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2013 Exeter and PCMI Morning Session

Page history last edited by Kate Nowak 7 years, 4 months ago

 

Documents! (problem sets and group work)

 


 

 

Principles & Guidelines for a TMC-Style Problem-Wrestling Session:

 

based on PCMI and Exeter problem-based learning principles

 

We are deliberately calling this session “problem-wrestling” rather than “problem-solving” because we would like to support you in focusing on the dynamics of the process rather than on driving toward a predetermined outcome.

What you can expect to be doing here:

1. Facing some challenging problems.  The problems we will work on are sequenced to develop over two days and are intended to be challenging for people like us — that is to say, middle and secondary math teachers (and associates) who are strong, courageous mathematical learners who already know the secondary math curriculum content backwards and forwards.  Rejoice! It means that if you find you have no clue where to start with a problem, you are exactly in the right place.  Slow down and wallow in the mathematics.  Tinker with things, talk about what you see or don’t see, or take private “think time” to gather your thoughts. Consider working forwards, backwards, sideways, or even backwards and in high heels.

2. Learning from each other and understanding each other’s reasoning.  We all have something to contribute and something to learn in this experience of problem-wrestling. As Max Ray of The Math Forum likes to say, listening to others is more powerful than listening for the right answer. As much as possible, keep an open mind. Try to believe in the possibilities of other people’s ideas and ask for clarification.

Corollary: NO SPOILERS! If you’re thinking, “Now would be a great time to teach everyone Euler’s BlazeeBlah Theorem,” please pause and reflect for a moment.  The idea is for mathematical understanding to be earned through exploring the problems at hand.  If you happen to know the punchline, but it’s ten steps ahead of everyone else, avoid the temptation to Drop Knowledge on people who aren’t there yet.

3.  Meeting our edges. We acknowledge that in any collaborative work situation, everyone is sometimes very clever and sometimes very not-clever.  Feeling at times clever and at times not-clever is a natural part of the process.  We value both of these states and are actively looking for ways to make room for both of them.

Be gentle with yourself whatever comes.  Pay attention to and acknowledge your reactions. Notice what helps you engage and what blocks you from opening to the mathematics. We are voluntarily stepping into a place we ask our learners to go to every day but where we don’t often find ourselves.  It might be uncomfortable sometimes. Notice your own discomfort and don’t be too quick to try and shake it off. It may have nutrition that you need.  One of the most effective ways to cultivate compassion for our students’ problem-wrestling experiences is to develop empathy as learners through experiences that cause us to meet our own edges in this work.

4. Reflecting on what is compelling, pleasurable, or valuable about the experience of problem-wrestling in this way. One of our goals is to explore how understanding different experiences of problem-wrestling might be deployed to good effect in our classrooms and curricula.  We will intentionally take some time to address these questions in a structured way.


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