Presentation #: 71 1 Speaker: Brianna Donaldson (brianna@aimath.org) - - PDF document

Presentation #: 71 Speaker: Brianna Donaldson (brianna@aimath.org) Title: Math Teachers’ Circles: The Practice of Mathematics in Middle School www.aimath.org www.mathteacherscircle.org 1 WHAT ARE MATH TEACHERS’ CIRCLES (MTCS)? Math Teachers’ Circles are professional development communities of mathematics teachers and mathematicians who meet regularly to work on mathematically rich, non-routine problems. They provide an opportunity for teachers to enrich their own knowledge and experience of mathematics, while building long-term, meaningful partnerships with other K-12 teachers and college and university faculty. MTCs started at the American Institute of Mathematics (AIM) in 2006. They were the idea of Mary Fay-Zenk, a middle school mathematics teacher at Miller Middle School in Cupertino, CA. Since 2007, AIM has held annual workshops on “How to Run a Math Teachers’ Circle,” which have resulted in the creation of nearly 60 MTCs in over 30 states. Each group involves 15 to 20 teachers and several college or university faculty. AIM continues to provide logistical support and resources to all MTCs nationwide through the Math Teachers’ Circle Network (www.mathteacherscircle.org). RESEARCH HIGHLIGHTS Many teachers report that participating in MTC has a positive influence on their views of mathematics, their classroom teaching, and their professional activities. A national study has shown that teachers’ mathematical knowledge for teaching increased as a result of participating in MTC. Another study reported that MTC participation increased teachers’ use of inquiry-based teaching practices. Please visit http://www.mathteacherscircle.org/about/results/ for more information. INTERESTED IN JOINING OR STARTING A MTC? Please check out our Member Circles page to see if there is a group near you: http://www.mathteacherscircle.org/member-circles/ If not, we invite you to consider applying with a team of teachers and mathematicians to a workshop on “How to Run a Math Teachers’ Circle”:

• June 23-27, 2014: Palo Alto, California
• July 14-18, 2014: Washington, D.C.

Workshop applications will be available at http://www.mathteacherscircle.org/upcoming- workshops/ starting in January 2014. Accepted teams receive full funding for travel, hotel, and meals. For more information about MTCs, please visit www.mathteacherscircle.org or contact Brianna Donaldson at brianna@aimath.org.

Presentation #: 71 Speaker: Brianna Donaldson (brianna@aimath.org) Title: Math Teachers’ Circles: The Practice of Mathematics in Middle School www.aimath.org www.mathteacherscircle.org 2 RESOURCES (IN THE ORDER PRESENTED) MTCircular Newsletter Read online or subscribe at http://www.mathteacherscircle.org/resources/mtc-newsletter/ This semi-annual newsletter features the latest news and ideas from MTCs around the country, along with mathematical problems and resources for your MTC or classroom. The 1-to-100 Problem Reference: Joshua Zucker and Tom Davis, “The 1-to-100 Problem,” available at http://www.geometer.org/mathcircles/numbercombine.pdf This problem is a wonderful introduction to a number of key problem-solving strategies, including trying a smaller problem, wishful thinking, and examining multiple

• representations. It also develops a deeper understanding of the commutative and

associative properties of multiplication and addition, in the context of formulating and manipulating algebraic expressions. Mathematics Teachers Circle Around Problem Solving Reference: Fernandes, A., Koehler, J., & Reiter, H. (2011). Mathematics teachers circle around problem solving. Mathematics Teaching in the Middle School, 17(2), 108-115. This article describes some of the key features of Math Teachers’ Circles and illustrates them with a vignette involving a session about the Frogs and Toads problem. For a two-dimensional version of the Frogs and Toads problem, see the Summer 2013 issue of the MTCircular newsletter at http://www.mathteacherscircle.org/resources/mtc- newsletter/. The best solution submitted to problemcircle@aimath.org will win a free book!

Presentation #: 71 Speaker: Brianna Donaldson (brianna@aimath.org) Title: Math Teachers’ Circles: The Practice of Mathematics in Middle School www.aimath.org www.mathteacherscircle.org 3 Sets, Planets, & Comets Reference: Baker, M., Beltran, J., Buell, J., Conrey, B., Davis, T., Donaldson, B., Detorre-Ozeki, J., Dibble, L., Freeman, T., Hammie, R., Montgomery, J., Pickford, A., & Wong, J. (2013). Sets, planets, & comets. The College Mathematics Journal, 44(4), 258- 264. Currently available for free download on the journal’s homepage at http://www.maa.org/publications/periodicals/college-mathematics-journal/the-college- mathematics-journal This 13-author paper grew out of a Math Teachers’ Circle session held at the American Institute of Mathematics. It describes a variation on the card game Set that makes use of the geometry of the game. For additional background on the mathematics of Set, you might take a look at this MTC session handout: http://www.mathteacherscircle.org/assets/session- materials/BConreyBDonaldsonSET.pdf Exploding Dots Reference: James Tanton, “Exploding Dots”:

• Instructor notes available at http://www.mathteacherscircle.org/assets/session-

materials/JTantonExplodingDots_EducatorsVersion.pdf

• Student notes available at http://www.mathteacherscircle.org/assets/session-

materials/JTantonDots_Boxes_Piles_Holes_MiddleSchoolNotes.pdf Exploding Dots is a popular Math Teachers’ Circle session that explores place value and different number bases, using alternative algorithms for various operations. The Locker Problem Reference: Elgin Johnston, “Lockers: An Open and Shut Case,” available at http://www.mathteacherscircle.org/assets/session-materials/EJohnstonLockers.pdf This handout has some fun extensions of the famous Locker Problem. To explore other Math Teachers’ Circle session notes, please visit http://www.mathteacherscircle.org/resources/session-materials/