A day that begins with this view on the way to breakfast is full of promise. And my first day at PCMI was full of a lot of math and a lot of collegiality. I’m still trying to sort through it all before the next one begins. It’s late, and this is unedited. I’m trying to document this whole experience for myself, so I apologize for any typos or rambling sentences. I always try to make my posts ‘sing’ a bit, but I’m don’t think I’ve hit that mark.
The morning session – “Some Applications of Geometric Thinking” – had participants working on some interesting problems, looking for patterns in simple problems which were clues for more challenging questions. I love the way the problems were scaffolded. It was interesting to note the different work habits and paces of my colleagues at the table, and I encountered my own frustration at having some ideas and discoveries shared before I was able to work towards them. An important part of this process is not only to do math, I think, but also to simulate a problem-solving classroom environment, so this frustration provides an opportunity to gain some insight into the student group work experience, as well as my own ability to counter it in myself. I’m looking forward to digging into it again tomorrow.
The second half of the morning was spent on “Reflections on Practice”, the theme of which is Eliciting Evidence of Student Thinking. We analyzed a video-taped rich middle school classroom activity in which students explored how changes in the shape of a quadrilateral affected its area, similar to a problem we had explored in the morning. Student thinking at several levels was apparent throughout the video, and we discussed and shared this evidence in both small groups and as a whole class. We examined some written student work, noting the difference in our own styles of analysis. I’m looking forward to seeing where this conversation goes.
In the afternoon, we were broken into working groups – I have been assigned to a small group that has been tasked with framing an online Geometry course for teachers to address the some of the content shift in the Geometry Common Core standards – to alleviate some teacher anxiety, address some possible misconceptions or murky areas, and provide ideas for weaving these ideas into the classroom. Today we
played explored transformations with patty paper – trying to stay away from coordinates – and examined how transformations could be used to prove theorems. The challenge of reshaping proof as it is taught in high school to include transformations as well as forms other than two columns is another big issue for many teachers, and a topic we are going to continue to address.
The rest of the day was devoted to self-replenishment and fun. After a rousing session of creating stellated figures out of Zomes for the PCMI float in the Park City 4th of July parade, I managed to get to the gym at this lovely resort and take a dunk in the pool (although at 95+ degrees all day, the water is more like a warm bath). The opening dinner was followed by even more bonding over Zome building.
There are so many nuances that I am processing – the wide range of attendants at this huge math event which from undergraduate math students barely older than my own, graduate students and math professors, the teachers from all over the country who readily share their stories and ideas, and the warm and welcoming organizers of this event who make even the newcomers like me feel as if they have been attending for years. But I have 3 weeks to make sense of this wonderful experience, so I’ll stop here for now.