Rich Histories, Bright Futures

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Dear Math Teachers’ Circle Network,

This issue’s feature articles focus on problems with rich histories that make for engrossing MTC topics. “The Roommate Game,” by Emily Dennett and Chris Bolognese, draws inspiration from a 50-year-old article to develop a nicely structured investigation of a type of stable matching problem, the stable roommate problem. (Be sure to check out their excellent accompanying resources if you are considering doing this session with your own MTC!) “Recruiting Change for a Dollar” by Craig Collins, Elizabeth Donovan, and Cynthia Kramer, describes how the authors used another classic problem—counting the possible ways of making change for a given amount—during recruitment sessions for their new MTC. It is an approachable problem with a quick set-up that nevertheless leads to some interesting and deep questions even within the span of a “demo” session.

Dan Finkel’s “65 Uses for a Paperclip” has appealing historical resonance even within our MTC community. His use of a simple grid of lattice points to generate questions for investigation brings to mind Tatiana Shubin’s classic “Grid Power” session, in which she begins by giving participants 7 minutes to write down questions inspired by staring at a sheet of grid paper. (You can see Tatiana facilitating this session in our Video Library.) Tatiana’s session, which she began developing more than 10 years ago, is the first MTC session I can remember that put a strong emphasis on problem posing. Dan’s article builds on that foundation by introducing two powerful but easy-to-implement techniques: a gamified version of a key mathematical process that he calls “Conjectures and Counterexamples,” and three surprisingly simple steps to support a “Thinking Classroom,” drawn from the research of Peter Liljedahl.

MTCs across the country continue to thrive. It’s especially exciting to see new MTCs grow near established ones, and also to witness the accomplishments of the teams who attended the MTC training workshop at the MAA last summer, including a major grant landed by the team from Oklahoma. I’m also proud to announce that an article describing case studies of MTC-participating teachers was recently published in the open-access journal The Mathematics Educator (“News and Views”). My co-authors and I are hopeful that the article will prove useful and will provoke some good discussion within the MTC community.

Happy problem solving, and here’s to more Thinking Classrooms in 2019!

Brianna Donaldson, Director of Special Projects

This article originally appeared in the Spring 2019 MTCircular.


The Roommate Game

An Exploration of Stable Matchings

Emily Dennett and Chris Bolognese

65 Uses For a Paperclip

Conjectures and Counterexamples in a Thinking Classroom
Dan Finkel

Recruiting Change for a Dollar

Patterns Don’t Solve Everything
Craig Collins, Elizabeth Donovan, and Cynthia Cramer

Contest: Turn Your World on Its Side

Win a Free Book from MAA AMC

Case Studies of MTC Participants Published in The Mathematics Educator

Oklahoma State Department of Education Awarded Federal Grant to Support Native Youth and Implement Math Circles Statewide


A Note from AIM

Rich Histories, Bright Futures

Dispatches from the Circles

Local updates from across the country