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Autumn 2019
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In “TicTacToe 2.0,” Catherine Pullin Lane and Lynne M. Pachnowski ponder a new take on the classic children’s game: one that involves game theory and plenty of openended questions for exploration. Plus, a decision tree showing a strategy to never lose at TicTacToe again! In “Circling to Connect,” we explore five programs that present opportunities to build math joy on the foundation of Math Teachers’ Circles: Circles of Inquiry, Julia Robinson Math Festivals, Math Monday, Math News Snapshots, and Journal of Math Circles. Which will you bring to your MTC or classroom this school year? And get to know 20year veteran math teacher and social justice champion Gloria Brown Brooks in “A Better World Through Math,” an interview by Jessa Barniol.
Spring 2019
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In “The Roommate Game,” Emily Dennett and Chris Bolognese are inspired by Dennett’s time as a Resident Advisor in a college dormitory to explore the theory of stable matchings. In “65 Uses for a Paperclip,” Dan Finkel provides teachers with a way to invite students into a real mathematical process using openended questions, conjectures and counterexamples, all in the setting of a groundbreaking “thinking classroom.” And in “Recruiting Change for a Dollar,” leaders of the largely rural Western Kentucky MTC, Craig Collins, Elizabeth Donovan, and Cynthia Kramer, ask, “How many ways are there to make change for a dollar?” This deceptively simple question quickly devolves into an engaging problem (with no discernible pattern to its solution!) that the authors’ experience shows is an ideal classroomadaptable entry point for teachers who are new to MTCs.
Autumn 2018
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In “We the People,” Lynne Pachnowski and Linda Saliga explore the timeless question; “Can voting ever really be fair?” In Nathan Borchelt’s “Good Things Come in Unexpected Packages,” a festive Christmas tradition leads to adventures in problem solving. Sayonita GhoshHajra ponders the unusual threedimensional shape inside of a Magic 8Ball in “I See Platonic Solids in Your Future.” And Dave Honda shares the geometry behind his awardwinning Snapology origami in “The Surprising Shape of Success,” an interview by Sonya Kohli.
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Page 4: Good things, Unexpected Packages

Page 8: I see Platonic Solids in Your Future

Page 12: We the People

Page 19: The Surprising Shape of Success

Spring 2018
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In “Touching Infinity,” Samuel Coskey, Paul Ellis, and Japheth Wood provide a lovely and accessible treatment of questions about infinity. Judith Covington’s “Tiling with Pentagons” captures the excitement of investigating brandnew mathematics during a MTC session. Peter Tingley draws inspiration from his preschoolaged daughter to bring a fresh perspective to problem solving in “Listen, Share, Play.” And Kimberly Adams and Donna Farrior lead their MTC in an escape room adventure in “Breakout Boxes.”
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Page 5: Touching Infinity

Page 9: Listen, Share, Play

Page 12: Tiling with Pentagons

Page 14: Locked Out

Page 17: Opportunities

Summer/Autumn 2017
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In this issue, Chris Goff (San Joaquin County MTC) traces the 2000year history of a fractal that inspired his MTC’s logo. Jeremy Aikin and Cory Johnson (Inland Empire MTC) share a math session motivated by patterns in musical scales. Anne Ho and Tara Craig (Coastal Carolina MTC) use a mathematical frame to guide a conversation about social issues. And for those looking for ways to empower your MTC participants’ mathematical thinking, Chris Bolognese and Mike Steward (Columbus MTC) provide plenty of food for thought.
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Page 4: A Problem Fit for a Princess

Page 8: Polygons and Prejudice

Page 13: Problem Posing

Page 16: MTCs Advocating for Math in ESSA Plans

Page 19: Global Math Week
Exploding Dots: a favorite topic for MTCs that was developed by Global Math Project founding team member James Tanton. 
Winter/Spring 2017
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In this issue, Katie A. Hendrickson (SouthEast Ohio MTC) shares how MTCs can affect teachers’ beliefs about themselves and about mathematics. Liza Cope (Mississippi Delta MTC) discovers that an MTC can extend the impact of a MathScience Partnership grant. Plus: Kimberly Muller (Eastern Upper Peninsula MTC) and Tom Clark (Northwest Iowa MTC) find deep mathematics in two very different games.
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Page 4: A Teacher and a Mathematician

Page 8: A Circle in the Delta

Page 10: Spot It!

Page 13: Freeing the Clones

Page 19: Opportunities

Summer/Autumn 2016
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This issue contains more math than ever, with writeups of four intriguing new sessions from MTC leaders across the country. Matt Roscoe (Montana MTC) finds beautiful symmetries in quilt blocks, Michelle Manes (MTC Hawai’i) investigates an unusual lottery scam, and Nina White (Wayne County MTC) poses questions about tiling the plane. Plus, avid cyclist Michael Nakamaye (Albuquerque MTC) wonders if it’s possible to have a concrete physical experience of √2 when riding a bike.
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Page 2: Connecting a Growing Network
 100Kin10 website
 What Makes a Good Problem? — An Educator Innovator webinar with C. Bolognese, B. Donaldson, F. Nguyen, P. Zeitz, and J. Zucker
Page 4: Quilt While You're Ahead
Page 8: Winning the Lottery
 Ellenberg, J. How Not to Be Wrong. New York: Penguin Press, 2014.
Page 11: Semiregular Tilings
 Session materials:
 The “Good Problem” Problem, J. Zucker
 Regular, semiregular, and Escherlike Tilings, A. Rodin
Page 14: Shifting Gears
 Bicycle Math, J. Tanton
Page 16: News and Views
 Henri Picciotto’s website
 Gordon Hamilton’s website
 SquareSum Pair Partitions, G. Hamilton, Kiran S. Kedlaya, and H. Picciotto
 International Congress on Mathematical Education website
 “Grid Power” video, MTC session materials, and middle school curriculum materials, R. Lomas and T. Shubin
Page 19: Math Without Words
 James Tanton’s website
 Without Words: Mathematical Puzzles to Confound and Delight, J. Tanton
 Natalya St. Clair’s website
Winter/Spring 2016
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In “Good Beginnings,” Gulden Karakok describes creative ways of helping teachers make classroom connections. In “TwoWay Street,” the Northwest Iowa MTC leaders describe some of the ways that professors benefit, too. Between Heather Danforth’s “Piece of Cake” classroom lesson on fractions and decimals and the “Flipping Pancakes” featured session by Katie Haymaker, we hope this issue will leave you hungry for more mathematics.
Solve the “Burnt Pancakes” Problem Circle by January 31 for a chance to win a free copy of Jim Henle’s The Proof and the Pudding: What Mathematicians, Cooks, and You Have in Common, from Princeton University Press! Through February 14, you can also use code P06143 to receive 30% off your purchase of The Proof and the Pudding at press.princeton.edu.
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/Page 4: Piece of Cake
 Tom Davis’ website, http://www.geometer.org
 AIM Math Teachers’ Circle website
 Common Core State Standards for Mathematical Practice
 Extensions for Heather Danforth’s “Fractions and Decimals” lesson plan: coming soon
Page 8: Good Beginnings
 Northern Colorado MTC website

National Council of Teachers of Mathematics’ “Principles to Actions”
Page 10: TwoWay Street
 Northwest Iowa MTC website
 James Tanton, “Bicycle Math” session materials and video
Page 13: Dispatches from the Circles
Page 14: News and Views
 Alibegovic, Taylor to Present at This Year’s MidSchoolMath National Conference
 Utah MTC website
 MTC of Santa Fe website
 MidSchoolMath National Conference
 Grant from North Carolina GlaxoSmithKline Foundation will benefit North Carolina teachers
 Smoky Mountain MTC Facebook page
 Western Carolina University Foundation press release
 Documentary on Navajo Math Circles to Air on Public Television and at Joint Math Meetings
Page 16: In Session: Flipping Pancakes
 Philadelphia Area MTC website
 B. Chitturi, W. Fahle, Z. Meng, L. Morales, C. O. Shields, I. H. Sudborough and W. Voit, “An (18/11)n upper bound for sorting by prefix reversals,” Theoretical Computer Science, Issue 410, 2009.
 Harry Dweighter, “Elementary Problem E2569,” Amer. Math. Monthly 82: 1010, 1975.
 W. H. Gates and C. H. Papadimitriou, “Bounds for sorting by prefix reversal,” Discrete Math. 27 (1979), 4757.
 Ivars Peterson, “Pancake Sorting, Prefix Reversals, and DNA Rearrangements,” Pi Mu Epsilon Lecture, Villanova University, April 28, 2015.
 Simon Singh, “Flipping Pancakes with Mathematics,” The Guardian, Nov. 14, 2013, retrieved at http://www.theguardian.com/science/blog/2013/nov/14/flippingpancakesmathematicsjacobgoodman.
 N.J. Sloane, Online Encyclopedia of Integer Sequences, https://oeis.org/A058986.
Page 18: Problem Circle: Burnt Pancakes
 Henle, J. The Proof and the Pudding: What Mathematicians, Cooks, and You Have in Common. Princeton: Princeton UP, 2015.
Page 19: Math Without Words
 James Tanton’s website
 Tanton, J. Without Words: Mathematical Puzzles to Confound and Delight. London: Tarquin Publications, 2013.
 Natalya St. Clair’s website, Art and Math
Summer/Autumn 2015
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How do you bridge the language barrier between teachers and mathematicians? How do you sustain a MTC over the long term? How can you connect MTCs across the state? MTCs across the country share their insights. Plus, lots of math, including an appealing look at building integers with 1, 2, 3, and 4; an investigation of perfect rulers; and a puzzle from James Tanton’s “Math Without Words” series.
Solve the “Problem Circle” by September 28 for a chance to win a free copy of Marc Chamberland’s Single Digits: In Praise of Small Numbers, from Princeton University Press! Through September 30, you can also use code P06096 to receive 30 percent off your purchase of Single Digits at press.princeton.edu.
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/Page 2: Parts of a Whole
 MTC video library, with annotated playlists of classic sessions
 MTC organizer toolkits, containing resources for beginning and sustaining your MTC
Page 8: Modeling With Mathematics: Developing a Common Language
 Materials for modeling sessions with mathematics
 Common Core State Standards for Mathematical Practice
 MTC of Hawai’i (MaTCH) website
Page 6: Hamburgers and High Ceilings: Knowledge for Teaching and Learning
 Philadelphia Area MTC website
References:
 Ball, D. L. & Bass, H. (2003). Toward a practicebased theory of mathematical knowledge for teaching. In B. Davis and E. Simmt (Eds.), Proc Ann Meeting of Canadian Math Ed St Group (2002) (pp. 314). Edmonton, AB: CMESG/GDEDM.
 Ball, D.L., Hill, H., & Bass, H. (2005). Knowing Mathematics for Teaching. American Educator, Fall 2005, 1422, 4346.
 Boaler, J. (2013 Nov 12). “The Stereotypes that Distort How Americans Teach and Learn Math.” The Atlantic. Retrieved on May 31, 2015.
 Boaler, J. (2014 Jun 16). “Why Students In the US Need Common Core Math.” YouTube video. Stanford, CA: Stanford University. Retrieved on May 31, 2015.
 Chapin, S., O’Conner, C. & Anderson, A. (2003). Classroom Discussions: Using Math Talk to Help Students Learn, Grades 16. Sausalito, CA: Math Solutions.
 Doerr, H.M., Goldsmith, L.T., Lewis, C.C. (2010). Mathematics professional development (Research brief). Reston, VA: NCTM. Retrieved on January 7, 2015.
 Green, E. (2014 Jul 23). “Why Do Americans Stink at Math?” New York Times Magazine. Retrieved on May 31, 2015.
 Smith, M.S. & Stein, M.K. (1998). Selecting and Creating Mathematical Tasks: From Research to Practice. Mathematics Teaching in the Middle School, 3(5), 344350.
Page 8: Banding Together: 430 Miles of Math in Nebraska
 Greater Nebraska MTC website
Page 9: Joining Forces in Ohio
 Ohio statewide network of MTCs websites
Page 10: A Circle of Friends: Unlikely Partnerships for Success
 East Texas MTC website
Page 11: Plan, Deliver, Build Community: Three Keys to Sustainability
 MTC of Thousand Oaks website
Page 12: One, Two, Three, Four: Building Numbers with Four Operations
 Visit Illustrative Mathematics for a more directed version of this problem for the classroom
 The “24” game website
Page 14: News and Views
 Bolognese, Taton Publish MTCRelated Articles
 Bolognese, C. (2014) “Brownie Points.” North American GeoGebra Journal, 2014.
 Taton, J. “Much More Than It’s CookedUp To Be: Reflections on Doing Math and Teachers’ Professional Learning.” Perspectives on Urban Education, Spring 2015.
 Hagan Named One of NPR’s 50 Great Teachers
 Turner, C. (2015 Mar 9). “The Teacher Who Believes Math Equals Love.” National Public Radio.
 Sarah Hagan’s blog, Math=Love
Page 16: Measuring Up: 'Perfect' Rulers
 Columbus MTC website
 Perfect ruler online tool
 Opensource Ruby code to compute the most efficient rulers of various lengths
Page 18: Problem Circle: Let Your Digits Do the Multiplying
 Extraterrestrial finger multiplication (additional challenges from James Tanton)
 Chamberland, M. Single Digits: In Praise of Small Numbers. Princeton: Princeton UP, 2015
Page 19: Math Without Words
 James Tanton’s website
 Tanton, J. (2008). “What Made Me a Mathematician.” Retrieved on August 21, 2015, from http://www.jamestanton.com.
 Natalya St. Clair’s website, Art and Math
Winter/Spring 2015
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In this issue, we describe our new process for beginning MTCs and highlight some upcoming changes for new and existing Circles. Bob Klein and Steve Phelps describe a session on “Liar’s Bingo,” and Corinne Cristiani shares a delightful middle school lesson connected with her MTC experience. Plus, a special cryptographythemed Problem Circle with prizes donated by Princeton University Press!
Contact us for a special promotion code to receive 30 percent off Alan Turing: The Enigma, by Andrew Hodges courtesy of Princeton University Press. The promotion has now been extended through February 15, 2015.
Correction: There is a typo in the fraction in this issue’s Problem Circle (p. 17). As printed, the fifth digit of the numerator is missing. The correct numerator begins “146560” rather than “14650.” The rest of the problem is printed correctly.
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/Page 5: Taking Root: Growing and Sustaining the Math Teachers’ Circle Network
 B. Donaldson, M. Nakamaye, K. Umland, and D. White, “Math Teachers’ Circles: Partnerships between Mathematicians and Teachers.” Notices of the American Mathematical Society, December 2014.
 Official MTC video library of math sessions from our “How to Run a Math Teachers’ Circle” workshops
Page 9: From the Circle to the Classroom: A Middle School Lesson Exploring Compositions
 Corinne Cristiani, 2 = 1 + 1… and Other Problems Cavemen Could Conquer
 Joshua Zucker’s MTC session on compositions
 Common Core State Standards for Mathematical Practice
 Julia Robinson Mathematics Festivals website
 “Why I love MTC,” short videos from Corinne Cristiani and others
Page 13: Pizza, Pipe Cleaners, and Lucky Numbers: Math from the Circles
 Curvature and Strength
 MTC of Hawai’i (MaTCH) website
 Aatish Bhatia, “How a 19th Century Math Genius Taught Us the Best Way to Hold a Pizza Slice.” Wired, September 2014.
 Numbers: Some Surprising, Some Mysterious, Some Lucky
 Tulsa MTC website
 “Mathematical Games,” a monthly feature in Scientific American
 Martin Gardner, “Lucky Numbers and 2187.” Mathematics Intelligencer, Spring 1997, 19(2), p. 26
 “Friedman numbers,” from the website Numbers Aplenty
 Yutaka Nishiyama, “Mysterious Number 6174.” +plus magazine, 2006.
 How Many Faces Does a 10Dimensional Cube Have?
 Boston MTC website
 Volumes Making Full (Math Teachers’) Circle
Page 15: News and Views
 Judith Covington Receives 2015 Haimo Award
 North Louisiana MTC website
 Fun with Triangular Numbers
 E. Medina, R. Grassl, and M. FayZenk, “Fun with Triangular Numbers.” Mathematics Teaching in the Middle School, September 2014.
 Paper Polyhedra
 “Mathematical Origami,” from the website Mathigon: The Mathematics Education Project
 Diana White Named Director of the National Association of Math Circles
 MTC Article Featured in the Notices of the AMS
 B. Donaldson, M. Nakamaye, K. Umland, and D. White, “Math Teachers’ Circles: Partnerships between Mathematicians and Teachers.” Notices of the American Mathematical Society, December 2014.
 Dispatches from the Circles
 Fairfield County MTC website
 Wayne County MTC website
 New York Math & Dinner website
 Queens College TIME2000 conference, November 2014. Keynote address given by Japheth Wood
 Queens College TIME2000 conference, November 2013. Keynote address given by James Tanton
 Smoky Mountain MTC Facebook page
 Tulsa Girls’ Math Circle website
Page 17: Problem Circle: Enigmatic Pi
 Paul Zeitz, “A SciFi Number Riddle for Pi Month,” from the Proof School website
 Andrew Hodges, Alan Turing: The Enigma. Princeton University Press, 2012.
 The Imitation Game movie website
Page 18: In Session: Liar's Bingo
 Complete set of Liar’s Bingo strips
 “Mathemagician” Chuck Sonenshine’s website
Summer/Autumn 2014
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A national survey shows the scope of Math Teachers’ Circle impact. The thriving MTC of Hawai’i shares how it integrates mathematics, teaching, research, and technology to connect teachers across islands. Plus: a twist on a common math contest problem, and a look at Escher’s tilings.
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/Page 4: The State of the Circles: National Survey Shows Scope of MTC Impact
 Explore 26 new sessions (all marked with NEW!) on our Session Materials page.
 For the most recent research on MTCs, please visit our Results page.
Page 10: Hitting New Heights in Hawai’i: Featured Circle Innovates to Overcome Obstacles
 MTC of Hawai’i (MaTCH) website
 Using Google Hangouts to involve remote participants
 Flickr.com, a photo sharing website
Page 14: News and Views
 Advisory Board Member Richard Ruscyzk Honored with Paul Erdos Award
 Art of Problem Solving website
 Fawn Nguyen Named Outstanding educator by Ventura County Math Council
 Thousand Oaks MTC homepage
 Fawn Nguyen’s blog, Finding Ways to Nguyen Students Over, was recently recognized at the top of a list of “awesome K12 math teacher” blogs by the American Mathematical Society’s Blog on Math Blogs
 Encouraging Mathematical Collaboration: AIM Partners with Julia Robinson Math Festival
 Julia Robinson Mathematics Festival website
 Dispatches from the Circles
Page 18: In Session: Art Meets Math: Escher’s Tilings
 MTC of Austin website
 Altha Rodin, Escher Tilings
 Doris Schattschneider, The Mathematical Side of M.C. Escher, from the American Mathematical Society’s website
Winter 2014
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A look at three new MTCs who held immersion workshops in Summer 2013. Plus, running a MTC session as a research experience, new research on how MTCs affect teachers’ Mathematical Knowledge for Teaching, a puzzle edition of Problem Circle, and a look at the geometry of the card games Set and Socks.
Correction: On p. 15, the URL listed for the New Haven County Math Teachers’ Circle is incorrect. The correct URL is www.quinnipiac.edu/nhcmtc.
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/Page 4: Best Foot Forward: Immersion Workshops Give New MTCs the Best Start Possible
 Northern Colorado MTC website and Summer 2013 immersion workshop website
 Heartland MTC website and Summer 2013 immersion workshop website
 Southeast Ohio MTC website and Summer 2013 immersion workshop website
Page 10: Ready for Exploration: MTC Participation as a Research Experience, and Game of Planet
 AIM MTC paper on the mathematics of the card game Set and the Planet variation:
 Baker, M., Beltran, J., Buell, J., Conrey, B., Davis, T., Donaldson, B., DetorreOzeki, J., Dibble, L., Freeman, T., Hammie, R., Montgomery, J., Pickford, A., & Wong, J. (2013). Sets, planets, & comets. The College Mathematics Journal, 44(4), 258264.
 MAA press release
Page 12: Learning Well, Teaching Well: Study Finds MTC Workshops Increase Mathematical Knowledge for Teaching
 Hill, H. C., Ball, D. L., Blunk, M. Goffney, I. M. & Rowan, B. (2007). Validating the ecological assumption: The relationship of measure scores to classroom teaching and student learning. Measurement: Interdisciplinary Research and Perspectives (5), 23, 107117.
 White, D., Donaldson, B., Hodge, A., & Ruff, A. (2013). Examining the effects of Math Teachers’ Circles on aspects of teachers’ mathematical knowledge for teaching. International Journal for Mathematics Teaching and Learning. Published online September 26, 2013, at http://www.cimt.plymouth.ac.uk/journal/
 For the most recent research on MTCs, please visit our Results page.
Page 14: News and Views
 Katie Hendrickson Of Southeast Ohio MTC Wins Buck Martin Statewide Teaching Award
 More information about the Buck Martin Award
 Charlotte McShea Named Mississippi College Mathematics Teacher of the Year
Page 14: Helpful Resources Now Available Online
 Exploding Dots, and More, Online (James Tanton): Exploding Dots Course at G’Day Math!
 The Collaborative Mathematics Project (Jason Ermer)
Page 16: Problem Circle: Puzzle Edition
 Tom/Tom on left, by Thomas Snyder, originally posted on http://gmpuzzles.com (07/30/13)
 Tom/Tom on right, by Thomas Snyder, written as a sample puzzle for the 2013 U.S. Puzzle Championship and originally posted on http://gmpuzzles.com, where you can also find the puzzle from the actual championship test
 Factory Killer Sudoku by Bram de Laat, http://puzzleparasite.blogspot.com
 If you think this is fun, you should also try the Sum Relations Sudoku at Bram de Laat’s Puzzle Parasite blog
Page 18: In Session: Game, Set, Match
 Set game
 Set puzzles at the Set game website and on nytimes.com
 MTC Session notes on Set (Brian Conrey and Brianna Donaldson)
 Socks game
Summer 2013
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The intersection of Math Teachers’ Circles with the Common Core State Standards. Plus, teaching colleagues who participate in Math Teachers’ Circles together, the ingredients of a great Math Teachers’ Circle session, and an exploration of function diagrams.
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/Page 4: The Road Ahead: The View from the Intersection of Math Teachers’ Circles and the Common Core
 The Common Core State Standards for Mathematics website
 Standards for Mathematical Practice
 “Tools for the Common Core Standards,” Bill McCallum’s blog
 The Progressions Project for the CCSM at the University of Arizona
 Illustrative Mathematics
 “Take Away” and more puzzles (Paul Zeitz): Mathematical Games
 “Minimizing a Sum of Distances” and more puzzles (Tatiana Shubin): The Biggest, the Smallest
Page 12: Escape from Teacher Island: Building Colleague Relationships Through MTC Participation
 MTC of Austin website
 Philadelphia Area MTC website
 North Louisiana MTC Facebook page
Page 16: News and Views
 Math for America website
 AIM MTC paper on the mathematics of the card game Set and the Planet variation:
 Baker, M., Beltran, J., Buell, J., Conrey, B., Davis, T., Donaldson, B., DetorreOzeki, J., Dibble, L., Freeman, T., Hammie, R., Montgomery, J., Pickford, A., & Wong, J. (2013). Sets, planets, & comets. The College Mathematics Journal, 44(4), 258264.
 Math Teachers’ Circles summer workshops calendar
Page 17: Problem Circle: Frogs and Toads
 Summer 2013 Problem Circle Solution
 Cut the Knot, Toads & Frogs Puzzle and “Toads & Frogs Puzzle 2D”
 NRICH, Frogs
 Puzzles.com, Jumping Coins
 Anthony Fernandes, et al., “Mathematics Teachers Circle Around Problem Solving,” Mathematics Teaching in the Middle School, Sept. 2011. Article available upon request to Anthony (dot) Fernandes (at) uncc.edu
Page 18: In Session: Function Diagrams
 New York Times Wordplay blog, Primes in Evenland
 Math Education Page, Nine Function Diagrams
 H. Picciotto, Math Education Page, Function Diagrams (Author’s note: See also the additional links at the bottom of the web page. The brief history and bibliography there cite many sources for these ideas. If i recall correctly, I first learned about function diagrams at a conference session led by a couple of teachers from the Illinois Math and Science Academy.)
 Sixteen Function Diagrams from Algebra: Themes, Tools, Concepts by A. Wah and H. Picciotto, Math Education Page
 Focus on Function Diagrams: Teacher Notes from Algebra: Themes, Tools, Concepts by A. Wah and H. Picciotto, Math Education Page
Winter 2013
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How do successful Math Teachers’ Circles keep their members coming back? Plus, what makes a good problem, a participant’s perspective on a “How to Run a Math Teachers’ Circle” workshop, and a look at Ron Graham’s sequence.
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/Page 8: The 'Good Problem' Problem
 The Game of SET, B. Conrey and B. Donaldson
 Codes, Ciphers and Secret Messages, M. Beck
 The Power of Wishful Thinking handout and hints, A. Rodin, and Two is Better than Infinity, P. Zeitz
 Grid Luck, T. Shubin
 Multicolored Multiplication Table, D. Millar
 Coins in Twoland, J. Zucker
 Exploding Dots instructor notes and student materials, J. Tanton
 Conway’s Rational Tangles
 After the Jug Band, E. Johnston, and The Three Jugs Problem, J. Zucker
 Fractions, Decimals, Ratios, Rates, Percents, Proportions, T. Shubin, and Fractions and Decimals, T. Davis
Page 12: Learning to Lead: Fawn Nguyen Offers Her Perspective on AIM’s 'How to Run a Math Teachers’ Circle' Workshop
 Fawn Nguyen’s blog: Finding Ways to Nguyen Students Over, and the MTC post
 Thousand Oaks MTC homepage
 Julia Robinson Mathematics Festival homepage
 The 1to100 Problem, J. Zucker and T. Davis
 The Art and Craft of Problem Solving, P. Zeitz
 Solve This, J. Tanton
 Mathematical Games, P. Zeitz
 How to Gamble, If you Must, P. Zeitz
Page 14: News and Views
 Conference Board of the Mathematical Sciences website; the Mathematical Education of Teachers II (MET2) document. (Read Chapter 6, “High School Teachers,” for a recommendation of MTCs!)
 World Sudoku Championship website
 Math for America website
 National Council of Teachers of Mathematics website
 2013 Joint Mathematics Meetings website
Page 17: Problem Circle: Simple, or Impossible?
Autumn 2012
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Being less helpful can be a good thing. Plus, a study of teacher networks, interviews with the Casco Bay MTC and teacher Horda Semdani of the North Louisiana MTC, and a session on compositions.
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/Page 4: Be Less Helpful
 dy/dan, Dan Meyer’s mathematics blog
 Algebra Teaching Study, Floden, Schoenfeld, and colleagues
 The Art and Craft of Problem Solving, P. Zeitz
Page 10: Five Cooks in the Kitchen: How the Casco Bay MTC Makes It Work with a FivePerson Leadership Team
 Casco Bay MTC website
 Exploding Dots, or Dots and Boxes, J. Tanton
 Handshakes and Graph Theory, E. Johnston
 A Trio of Friendly Problems: Handshakes, Diagonals, and Triangular Numbers, M. FayZenk
 Dominoes and Rectangles and Tiling Torment, J. Zucker
Page 12: Poetry and Proportions: Five Questions for Horda Semdani of the North Louisiana MTC
 North Louisiana MTC website
 Math Doesn’t Suck, Danica McKellar
 One Inch Tall, a poem by Shel Silverstein
 Shreveport news station KTBS.com segment on the North Louisiana MTC
Page 14: News and Views
 Arcadiana MTC website
Page 16: Problem Circle: Number Sum Triangles
 Autumn 2012 Problem Circle Solution
 Bay Area Math Olympiad for Teachers website
Page 18: In Session: Compositions
 Compositions, J. Zucker
Winter 2012
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Ten ideas for funding your Math Teachers’ Circle. Plus, a mathematician’s perspective on leading a Math Teachers’ Circle session, profiles of the Twin Cities Math Teachers’ Circle and teacher Elizabeth Tarbutton of the Rocky Mountain Math Teachers’ Circle, and a look at “what is like a square.”
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/Page 4: Adding It All Up: Ten Ideas for Funding Your Circle
 Foundation Directory Online: an online search tool for funding resources
Page 10: Something New: A Mathematician’s Perspective on Leading a Circle
 Cal Poly Department of Mathematics Puzzle of the Week
 Factorials and Squares, E. Basor
Page 12: Featured Circle: Twin Cities MTC
 Twin Cities MTC website
 F. Morgan, E. R. Melnick, and R. Nicholson, “The Soap Bubble Geometry Contest.” From Mathematics Teacher, December 1997, Volume 90, Number 9, pages 746750
 ZomeTool Lesson Plans: Handson activities for students of Elementary Grades through High School
Page 14: Real Math at Work: Five Questions for Elizabeth Tarbutton of the Rocky Mountain MTC
 Rocky Mountain MTC website
 Mathematical Card Tricks, T. Davis
 Mathemagical Card Tricks: Participant and Leader documents, S. Santorico
Page 16: News and Views
 National Science Foundation Discovery Research K12 program
 Mathematics Teaching in the Middle School journal
 Chevron Human Energy video segment on the American Institute of Mathematics (the part about MTC starts at 3:10!)
Page 18: In Session: What Is Like a Square?
 Julia Robinson Mathematics Festival website
 “Four Points, Two Distances,” A. Amit’s blog, “Affine Mess”
 What Is Like a Square? J. Zucker
Page 19: Problem Circle: Number Bases
Summer 2011
Our inaugural issue! Math Teachers’ Circles inspire research on the mad veterinarian problem, interviews with the Lincoln Area Math Teachers’ Circle and teacher Susan Holtzapple of the AIM Math Teachers’ Circle, and a look at Tatiana Shubin’s “Grid Luck” session.
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/Page 2: Featured MTC: The Lincoln Area Math Teachers’ Circle
 Lincoln Area MTC website
 Jug Problem video clip from Die Hard 3
 The Jug Problem: After the Jug Band, E. Johnston. Three Jugs, J. Zucker
 Instant Insanity Cubes, S. Hartke
Page 4: Problem Circle: Have Colors – Will Paint
Page 5: MTC of Austin Wins Outreach Award
Page 6: 'Leavitt' to the Mad Vet: MTC Session Inspires Research Connection
 Pikes Peak MTC website
 G. Abrams and J. Sklar (2010). The Graph Menagerie: Abstract Algebra and the Mad Veterinarian. Mathematics Magazine, Vol. 83, No. 3, pp 168 – 179.
 The Mad Veterinarian on Mathematical Safari: notes and slides, G. Abrams
Page 7: Featured Teacher: Susan Holtzapple
 AIM (Palo Alto) MTC website
Page 8: MTC Sessions: Grid Luck
 Grid Luck, T. Shubin
 Mathematics: A Human Endeavor, H. Jacobs, 3rd Ed., 1994.
 The Bouncing Ball Problem, J. Zucker