Exeter Part 1

I am attending on of the best math conferences. It is hosted by Philips Exeter Academy. It is a conference that combines week-long classes and shorter 75-minute classes. Here are some thoughts from the first few days.

Project-Based Learning (Carmel Schettino)
There is lots of research showing that Project-Based Learning (PBL) is a better teaching technique than traditional pedagogy. It is more complicated that being a "sage on a stage" and takes practice. Moreover, students not used to being pushed will find it uncomfortable. Some of the characteristics of project-based learning:

• teachers step back; teachers physically reposition themselves and there is an alternate generation of directions
  
• when they teach, they generally model, rather than how a specific process
  
• it relies on discourse and discovery; there is often physical activity
  
• it is student-directed, which increases ownership; teachers allow, encourage and validate discomfort
  
• teachers need to understand the cognitive apprenticeship model of model, coach, scaffold, and fade
  
• it is very important for teachers need to keep the learning goal in mind; otherwise the students may feel lost and complain that they are not learning (which in turn will generate complaints from parents)
• Cindy Hmelo-Silver has done a lot of research on the effectiveness of PBL
• Several schools use PBL exclusively - Phillips Exeter Academy and the Illinois Math & Science Academy.
• Other resources include: New Tech Foundation, Buck Institute, and Montana's SIMMS initiative.

In practice, teachers using PBL should be aware of the following:

• there is always a balancing act between the time spent and letting them explore tangents that may have nothing to do with the learning goal
• "revoicing" is a form of repeating information back to students and is an effective scaffolding strategy; it lends credence; causes reflection; validates their authority
  
• "revoicing" can also be effective in explicitly mapping cause in effect from their discourse and questions; it can also encourage construction of visuals ("please show me")
  
• encourage student to use patient problem solving
• encourage them to try multiple approaches
• the teacher should present compelling questions
• scaffolding can be done with images and videos
• keep in mind that students must take ownership, which means responsibility

One potential pitfall of PBL is to use it for every aspect of a lesson. Discovery is not necessary in all cases. It is fair to "tell" students:

• when introducing conventional terminology
• remind students of conclusions they have already reached
• rephrase students comments and questions (as in "revoicing")
• alert students than their ideas are unclear

Ron Lancaster of the Ontario Institute for Studies in Education at the University of Toronto
He is the master of authentic learning. He travels around the world and snaps pictures and videos of anything that can be analyzed mathematically. He has a huge collection of images/videos from his travels. We reviewed several and discussed what questions we could ask about them. He is a big fan of having students import images into Geometer Sketchpad and draw analyze them by adding geometric constructs. He also mentioned an interesting math field trip that he does to a local shopping center. He visits the stores ahead of time and finds interesting data. He contacts the stores ahead of time and students visits in small groups. Each group starts at a different store to alleviate crowds (similar to a shotgun stat in golf). I marvel at his ability to literally see math data everywhere in the world - from store signs, to interesting buildings, to sculptures, to a sin wave as part of a company logo.