Continuous formation

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...

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 spri...

PCMI is a 3 week program; each day from about 830 to 1040 we have what can best be described as a math class. But it's unlike any math class most people have ever had. Each day starts with its own problem set designed by the class' organizers, folks from the Education Development Center and Harvey Mudd College . The problem set is well structured, beginning with a simple idea or concept and then continually developing in both depth and breadth, although this may be obvious only several days later. The questions are also in categories: Important (things you'll need to know for upcoming days), Neat and Tough (can be really tough! Clay Prize tough!) -- we aim to get through at least the important stuff in our morning together. The classroom is composed of 12 tables of 5-6 people each (we do have guests from the other programs) and as a table we tend to worth through things together; there's a table sandbox monitor who is there to ensure that the teachers exercise a...

I've had the opportunity to come early to Park City and help set things up: there's actually a lot of infrastructure to put in to place. With (at least) 7 different groups running simultaneously around the conference centre, there's the usual classroom/lecture facilities to complete but nowadays we add on a considerable amount of technology: LCD projectors, wireless & wired networks, speaker systems, the typical. And, because we're mathematicians... a lot of chalk boards and coloured chalk. Lots. And old school overhead projectors. But in the teacher room, because we've got at least 60 participants spread across 12 tables, we have a desk-based microphone/speaker system so that they can hear each other across the room, two Mimio electronic whiteboards (an excellent alternative to Smartboards!) tied into an ELMO document camera and three LCD projectors and, because we break this large room up into three smaller rooms, the need to have it all work as a com...

So the end of school was a bit of a flurry and I left meetings early to head out to Park City, Utah (home of the Sundance Film Festival ) to participate in the Park City Mathematics Institute for the seventh time. If you're a math teacher and never been... you're missing out! I first attended PCMI in 2002 -- by pure luck. I was teaching Ontario's Linear Algebra course and stumbled across their webpage which discussed that summer's topic, Gaussian Integers . I cross my fingers & applied. After attending as a participant for two years I got invited back to help out as staff. It's a lot of work and I don't get all the fun that participants have but I learn about math and teaching and learning in a different way. And I get to work some amazing people, both staff and participants, and great friends. PCMI is hard to describe. I call it "math camp" when asked just to make things easier. Let me try to be more descriptive since I have the time: P...

One of the reasons we've decided to jump into this CAS process at this point in time is that the new interface is far more student-friendly. We were loath to start with a CAS when the learning curve would be so great. While I know that some would say that the TI is a possibility, it's short-sighted; no one uses the TI software/handhelds beyond highschool. And the hand-helds are a button-intensive, small screen mess. It's a toss-up between Maple and Mathematica - and we have an existing relationship with Maple (it's HQ is down the road an hour). The interface is now far more point & click with no (okay, few) arcane (to students) commands and it describes the step that has been performs. Graphing is a lot easier (you can drag an expression onto a grid and it graphs!) and parameters can be automated with a click. That, of course, is the easy part done. Now, the hard part: what questions do we ask to develop understanding, concepts, algorithms? how do we encourage ...