Paul Zeitz Demo Circle for Meeting Participants
Math Circle Demo Led by Japheth Wood and Sam Vandervelde  Saturday January 12
Starting a Math Circle Workshop  Sam Vandervelde and Japheth Wood
Math
Circle Poster and Activity Session
Joint Math Meetings 2013 San Diego CA
Friday,
January 11, 2013, 14 PM
Organizers:
Philip B. Yasskin, Texas A&M University, yasskin@math.tamu.edu,
9798453734
Sam Vandervelde, St. Lawrence University, svandervelde@stlawu.edu,
3152295946
Tatiana Shubin, San Jose State University, shubin@math.sjsu.edu,
4089245146
James Tanton, St. Mark's School, jamestanton@stmarksschool.org
, 5084600350
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
(SIGMAAMCST) 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/JMM2013.
Presentation Time 
Table 
Table 
Table 
Table 
1:00 
4 

5 
9 
1:30 
3 
11 
7 
10 
2:00 
8 
10 
4 
2b 
2:30 
6 
9 
3 
1b 
3:00 
1b 
5 
8 
11 
3:30 
2b 
7 
6 

Table 0: Organization: SIGMAAMCST http://sigmaa.maa.org/mcst/ Help for
Student and Teacher Circles
Activity: Information and Registration Table
Presenters:
Sam Vandervelde svandervelde@stlawu.edu
St. Lawrence University
Tatiana
Shubin tatiana.shubin@sjsu.edu
San Jose State University
Philip
Yasskin – yasskin@math.tamu.edu
Texas A&M University
James
Tanton jamestanton@stmarksschool.org
St Mark's School
Edward Keppelmann – keppelma@unr.edu
University of Nevada, Reno
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 semiformal,
sustained enrichment experience that brings mathematics professionals in direct
contact with precollege 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 1a: Organization: National
Association of Math Circles http://www.mathcircles.org/
Help for Student and Teacher Circles
Activity: Information Table
Presenters:
Brandy Wiegers brandy@msri.org
Math Science Research Institute
Amanda
Serenevy viajera6@gmail.com
Riverbend Community Math Center
MSRI Director of Educational and Outreach Activities: Alissa Crans acrans@msri.org
Math Science Research Institute
Organization Description: The National Association of
Math Circles, at the Mathematical Sciences Research Institute, 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, and a useful 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 http://www.mathcircles.org/, add your
circle to our list, and apply for a minigrant!
Table 1b: Presentation Times: 2:30 3:00 Organization:
San Francisco Math Circle http://www.sfmathcircle.org/index.html/
Student & Teachers, all grades
Activity: Keeping Safe: Lessons Learned Working
with SFMC Elementary Students
Presenter: Brandy Wiegers
brandy@msri.org
Math Science Research Institute
Organization
Description: SFMC is a weekly program
for teachers and students centering around a community of students who want to
work together on intriguing and challenging mathematical problems. We are
excited to add a new program to San Francisco Math Circle (SFMC) aimed at
students in grades 2, 3, 4 and 5. The program, SFMC Elementary, is designed to
develop a positive attitude towards mathematics by introducing young children
to elements of mathematical culture. It has the same mission and philosophy as
the SFMC.
Activity Description: We have learned a lot about best practices in working with elementary
students to keep everyone safe over the last year. I would like to use my
activity session to share some of these lessons and talk with anyone who might
have questions about their own location. I would also share a few of our
favorite activities.
Table 2a: Organization: Math
Teachers' Circles Network http://www.mathteacherscircle.org/
Help for Teacher Circles
Presenters: Diana White Diana.White@ucdenver.edu
University of Colorado Denver
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 (http://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: 2:00 3:30 Organization:
Math Teachers' Circles Network http://www.mathteacherscircle.org/ Teacher
Circles
Poster: Research Update on Math Teachers' Circles
Presenter: Diana White Diana.White@ucdenver.edu
University of Colorado Denver
Poster Description: This poster/activity will update
the national Math Circle community on the status of the research related to
Math Teachers' Circles as part of an NSF DRK12 grant.
Table 3: Presentation Times: 1:30 2:30 Organization:
Navajo Nation Math Circles Project no web site –
Students and Teachers
Activity: NavajoRelated Math Circle Activities
Presenters:
Tatiana Shubin tatiana.shubin@sjsu.edu
San Jose State University
Henry Fowler tatiana.shubin@sjsu.eduDine
College, Tsaile
Organization
Description: The Navajo Nation Math
Circles Project (NNMCP) is an initiative to launch and sustain math circles for
students and teachers on the Navajo Reservation. The project began with first
circles started in September, 2012, at two locations St Michael Indian School
and Chinle High School, and a math circlestyle
sessions conducted for preservice teachers at the Dine College in Tsaile. The project is supported by NSF, AIM, MSRI, and
EAF.
Activity Description: The activities reflect the highly
visual nature of Navajo kids' learning style and their tendency to be reserved
yet cooperative.
Table 4: Presentation Times: 1:00
2:00 Organization: Riverbend Community
Math Center http://riverbendmath.org/
Student and Teacher Program
Activity: Exploring Lill's
Method for Finding Polynomial Roots
Presenters: Amanda Serenevy
viajera6@gmail.com
Riverbend Community Math Center
Organization Description:
The Riverbend Community Math Center is a
nonprofit organization located in South Bend, Indiana that started offering
programs during the fall of 2006. Our mission is to promote interest and
confidence in mathematics among people of all ages. Our organization provides
several different types of programs including a Math and Technology Academy, a
Math Studio, Math Circles, professional development workshops for teachers, and
custom events with handson activities.
Activity Description:
Lill's method is a visual
method for finding roots of a polynomial of any degree, and was developed in
1867 by Austrian engineer Eduard Lill. This method
was used by Margharita Beloch
in 1936 to solve cubic equations via origami constructions. During this Math
Circle session, we will first play with Lill's method
to see how it works in quadratic and cubic cases, and then extend the method to
polynomials of higher degree. We will follow the presentation in the following
reference: Thomas C. Hull (April 2011). "Solving Cubics
With Creases: The Work of Beloch and Lill", American Mathematical Monthly: 307315. This
circle could work for students or teachers who are familiar with quadratics and
polynomials. It works especially well for students in intermediate algebra,
precalculus, and calculus courses, or for teachers who teach these courses.
Table 5: Presentation Times: 1:00 3:00 Organization:
Albuquerque Math Teachers' Circle http://www.unm.edu/~mathtcTeacher
Circle
Activity: What is in that Can of Soda?
Presenter: Michael Nakamaye
nakamaye@gmail.com
University of New Mexico
Organization
Description: The Albuquerque Math
teachers' circle started up two years ago. While our target audience is middle
school teachers, we have several elementary school teachers who are regular
participants and a couple of high school teachers as well. Most of our
participants come from the very large Albuquerque Public School system but we
frequently have teachers from private schools or from the suburbs in
attendance. We have 6 meetings a year during the school year and have also had
two summer workshops. Right now we are looking to build a core group of
teachers who will eventually determine what direction our circle takes.
Activity Description: Participants will be presented with a can of soda and asked how they
might go about determining how thick the can is. Cutting the can open and
measuring is the most straightforward approach but it is dangerous because the
can is quite sharp. The average thickness can be estimated indirectly, however,
by approximating the surface area of the can (a good geometry exercise) and
then using the density of aluminum. Alternatively, it is possible to find the
volume of aluminum in the can directly using an idea of Archimedes: crush the can,
submerge it in water, and measure the amount of water displaced. Once this is
known, the thickness can again be approximated by dividing the volume by the
surface area. The activity is geometrically rich while dealing with a simple
every day object. For the Common Core  Archimedes and the King's Crown
Table 6: Presentation Times: 2:30
3:30
Organization: University of Wisconsin
Milwaukee (UWM) Math Circle https://pantherfile.uwm.edu/gapinter/www/mc_index.html
Student Circle
Activity: Operation Cookie Jar
Presenter:
Gabriella Pinter gapinter@uwm.eduUniversity
of Wisconsin, Milwaukee
Authors: Klara
Pinter University of Szeged and Istvan
Lauko University of Wisconsin
Organization
Description: Our UWM Math Circle
started in September 2011, and is led by three UWM Mathematics faculty, Gabriella Pinter, Chris Hruska
and Boris Okun. We focus on open ended problem
solving activities for students in grades 712. Our goal is to stimulate
discussion, and to support the students in further explorations of problems. We
emphasize rigorous arguments once the idea of a solution is outlined. We
encourage students to ask new questions, and formulate new problems. Our Math
Circle is free and students can join any time.
Activity Description: There
are 15 cookie jars, numbered consecutively from 1 to 15. The number of cookies
in each jar is equal to the number of the jar. A “move” consists of choosing
one or more jars, then removing one or more cookies from the chosen jars—but
the same number of cookies from each jar. Your task is to work out how to get
all the cookies from all the jars in the smallest number of moves. (from The Inquisitive Problem Solver by P. Vaderlind, R. Guy and L. Larson, MAA, 2002. P34. Page 7.)
1.
Discussion
of approaches; Different representations, different ways of emptying jars
2.
Problem
solving strategy: try a simpler problem with smaller numbers (manipulate actual
jars with tokens)
3.
Recognize
a pattern, formulate strategies of emptying jars (e.g., ‘take the most
cookies’, empty the most jars’, ‘binary algorithm’)
4.
Formulate
conjecture, and prove. Generalization for n jars with 1,2,3,…,n
cookies.
5.
New
questions:
(a)
What if the jars contain cookies: a, a+1,a+2 ? Two or three steps?
(b) What if we consider a, a+d,
a+2d, …, a+(n1)d ? (n jars,
number of cookies forming an arithmetic sequence – which strategy gives optimal
results?)
(c) How to fill three jars so that 1,2
or 3 steps will be needed to empty them? What about four jars? Can n jars be
filled in a way that n steps are needed to empty them? (Interesting fact: Jars
with {1 2, 4, 8, 16} does not require 5 steps if
negative steps (i.e., adding cookies) are also allowed: steps 5, 1, 7 and 9
would empty the jars, but here the order of steps would matter, while it did
not matter in the original problem.) The discussion can be steered in different
directions based on responses and ideas from the audience and can fill a whole
hour or even more.
6. The original problem is
interesting, because it is an intriguing ‘roots to research’ problem. The idea
of finding an optimal subset representation for an arbitrary set of positive
integers has attracted some attention in recent years. The abstract problem has
consequences for finding approximation algorithms for minimizing segments in
intensity modulated radiation therapy. In fact, a simple demonstration could be
devised to illustrate the practical problem, and show its connection to the
‘cookie jar’.
Table 7: Presentation Times: 1:30
3:30
Organization:
Fairfield County Math Teachers’
Circle http://www.sacredheart.edu/academics/collegeofartssciences/academicdepartments/mathematics/fairfieldcountymathteacherscircle/
Middle School Teachers’ Circle
Activity: Pool Table Geometry
Presenters:
Hema Gopalakrishnan
GopalakrishnanH@sacredheart.edu
Sacred Heart University
Stephanie Furman sfurman@darienps.org
Darien Public School, Darien CT
Organization
Description: The Fairfield County
Math Teachers’ Circle is a newly formed teachers’ circle that held its first
summer immersion workshop in July 2012. Seventeen middle school math teachers
enthusiastically participated in problem solving during the workshop. They were
very grateful for the opportunity and expressed that the workshop did not
compare to any class that they have taken. The pool table activity is one of
the many successful activities at the summer workshop. Participants of the
summer workshop are eager to return to Sacred Heart University for the six
academic year meetings during the 2012 – 2013 school year.
Activity
Description: This is a fun activity
that examines the path of a ball on a pool table with pockets only at the four
corners of the table. The ball starts at the bottom left corner at a 45 degree
angle. Students can consider pool tables of different dimensions, draw
pictures, gather data and find patterns. They can explain their observations
and answer several questions using concepts from number theory and geometry
learned in elementary and middle school.
Table 8: Presentation Times: 2:00 3:00 Organization:
Richmond Math Salon http://mathmamawrites.blogspot.com
– Students, Teachers, Parents
Activity: What's Up With Spot It?
Presenter: Sue VanHattum mathanthologyeditor@gmail.com
Contra Costa College
Organization Description:
The informal math
party held at my home can be seen here:
http://mathmamawrites.blogspot.com/2010/08/richmondmathsalonsweetsampling_08.html
We used to meet monthly; now we meet once in the fall and once in the
spring. It's a whole family event. The parents want to provide math enrichment
for their kids, and I want to get the parents pulled in too.
Activity Description:
The game of
Spot It has 55 cards with 8 pictures on each card. The object of the game is to
find a match between your card and the center card before your opponents do.
It's a fun game to play in a group of adults and kids sometimes the youngest
ones win. There's no math in the playing of this game, but you might have some
math questions after you play it. We'll play a few rounds, talk about the
questions participants have, and then think about those questions together.
Table 9: Presentation Times: 1:00 2:30
Organizations: Math Teachers’ Circle of Austin https://sites.google.com/site/mtcaustin/
Middle School Teachers’ Circle
Activity: Folding Polygons
Presenters: Altha
B. Rodin rodin@math.utexas.edu
University of Texas at 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 been joined by two new members of the
mathematics department, Zachary Miner and Cristina Caputo. We are fortunate to
have a vibrant group of middle school math teachers in the Austin area who
regularly attend our problem solving sessions. For more information, please
visit our web site: http://sites.google.com/site/mtcaustin/
Activity Description: One may take a long, thin strip of paper, fold it up
then unfold it to see the angle formed by the crease line and the bottom edge
of the paper. The paper can then be folded down so that the top edge of the
paper falls along the first crease line. If one continues folding in this way,
alternating folding up and down along the crease lines, the angles formed by
the crease lines and the edge of the paper stabilize and the triangles that
appear seem to be equilateral. If the first few triangles are cut off and
thrown away, the resulting strip of paper can be folded to form a hexagon. We
will see why the angles stabilize and will investigate other folding sequences
to determine what angles they produce and which polygons can be folded from the
resulting strip of paper.
Table 10: Presentation Times: 1:30 2:00 Organization:
Texas A&M Math Circle http://mathcircle.tamu.edu
Middle School Student Circle
Activity: Hyperbolic Soccer Ball
Presenter: Frank Sottile sottile@math.tamu.edu
Texas A&M University
Organization
Description: The TAMU Math Circle
meets weekly at Texas A&M University each Saturday for students in grades
58. It is organized by Sottile and Phil Yasskin of the Mathematics Department and Alex Sprintson of the Electrical and Computer Engineering
Department at Texas A&M, and supported by parent
volunteers, graduate students, and postdocs. Each
meeting begins with a half hour of unstructured mathematical activity (games,
puzzles, or mathematical toys) after which the students split into two groups
for a 90 minute structured activity (including a snack break). For more, see its
web page: http://mathcircle.tamu.edu
Activity Description: I will present the activity "Hyperbolic Soccer
Ball". This is suitable for all ages, having been tested on middle school
students, on undergraduates, and on college teachers in Nigeria. It illustrates
key geometric features of the hyperbolic plane, and the participants create a
beautiful and thoughtprovoking mathematical model.
Table 11: Presentation Times: 1:30
3:00 Organization: SIGMAAMCST http://sigmaa.maa.org/mcst/ Help for
Student and Teacher
Poster: Math Circles and the Common Core State
Standards
Presenters:
Amanda Serenevy viajera6@gmail.com
Riverbend Community Math Center
James Tanton jamestanton@stmarksschool.org
St Mark's School
Poster Description: The Common Core State Standards are a set of math content and practice
guidelines for K12 math education in most states. States are ramping up
towards implementation now, with full transition to the standards at every
grade level slated for 2014. The Common Core State Standards present an
opportunity and a challenge. These standards oblige all teachers to implement
mathematics curricula grounded in conceptual understanding, higher level
critical thinking, and mathematical modeling. While previous state standards
were written with the intention that good teachers would incorporate these
aspects of instruction, the Common Core State Standards make these requirements
more explicit. Effective implementation of the Common Core State Standards
would radically improve math instruction in the United States. However, the
change from past modes of instruction is significant, and teachers will need
support to make the transition from the instructional methods they have always
known. The depth of content knowledge required is also much greater, especially
for 3rd through 8th grade teachers, and teachers are under a great deal of
pressure to learn the content they need to know and to find curricula they can
use. Mathematicians can help by assisting local teachers with additional
training in content knowledge, by carefully reevaluating the training of
future teachers conducted under the auspices of the math department or in
collaboration with schools of education, and by helping to identify high
quality topics/activities/curricula which teachers could use in their
classrooms. At this poster, we invite participants to look at the principal
content topics in the 6th and 7th grade standards to brainstorm ideas for great
related Math Circle topics. Please stop by to add your ideas to the list!
