Math Circle Poster and Activity Session

Joint Math Meeting 2012, Boston, MA,

Saturday, January 7, 2012, 1-4 PM

 

Organizers:

Philip B. Yasskin, Texas A&M University, yasskin@math.tamu.edu, 979-845-3734

James Tanton, St. Mark's School, jamestanton@stmarksschool.org , 508-460-0350

Tatiana Shubin, San Jose State University, shubin@math.sjsu.edu, 408-924-5146

Sam Vandervelde, St. Lawrence University, svandervelde@stlawu.edu, 315-229-5946

 

Come join us for the chance to experience a math circle firsthand.  Math circles vary widely in format and frequency, but they all bring groups of interested students or teachers together with professional mathematicians to investigate and discover mathematics.  Ten math circles from around the country will display a poster describing that circle along with a live activity to try out.  These activities are intended to provide ideas for lessons to use at your own circle or school.  Activities will restart every 30 minutes.

 

The session is sponsored by the Special Interest Group of the MAA on Math Circles for Students and Teachers (SIGMAA-MCST) with collaboration by the National Association of Math Circles (NAMC) and the Math Teachers’ Circle Network (MTCN). Each of these organizations will also have an information table. For a schedule of talks as well as abstracts and handouts, please see http://sigmaa.maa.org/mcst/PosterActivitySessions/JMM2012.

Presentation Time

Table

Table

Table

Table

1:00

1b

7

6

12

1:30

2b

5

8

11

2:00

6

 9

3

2b

2:30

8

10

4

1b

3:00

3

11

7

10

3:30

4

12

5

 9

 

 

Table 1a:                                                                                                                                                                                                                                                                            

Organization:

SIGMAA-MCST -- http://sigmaa.maa.org/mcst/ -- Help for Student and Teacher Circles

Activity: Information and Registration Table

Presenters:

James Tanton -- jamestanton@stmarksschool.org -- St Mark's School

Sam Vanderveldt -- svandervelde@stlawu.edu -- St. Lawrence University

Philip Yasskin – yasskin@math.tamu.edu -- Texas A&M University

Edward Keppelmann – keppelma@unr.edu -- University of Nevada, Reno

Amanda Serenevy -- viajera6@gmail.com -- Riverbend Community Math Center

Organization Description:

SIGMAA MCST (Special Interest Group on Math Circles for Students and Teachers) is sponsoring a poster and activity session to illustrate and celebrate the power and effectiveness of Math Circle work. A Math Circle is broadly defined as a semi-formal, sustained enrichment experience that brings mathematics professionals in direct contact with pre-college students of all ages and/or their teachers. Circles foster passion and excitement for deep mathematics. There are currently over 120 math circles across the nation.

This poster outlines the history of math circles, provides a brief sampler of math circle styles and approaches, and offers a list of resources for learning more about math circles and finding support to start one of your own. Additional information, of course, can be found at the SIGMAA website, http://sigmaa.maa.org/mcst, at the National Association of Math Circles, http://www.mathcircles.org, and at the Math Teachers’ Circle Network, http://www.mathteacherscircle.org. Please join the SIGMAA on Circles by adding the SIGMAA when you renew your membership with the MAA.


Table 1b:              Presentation Times: 1:00  2:30                                                     

Organization:

NAMC -- http://www.mathcircles.org/ -- Help for Student Circles

Activity: Rolling Dice

Handout

Dice Video

Presenters:

Dave Auckly -- auckly@msri.org -- Math Science Research Institute

Brandy Wiegers -- brandy@msri.org -- Math Science Research Institute

Joshua Zucker -- joshua.zucker@stanfordalumni.org -- Math Science Research Institute

Organization Description:

The National Association of Math Circles runs the mathcircles.org website which provides a central resource for people wishing to start new math circles or sustain existing ones.  For new math circle leaders, the NAMC provides a comprehensive guide to math circles, the Circle In a Box book, in the form of a wiki.  The site includes links to dozens of math circles all over the country as well as some international circles, a problem database and lesson plan collection, videos of math circle sessions, information about math circle minigrants, and descriptions of math circle events at national math meetings as well as at the annual Circle on the Road conference.  Whether your circle is new or has been running for years, please register for an account at mathcircles.org, add your circle to our list, and apply for a minigrant!

Activity Description:

We can turn dice with various numbers of sides on different kinds of grids: a cube on square grid paper, or a tetrahedron or octahedron on triangular grid paper, for example.  Here "turning" means carefully rotating the die so it tips over onto an adjacent face, remaining aligned with the grid.  Beginning with the die oriented in one particular direction, we wonder what orientations it can have upon returning to its original location.  We investigate what closed loops are possible that also preserve orientation.  What if we use a rectangular parallelepiped instead of a cube?  What if the grid has holes? Depending on the audience, this activity can be connected to topics including parallel transport, holonomy, angle defect, curvature, categories and groupoids, and the Euler characteristic. There are also games (such as Cuboid) and puzzles (such as Tip Over) that use a similar mechanic.

 

Table 2a:                                                                                                                           

Organization:

MTCN -- http://www.mathteacherscircle.org/ -- Help for Teacher Circles

Presenters:

Brianna Donaldson -- brianna@aimath.org -- American Institute of Mathematics

Tatiana Shubin -- tatiana.shubin@sjsu.edu -- San Jose State University

Organization Description:

Math Teachers' Circles (MTCs) are groups of teachers who meet regularly with mathematicians for highly interactive sessions focused on problem solving in the context of rich mathematics. The goal is to involve these teachers in the mathematical community by putting them in direct contact with mathematicians and engaging them in an authentic, ongoing mathematical experience that will ultimately impact their understanding and teaching of mathematics.

The MTC Network (www.mathteacherscircle.org) is a project of the American Institute of Mathematics (AIM; www.aimath.org) that links together MTCs throughout the United States. To help the MTC community grow, the Network organizes two workshops on “How to Run a Math Teachers’ Circle” each summer and provides extensive mathematical and logistical resources to local MTCs. This poster gives an overview of MTCs and their outcomes, and describes the workshops and other resources offered by the MTC Network.

 

Table 2b:              Presentation Times: 1:30  2:00                                                    

Organization:

Rocky Mountain Math Teachers' Circle -- http://rmmtc.ucdenver.edu -- Teacher Circle

Poster: Math Education Perspective on Math Teachers' Circles

Presenter:

Diana White -- Diana.White@ucdenver.edu -- University of Colorado Denver

Poster Description:

The goal of this poster is to help participants understand how Math Teachers' Circles (MTCs) fit into current research in mathematics education. We will describe how the MTC model relates to what is known about teacher professional development and discuss preliminary research results on the national MTC Program. We will also describe how MTCs relate to the mathematical practice components of the Common Core State Standards.

 

 

Table 4:                                 Presentation Times: 2:30  3:30                      

Organization:

Math Circle in the Triangle -- http://www.math.ncsu.edu/MathCircles/ -- Middle School Student Circle

Activity: Peering Through Tubes

Handout

Tubes Video

Presenters:

Molly Fenn -- mafenn2@ncsu.edu -- North Carolina State University

Christina Erbacher -- ceerbach@ncsu.edu -- North Carolina State University

Melissa Tolley -- mmtolley@ncsu.edu -- North Carolina State University

Organization Description:

The Math Circle in the Triangle began in January 2010 as a weekly math circle for middle school aged students in Raleigh, North Carolina and the surrounding Research Triangle area.  The Circle is organized by members of the Mathematics Department at North Carolina State University with Dr. Molly Fenn as Director.  Attendance at each session is typically 15 to 20 students and we hold around 10 sessions each semester.  You can find more information about The Math Circle in the Triangle at: http://www.math.ncsu.edu/MathCircles/

Activity Description:

The Peering Through Tubes activity has been used in our math circle as well as in courses for in-service high school teachers.  It involves an active component where students are taking measurements and gathering data, a search for patterns in the data collected, a simple geometric explanation for those patterns, and the potential for a follow-up discussion on error in data collection.  We have provided a complete lesson plan for a full 90-minute math circle session as well as a description of how we have adapted this activity for the 25-30 minute sessions at the Join Mathematics Meetings.

 

Table 5:                                 Presentation Times: 1:30  3:30                      

Organization:

Little Circle at Florida International University -- http://mathcircles.fiu.edu -- Middle School Student Circle

Activity: Drawing Pictures: How Projective Geometry was Discovered

Handout

Presenter:

Mirroslav Yotov -- yotovm@gmail.com -- Florida International University

Organization Description:

The Little Circle is designed for middle school students, and, together with the Big Circle, is a part of the Math Circles at FIU. Early afternoon of every other Saturday, 5-15 kids get together in the Circle at FIU and learn math more interesting as facts, and deeper as knowledge then what they get at school. Some of the standard topics for discussion and problem solving are Arithmetic, Combinatorics, Geometry, and Elements of Logic. In our work, we try to emphasize the connection of math to the sciences and the arts, and how this connection helps the disciplines involved develop. Two popular topics have been "The Gravity Center in Mechanics and Mathematics", and "Linear Perspective -- Art and Math Aspects".

Activity Description:

The activity teaches the students about one, two, and three-point perspective, how to use these to draw/sketch basic pictures, and how the notion of points at infinity, borrowed from the method of linear perspective, transformed the classical Euclidean geometry into projective geometry. As a model of the projective plane, the Riemann spherical geometry is discussed including some properties of the main figures (triangles) thereof. The activity is accessible to middle school students with basic knowledge of elementary Euclidean geometry.


 

Table 6:                                 Presentation Times: 1:00  2:00                      

Organization:

Bay Area Circle for Teachers -- http://bact.mathcircles.org/ -- Teacher Circle

San Francisco Math Circle Teachers’ Circle -- http://www.sfmathcircle.org/teacherscircle.html -- Teacher Circle

Activity: Slide Rules Rule

Handout

Slide Rule Video

Presenter:

Brandy Wiegers -- brandy@msri.org -- San Francisco State University, National Association of Math Circles Coordinator

Organization Description:

The Bay Area Circle for Teachers and San Francisco Teachers’ Circle are meant to be professional learning communities that build of the foundation of the long Bay Area tradition of Math Circles for students.  The aim of these Circles is to equip educators with an effective problem-solving approach to teaching mathematics. The programs immerse groups of interested elementary, middle, and high school math teachers in engaging mathematics and expose them to a dynamic style of classroom presentation. Both programs rely on the community of teachers in the Bay Area to support and develop the program. BACT meets with a weeklong summer institute and 1 day winter workshop. SFMCTC instead uses monthly teacher dinners throughout the year.

Activity Description:

Math Circles provide opportunities to introduce students to mathematical topics they won’t see in a K-12 classroom and to share with them aspects of mathematical community and lore. Slide Rules fit right into these program components. We know that a stereotypical mathematician’s tool is a slide rule but how many teachers or students have ever seen or used one?  This lesson starts at the addition and multiplication tables and builds up to the idea of exponentials. From there we hand out the slide rules and let the good times rule!  We’ll end with a discussion of where to find your own slide rule resources!

 

Table 7:                                 Presentation Times: 1:00  3:00      

Organization:

Julia Robinson Math Festival -- http://jrmathfestival.org -- Travelling Show for Students, Teachers and the Public

Activity: Tiling Torment

Presenter:

Joshua Zucker -- joshua.zucker@stanfordalumni.org -- Director, Julia Robinson Mathematics Festivals

Organization Description:

The Julia Robinson Mathematics Festivals are a program of math events for students, typically in middle school. We fill a large room with tables with various mathematical activities and problem sets. These are designed to begin with easily accessible problems and end with problems that are challenging even to the top students, including open problems in some cases.  Rather than fostering competition, these events support collaboration both among the students and between the students and the professional mathematicians who staff the tables. Prizes are awarded by raffle, with raffle tickets being distributed to students who persist, not only to those who find the quickest answers.  For more information, and a large collection of festival activities, please visit http://jrmathfestival.org or contact joshua.zucker@stanfordalumni.org

Activity Description:

These tiling challenges begin with some simpler problems that require an understanding of odd and even at the level of an elementary school student, progress through more sophisticated parity arguments, and end with some quite challenging problems requiring even more flexible thought.  There's something here both for the students who want to tinker with something hands-on as well as for those who want to think more deeply about the underlying mathematics.

 

Table 8:                                 Presentation Times: 1:30  2:30      

Organization:

Math Teachers’ Circle of Austin -- http://sites.google.com/site/mtcaustin/ -- Teacher Circle

Activity: Symmetries of the Trihexaflexagon

HANDOUT

Trihexaflexagon Video

Presenters:

Altha Rodin -- rodin@math.utexas.edu -- University of Texas, Austin

Adriana Sofer -- asofer@math.utexas.edu -- University of Texas, Austin

Organization Description:

The Math Teachers’ Circle of Austin has been in operation since the summer of 2010 when we held our first Summer Immersion Workshop.   The founding members of the MTCA are Altha Rodin and Adriana Sofer, faculty members in the math department of The University of Texas, Jason Ermer, who is part of the UTeach program, and Patty Hill and Michael Word, teachers at the Kealing Middle School Magnet program.  We have an enthusiastic core group of teachers who regularly attend our monthly meetings and thanks to their help in spreading the word about the program, we have seen our attendance more than double since the program began. For more information, please visit our web site: http://sites.google.com/site/mtcaustin/.

Activity Description:

A symmetry of a geometric object can be thought of as an undetectable motion.  Symmetry groups can be introduced in a natural way by considering symmetries of familiar geometric objects such as a rectangle or a square.  A fun and surprising activity on symmetries involves discovering the symmetries of the trihexaflexagon, a geometric object discovered in 1939 by Arthur H. Stone, while a student at Princeton.  A trihexaflexagon is constructed by folding a strip of paper made up of nine equilateral triangles into the shape of a hexagon.  The resulting object can be transformed by “flexing” to reveal three distinct faces.  By decorating the triangles in different ways, we can develop an understanding of how the triangles that form faces are transformed during the flexing.

 

Table 9:                                 Presentation Times: 2:00  3:30      

Organizations:

A² Math Teachers’ Circle -- no web site yet -- Elementary School Teachers Circle

Metro Atlanta Math Teachers’ Circle -- no web site yet -- Middle School Teachers Circle

Osborne Math Teachers’ Circle -- no web site yet -- High School Teachers Circle

Activity: 3×3 Magic Squares

Handout

Presenters:

Virginia Watson -- vwatson@kennesaw.edu -- Kennesaw State University

Mary Garner -- mgarner@kennesaw.edu -- Kennesaw State University

Beth Rogers -- mroger47@kennesaw.edu -- Kennesaw State University

Angelique Smith-Hunt -- angelique_l_smith-hunt@fc.dekalb.k12.ga.us -- Champion Theme Middle School

Organization Description:

The leadership team at Kennesaw State University (KSU) runs three Math Teachers' Circles.  The A2(squared) Math Teachers' Circle is for elementary teachers.  Currently it is made up of elementary teachers at five schools in the area 2 district of Cobb County GA. The Metro Atlanta Math Teachers' Circle is for middle grades teachers.  Currently members are from Cobb County and Dekalb County.  The Osborne Math Teachers' Circle is for high school teachers in the Osborne and Campbell high schools in Cobb County GA.  The A2 and Osborne MTC were supported last year through a Teacher Quality Partnership Grant administered through the Bagwell College of Education at KSU.  All three meet three times a semester.

Activity Description:

The activity involves discovering the patterns in 3x3 magic squares.  We present the participants with the handout and ask them to discover any patterns and use the patterns to create their own 3x3 magic squares.  We then work on proving why the patterns exist.


 

Table 10:                              Presentation Times: 2:30  3:00      

Organization:

Melrose Math Circle -- http://sites.google.com/site/melrosemathc/ -- Elementary School Student Circle and Teachers’ Circle

Activity: The Handshake Problem

Handshake Video

Handshake Poster

Presenters:

Maura Mast -- Maura.Mast@umb.edu -- University of Mass, Boston 

Jack Reynolds -- jack.jreynolds@verizon.net -- Melrose Math Circle

Joanne Kimball-Sherman -- jkimballsherman@melrose.mec.edu -- Roosevelt Elementary School

Organization Description:

The Melrose Math Circle formed in August 2010 and is currently held at the Roosevelt Elementary School in Melrose, MA.  The focus is on children in 1st through 5th grade.  In spring 2011 the organizers worked with several elementary school teachers and offered two 6-week sessions, enrolling an average of 20 children in each group.  For fall 2011 there will be two separate groups, one for children in 1st and 2nd grade and another for children in 3rd and 4th grade; each group will run for 6 weeks and will meet once a week.   In addition to the circles for children, the participating teachers from the elementary school will meet weekly with the organizers for an informal teachers’ circle.  The Melrose Math Circle is primarily organized by Dr. Maura Mast, a mathematics faculty member at the University of Massachusetts Boston, and her husband Jack Reynolds, MEd.  The Melrose Math Circle gratefully acknowledges support from the Mathematical Sciences Research Institute.

Activity Description:

The handshake problem is a classic, fun problem that can be done with different age groups.  The basic problem is:  if everyone in a group shakes hands, how many total handshakes are there?  There are some basic ground rules that need to be clear:  no shaking hands with yourself, and you only shake hands with another person once.  The first step is to try out some examples and look for a pattern.  This leads to a suggested solution:  with n people, there would be 1 + 2 + 3 + … + (n-1) handshakes in total.  The next step is to verify that this solution really works.  Finally, we discover that we can write this sum as n(n-1)/2. We have done this activity with a group of children in 1st, 2nd and 3rd grade.  It could easily be adapted for an older group.

 

Table 11:                              Presentation Times: 1:30  3:00      

Organization:

Eastern Kentucky Math Teachers’ Circle -- http://math2.eku.edu/transitions/ekmtc.php -- Teacher Circle

Activity: Making Change for a Dollar

Handout(pdf)

Handout(word)

Change for a Dollar Video

Presenters:

Cheryll Crowe -- Cheryll.Crowe@eku.edu -- Eastern Kentucky University

Nancy Blue Williams -- nancy.williams@eku.edu -- Eastern Kentucky University

Michele Anderson -- michelle.anderson@corbin.kyschools.us -- Corbin Middle School

Cindy Davis -- cynthia.davis@corbin.kyschools.us -- Corbin Middle School

Organization Description:

The Eastern Kentucky Math Teachers’ Circle (EKMTC) was established in summer 2011 through a grant from the American Institute for Mathematics Summer Immersion Workshop.  Following the workshop, EKMTC has participated in the MAA MathFest, presented a circle activity at the Kentucky Council of Teachers of Mathematics Annual Conference, and held a kick-off event/meeting on November 14 in Corbin, Kentucky. The goals of EKMTC are to: (1) Support and emphasize middle school teacher content knowledge in light of the new standards (KCAS). (2) Network with middle school teachers throughout eastern Kentucky. (3) Continue collaboration with university math faculty and middle school teachers, specifically focused on content and pedagogy. EKMTC consists of mathematicians and mathematics educators from Eastern Kentucky University (EKU) and middle school math teachers across eastern Kentucky.  The leadership team is comprised of two math teachers from Corbin Middle School and two university faculty members from the Department of Mathematics and Statistics at EKU.

 

Activity Description:

The “Making Change for a Dollar” activity emphasizes critical thinking and problem solving through an exploration of combinations related to making change for a dollar.  The activity begins by opening with the broad question of how many ways can a person make change for a dollar and then provides scaffold activities to answer to this question.  The activity concludes with a real-life “dilemma” of mathematical reasoning.

 

Table 12:                              Presentation Times: 1:00  3:30      

Organization:

The Bard Math Circle -- http://bardmathcircle.blogspot.com/ -- Student Circle

Activity: Six Choose Three

HANDOUT

Presenters:

Japheth Wood -- jwood@bard.edu -- Bard College

Jeannette Benham -- jbenham08@gmail.com -- Bard College

Lauren Rose -- rose@bard.edu -- Bard College

Joy Sebesta -- jlsebesta@msn.com -- Bard College

Shelley Stahl -- smartershelley@gmail.com -- Bard College

Organization Description:

The Bard Math Circle began in 2007, led by Bard math professors Lauren Rose and Japheth Wood and undergraduate math majors in the Trustee Leadership Training program. Math circle events take place at local libraries in the area surrounding Bard College, and target middle and upper elementary school students. Recently, several local middle school teachers have been attracted to our events, and report that what we intend for a student audience has turned out to be more valuable to their mathematical understanding and pedagogy than all but one district-provided professional development offering over the last 15 years. This interest from teachers has led us to consider starting a teachers' math circle, and also to invitations for a more formal involvement with the local school districts. Please visit our blog/webpage at bardmathcircle.blogspot.com for specific information about our programs.

Activity Description:

The “Six Choose Three” activity was used in our Spring 2011 math circles activities to build an understanding of a basic combinatorial function, as well as to give insight into the notion of isomorphic mathematical structure. After having time to work on the problems, participants were encouraged to find the mathematical connection between any two problems, each of which is some representation of C(6,3) = 20. In addition to problem sheets like these, each math circle event features math games, logic puzzles, and a hands-on mathematical project that students can build and take home.

 

Presentation Time

Table

Table

Table

Table

1:00

1b

7

6

12

1:30

2b

5

8

11

2:00

6

 9

3

2b

2:30

8

10

4

1b

3:00

3

11

7

10

3:30

4

12

5

 9