Category Archives: Pedagogy

Working Groups

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Before I start dealing with reflecting on the content of the classes, I’ve got two more aspects of PCMI to mention.
The first is the most productive: The working group. Each of the teachers is assigned a working group in a topic of secondary mathematics for the afternoon (Wednesdays off) in which they, typically in groups, will produce a product useful to classroom teachers.
As the person in charge of a group this can be very challenging: these are all energetic, enthusiastic and talented teachers — who all teach in very different classrooms. So what may be appropriate for one school system could fail utterly in another, not just in terms of content but departmental expectations, school standards, etc. As the working group leader I have to steer these folks towards a consensus: a project that is meaningful to them, useful to others, and able to be accomplished in three weeks. Most of the time this takes the form of a lesson plan or activity that is refined throughout the three weeks — I find that too limiting and I’ll discuss what we did in a later post. I will say my group this year (go Discrete Math!) took on a huge challenge and did an amazing job; I was overwhelmed with how they took on their responsibilities and always questioned “how can we do this better, or different?“
We also spend some time looking at different problems in the mathematical area and we’re always fortunate to have 200 world-class mathematicians running around in the corridor (well, they don’t run so much as shuffle) to snag for a few hours. It’s funny when you speak to them at lunch and then after lunch realize WHO they really are. They typically stride the mathematical world like colossus and you’ve asked them if they liked the carrot cake! :) We were lucky enough to have Joe Malkevitch (yes, THAT Joe Malkevitch) spend almost two hours discussing problems with us — starting with the Art Gallery problem and then seeing where that took us. That is how lucky we are at PCMI!
The other group of activities I have to mention are the cross-program ones. This is a huge umbrella and can cover things like I mentioned below, James Heibert discussing the TIMSS Video Study results, at least two Clay Scholars every year discussing their work (with us! High school teachers!), Gov. Huntsman (at the time) speaking of math at the state/national level, and even Tom Garrity explaing how “Functions describe the world”. The level and content varies so greatly, an exhaustive list would be its own (rather dull) blog post. Suffice it to say, it’s the kind of opportunity you would have to hang around Harvard for, for at least a few years.

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Reflecting on Practice

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Once we’re done the morning of math (with a brief coffee break) the teachers all get back together for an hour of math education pedagogy. Like the mathematics we cover, each year is something a little different. For example, in previous years we’ve focused on Lesson Design (with Drs. Nicole Bannister & Gail Burrill), Teaching through Problem Solving or Learning the Open-Ended Approach (with Dr. Akihiko Takahashi).
This year the organizers tried something a little different; they tapped six of the returning participants to look at Questioning in the Classroom from the practicing teachers’ perspective. As one of those teachers leading the professional development it was a considerable challenge to not only meet the expectations of the participants and the organizers but also our own expectations — my colleagues are amongst the premier educators in the States (National Board certified, AP consulants, you name it). We began with a working weekend in Denver in the spring, pulling together resources and a timeline — our biggest fight was avoiding putting too much in. And then, when actually talking about pedagogy with professional teachers there is a huge struggle against anecdotes; everyone wants to share their stories. In discussing Questioning we want to move beyond what we do now and move towards something better. And so we start with what the research said.
This blog post is only to set the scene for a series of posts; I will go into this at greater depths in the future but our motivation was the results of the 1999 TIMSS video study — James Hiebert presented the results to us in 2003 at PCMI and it was the most astonishing moment I’ve had in a lecture in a long time and it has been the prime motivator in my teaching ever since:

Almost all (ed: statistically 100%) of the problems in the U.S. that start out as making connections tasks are transformed, in a variety of ways. Often a teacher steps in and does the work for the students-sees students struggling, gives a hint that takes away the problematic nature of the lesson, and tells students how to solve it. These are not incompetent or poorly intentioned teachers but simply teachers who have picked up very well an American way of teaching mathematics. One of the cultural agreements we have made in this country, with ourselves as teachers and with students, is that it is the teacher’s job to tell students how to do the problem and how to get the right answer-that it is not fair to allow students to struggle or be confused.

In other words: we are far too nice. So, for the past six years I have worked hard not to be nice and tried to persuade colleagues near and far to cowboy up1. I’ve presented on this at OAME directly and in any other presentation that I’ve done I’ve pressed the point. It was encouraging to see Dan Meyer come to a similar conclusion in his presentation to open source programmers (yes, the context is a bit bizarre but makes sense if you follow his blog). Be sure you should watch the video.Reblog this post [with Zemanta]
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1I include “cowboy up” only because I had to explain the phrase to Gail this year :)

Graph is created from data produced in the TIMSS video study and is from here: http://www.mathforum.com/pcmi/hstp/sum2009/reading/Hiebert_Improving_Math_Teaching_2004b.pdf