Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Monday, August 1, 2011

Summer Learning, PCMI Edition: Odds and Ends

This is a series of posts that are reflections from the Park City Mathematics Institute Secondary School Teachers Program.

This is a catch-all for things I want to remember and post that aren't big enough for their own post.

In a 5-minute short, Cal Armstrong presented his use of Livescribe smart pens. I had a little "holy cow" moment during his presentation, because I've long dreamed of kids' recording their problem-solving process, but there's only one smartboard in the room, and writing with a mouse is hard. Enter the Livescribe pen which records both your writing as you write, and audio along with it. And they are only like $100 a pop. I could ask kids to record a livescribe of them solving a problem as their reassessment, or record a tutoring session of them teaching it to someone else. We could put them on blackboard and build up a little library of these, or upload them to voicethread for feedback.

Google Forms for Recording Small-Group Discussion
I am pretty good at incorporating small-group or partner discussion, but I don't often have an efficient way for groups to share their thinking. One technique I noticed frequently deployed at PCMI was to give groups a link to a google form, so that each group could send in a summary of their discussion or response to a prompt. We aren't a 1:1 school, but it would be sufficient for each group to have one laptop for this purpose, and I'm pretty sure I could secure 5-6 laptops to keep in my room. Then again, I am supposed to have a TI-navigator system next year, so maybe I could just use it for this purpose.

Other Kinds of Tasks
Do you ever get stuck in a problem-writing rut? I do. Throughout, I was keeping track of all the tasks I saw that were something other than "find the missing value:"
  • write an equivalent expression
  • give an example
  • show that two expressions are equivalent
  • interpret expressions/equations in writing
  • interpret a graph in writing
Metacognition: See How I Think
We spent a few days talking about what is metacognition, and ways for students to "do" metacognition. We participated in an exercise that I think could be adapted for students to use. In a group of three, students take on three roles: problem solver, listener, notetaker. The listener is NOT HELPING solve the problem, just asking the problem-solver to clarify their process and state it out loud. Meanwhile, the notetaker is writing down any evidence of metacognition or "thinking about thinking" that she hears. I think this could be very beneficial in helping students see how the same thought processes (making use of structure, considering extreme cases, organizing data, etc) cut across mathematical content, but I wonder at designing it in such a way that they can see the point. I need to spend some more time thinking about this.

The Vampire Animations
I worked on a lesson as part of our working group, and I don't think I'm supposed to disclose all the inner-workings of the lesson because it may be reviewed for publication as part of a larger project, but I do want to share this super-fun simulation we made. If you can use it, steal away.

Here is a "question" video of an infection spreading up to 64 victims:

And here is an "answer" video up to 512 victims:

Arts and Crafts
Finally, what is camp without crafts?