own mistake, will say something like “Ok, that was my eighth grade science self. Let’s see what’s wrong.” In fact, “eighth grade self” has become a very popular phrase this year (although last year my students preferred to blame Aristotle, rightly or wrongly, for everything). This just happened yesterday, in the same way, in both of my Honors classes. We are about three days into studying the central force particle model (uniform circular motion). In each class, someone spoke up asking “Wait… if the speed is constant, how is there a net force on the object?” I asked what principle or model the student was applying and in both cases the answer was something like “My gut.” They know by now that their gut is not any better at physics than Throcky. The class then puzzled out the answer. About half knew right away what the mistake was, but, because they are extraordinarily kind and gentle, didn’t say anything until the answer emerged naturally from those having what they called an “eighth grade moment.” It was beautiful, mainly because the students expect this to happen.
I’m not saying none of my students get frustrated. I had a minor meltdown (including tears) to deal with after dinner two nights ago. But the student was much better when he realized that, even though he hadn’t truly learned how to use vectors to do momentum problems yet (even after three months), he had learned something very valuable about what kind of practice doesn’t work. And his assumption is that tomorrow he will understand more about momentum and vectors than he does today.
If there is one thing middle school teachers could instill in students that would help them the most in high school, it is the idea that their own conceptions of the world are bound to change. They should seek out the opportunities to change these conceptions and celebrate the replacement of old concepts with new. I have seen this trait in some students (locally, the Newark Center for Creative Learning teaches this habit fantastically), so I know it is possible to do. This makes students much happier and eager learners.