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.

MTCs strive to:

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 circles@aimath.org. 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

Entertaining/enjoyable

Buy-in for participants

Community

Group of common professionals

Relaxed, non-threatening atmosphere

Classroom connections without focus on classroom

Interesting presentation of problems

All levels of mathematics

Overplanning

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)

Memorable

Wine

No whine

Different presenter personalities

Appropriate amount of room

Good number of participants

Humor/laughter

Make friends

Noncompetitive

Supportive

Multiple strategies

Include failure

Hook

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

Focus

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

T-shirts

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

Engaging

Knobbifiable (problems can be made harder or easier)

Low-level entry

Multisensory/multimodal

Mystery

Leads to more questions

Out of the box

Initially simple

Folkloric

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

Physical/"crafty"

The list in its original form (photo Hana Silverstein)

Abstract/thoughtful

Has a hook

Clear parameters

Real world

Not too intimidating

Challenging

Easy to generate data

Strategies embedded

Associated with a lesson

Moral to the story

Cognitive dissonance

Surprise

Some closure

Some open endedness

Group or individual

Multilayered problems

Opportunities for discussion

Little intro prep/setup

Patterns

Connections within mathematics

Multiple pathways

Gives participants something to bring home

Reasoning/argumentation

Memorable problems

Spatial

Games

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!!!