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
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
3: Presentation Times: 2:00 3:00
Organization:
Louisiana State University Math Circle -- http://www.cain.lsu.edu/MathCircle/index.html
-- High School Summer Program
Activity: Excel vs. Fibonacci
Presenters:
Lee Windsperger -- windsplg@math.lsu.edu -- Louisiana State University
Jesse Levitt -- jlevit3@lsu.edu -- Louisiana State University
Steven Olsen -- solsen2142@gmail.com
-- Baton Rouge Magnet High School
Sensitive Dependence on Initial Data in Backwards-In-Time Difference Equations
Marie
Neubrander -- marie1@cox.net -- Glasgow
Middle School
Organization
Description:
The
LSU MathCircle program is a three-week summer program
run by LSU math graduate students. The
residential day camp attracts high level high school students from around the
United States as well as international locations. The program consists of typical math circle
investigations and discussion of topics and material that are not normally
covered in the standard high school curriculum.
In our third week, the participants fully investigate a problem topic of
their choice and then present their progress to LSU undergraduate REU, graduate
students, and professors. During the
academic year, we encourage participants to continue working on their
investigations with their graduate student mentors. We also send our graduate students to local
high school math clubs to run traditional math circle sessions.
Activity
Description:
The
“Excel vs. Fibonacci” project is an investigation of the “backwards-in-time”
Fibonacci sequence given arbitrary starting values as well as the limits of our
everyday technology when doing so. Given
two consecutive values of a Fibonacci-type sequence, we will attempt to
determine when is it possible to successfully run spreadsheets backwards to
accurately determine our starting values.
Furthermore, we will attempt to predict for which starting values does
the Fibonacci sequence mirror itself (up to oscillations) when the sequence is
computed in both directions. We will
also explore strategies for recovering information when the technology
fails. Students should gain from this
activity a better understanding of difficulties one encounters when modeling
“backwards-in-time” problems, the binary number system, Binet’s
formula, and averaging.
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
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
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
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
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
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
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 1^{st}
through 5^{th} 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 1^{st} and 2^{nd} grade and another
for children in 3^{rd} and 4^{th} 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 1^{st}, 2^{nd} and 3^{rd}
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
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
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 |