Post-game analysis: model analysis & synthesis, reflective thinking
COMPILATION: post-game analysis (model analysis & synthesis; reflective thinking)
Date: Fri, 9 Sep 2011
From: Matt Greenwolfe
Subject: post-game analysis for better whiteboard discussions
I've been trying to better communicate to my students what I want out of the board meetings. In the past, the meetings were ***about*** presenting each group's work to the class as a whole and I was secretly hoping that a deeper analysis would come out of that. When it fell short, I was then trying to drive the class to a deeper level with my Socratic questioning. This year, I'm trying to make the meetings primarily about the deeper analysis, with some presentation of whiteboards happening incidentally along the way.
To do this, I'm telling the students about post game analysis (PGA). David Hestenes tells the story of master chess players, who sit for hours after a game, analyzing mistakes, looking for alternate strategies or better more powerful ways to view the action, replaying the game is it might have gone had someone made a different decision, spending often several times the amount of time it took to play the game in the first place. What do professional athletes do after a game? Watch game film. They are not looking for the sports center highlights when they scored or made a great play, they are actively seeking out their mistakes and thinking about how to correct them because they want to get better. This is beyond simply being comfortable with having their mistakes exposed. This is actively seeking them out, not dismissing them as careless, but trying to think if there is a way to avoid them. Professionals in all fields do the same. ... etc. you can see where it goes.
So each section keeps a PGA board (one or two whiteboards), where we record things like common mistakes and how to avoid them, or anything judged important enough that it should get recorded in a prominent place and not left in the details of the solution to a particular problem. When a student makes a really perceptive comment, they get the PGA board and are asked to write down their observations.
I'm just in the third week of actual classes. The first couple of board meetings I did ask someone to start it off by presenting what they did, then at the end asked for PGA. But yesterday, I looked around. Everyone had pretty much the same stuff. So I just said, "Let's start with PGA." I immediately got some good insights about unit 1 - "It helps to know the meaning of the equation and not just randomly select it." "Don't confuse units with variables." "Graphs have different shapes and aren't always linear." "About five major divisions is good on an axis. Too many is confusing." Also some stuff about mistakes made and how to avoid them.
After that, I did ask a couple groups to show and explain how they figured out the units of the constant in the equation, as that was the latest thing that was introduced. Some students did tune out at that point, hopefully because they already understood how to do it. But it was a nice contrast from students tuning out during presentations of whiteboards that had become too routine, and then facing a struggle to tune back in when we got to the more important stuff. We got to the most important things first, this way. I also think the discussion was more productive, but took less time than it would have the other way.
I also did this with workshop participants this last summer, and am looking forward to hearing whether they tried it and how it went. I'll see them in a few weeks.
------
Date: Fri, 9 Sep 2011
From: Lee Trampleasure
Wow, great idea Matt.
I'm thinking this would be good to do online using a computer and projector instead of a whiteboard. This way the PGA boards could be accessed later. We use Moodle, so it would be easy to have a separate "board" for each group.
This would make sketching harder, however. How many of your PGA boards have sketches? Maybe I should just take a photo of the PGA boards and post those to the web.
Does anyone have thoughts on posting PGA boards to the web, either interactively or via photographs.
------
Date: Fri, 9 Sep 2011
From: Matt Greenwolfe
Re. Lee's comment. There was a lot of discussion at the workshop this summer about how to implement the PGA board, with technological solutions and others proposed. That's one reason I'm eager to hear what each of the teachers did and how it worked out.
------
Date: Nov. 18, 2011
From: Jane Jackson <>
Subject: DAVID HESTENES on post-game analysis (in whiteboarding - board meetings)
David Hestenes was a champion chess player. In the quote below, he describes how post-game analysis (PGA) can improve science instruction (in board meetings). This builds upon Matt Greenwolfe's listserv posts of Sept. 9, 2011.
"Modeling Games in the Newtonian World", by David Hestenes (American Journal of Physics, 1992)
A ten year period is typical for the development of grandmaster strength [in chess]. The secret of this continued growth appears to lie in their approach to the game. Many players with obvious ability do not continue to develop so. The secret of those who do can be seen in the practice of post-game analysis, which is widespread among professionals.
Immediately after the game the opponents sit down together at a chess board to review the entire game while it is fresh in their minds -- discussing strategic and tactical themes, analyzing promising alternatives at critical points, trying to identify losing moves and so forth. This is an ideal activity for inducing conceptual change -- discovering weaknesses (bugs, misconceptions) in old thinking patterns and better patterns to replace them. It is an excellent way to promote the ability for what Piaget calls reflective thinking, namely, the ability to critically analyze ones own conceptual presuppositions and thinking patterns.
Post-game analysis has been explicitly incorporated into the instructional method of Malcolm Wells, and it is certainly one of the keys to his success. In his laboratory-based curriculum, performing an experiment, collecting data, and all that is only the first half of a laboratory activity. The second half, to which equal time is allotted, consists of a post-game of the first half involving the entire class of about 24 students. This is probably when the most significant learning takes place, but is must be designed and directed with skill.
Another place where systematic post-game analysis would improve instruction is in problem solving, The homework submitted by most students shows little evidence of the reflective thinking which is essential to a high level of skill development. Even graduate students are satisfied with the most perfunctory solutions to problems, anything that arrives at the coveted "answer." But the opportunity for deepest learning is post-game analysis after the problem has been solved, addressing such questions as "What was the key to the solution? Can the argument be simplified? How can the result be verified? Are there other ways to solve the problem? Which is the best? Can the problem and solution be generalized? Of what interest is the result?" Such questioning is characteristic of the reflective thinking of professional physicists. Perhaps it is so rare among students because so little is done to promote it.
1