Thursday, November 6, 2014

Math Teachers’ Circles: What Makes a Good One?

by Angie Hodge

Math Teachers’ Circles (MTCs) bring together middle school math teachers and professional mathematicians to enrich the teachers’ experience of mathematical problem solving and to build mathematical community. Free math club-like events, MTCs give teachers the chance to have fun doing math three or four times per semester.

  1. increase the confidence of middle school math teachers in their problem-solving ability;
  2. deepen teachers’ content knowledge through exploring mathematically rich problems and developing an arsenal of techniques for solving unfamiliar and challenging problems;
  3. form long-term professional relationships between teachers and mathematicians through regular, highly interactive meetings; and
  4. provide support for teachers who want to bring richer mathematical experiences to their students.
Teams interested in starting a Math Teachers’ Circle in their area should contact AIM at Six teams of four or five teachers attended workshops on How to Run a Math Teachers’ Circle in 2014. At the 2014 workshop in Washington, D.C., the teams were asked to answer two questions:
  1. What makes a good Math Teachers’ Circle session? 
  2. What makes a good Math Teachers’ Circle problem?
Workshoppers were asked to brainstorm with a focus on "quantity versus quality," and they came up with quite a list. Just perusing it gives even someone unfamiliar with MTCs a pretty good idea of what they’re all about:

What makes a good Math Teachers' Circle session?

Snack break
Good snacks
Engaging problems
Aha! Moment
Leader ready to scaffold/backfill/support
Leader ready to give next challenge
Focus on math
Out of comfort zone
All participants feel comfortable with math and other participants
Safe environment for failure
Discussion and collaboration
Buy-in for participants
Group of common professionals
Relaxed, non-threatening atmosphere
Classroom connections without focus on classroom
Interesting presentation of problems
All levels of mathematics
All participants are involved
Generate enthusiasm
Participants explain and present
Variety of participant backgrounds
Pacing good
Participants in the workshop in Washington, D.C. (photo Hana Silverstein)
No whine
Different presenter personalities
Appropriate amount of room
Good number of participants
Make friends
Multiple strategies
Include failure
Not lecture-y
Celebrate discovery
Good flow
Participants sharing discoveries
End loving/wanting more
SWAG (Sell your MTC by advertising it!)
Climate of respect
Knowledgeable leaders
Critiquing mathematics/solutions (safe for people)
Providing resources to learn more
Inter-workshop closure, info, etc.
Leader's love of math is transmitted
Plenty of time
Time flies
Time to explore
Time to fail before seeing solution
Good entry/exit
Freedom to digress/follow tangents/not too fixed a goal
Individualized closure

What makes a good Math Teachers' Circle problem?

Hands on
Knobbifiable (problems can be made harder or easier)
Low-level entry
Leads to more questions
Out of the box
Initially simple
Variety of strategy and/or tactics
Minimal lecture
Lets participants get to board
Novelty to participants
Not textbook
Good lead-in
More than an hour to solve
Interesting to different groups
Some element of fun
Joy of math
The list in its original form (photo Hana Silverstein)
Has a hook
Clear parameters
Real world
Not too intimidating
Easy to generate data
Strategies embedded
Associated with a lesson
Moral to the story
Cognitive dissonance
Some closure
Some open endedness
Group or individual
Multilayered problems
Opportunities for discussion
Little intro prep/setup
Connections within mathematics
Multiple pathways
Gives participants something to bring home
Memorable problems
Intro fun
Not too much tedium
Aha! moment

For the MTC veterans out there, do the items on the lists above square with your experience of what makes a good Math Teachers’ Circle?

Note: This exercise was given as a way to create closure for the How to Run a Math Teachers’ Circle workshop. Participants had been working problems in MTC sessions all week and this gave them a chance to reflect on the experience. I think this exercise of thinking about good problems and a good class session could also be used in other mathematics courses. Imagine your own classes generating lists about what makes a good student, a good teacher, a good exam, a good problem set, etc. The possibilities are endless! Happy list generating!!! 

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