Talking Stick Learning Center

“There is a unicorn dying at the end of a bridge.  He has 17 minutes left to live, unless 4 people can join hands around him and recite a magical spell.  There are 4 people on the other side of the bridge, but it is very dark, they have one flashlight, and the bridge can only hold 2 people at a time.  Ginny can cross in 1 minute, Ron in 2, Fred in 5, and Percy in 10.  Can they save the unicorn?” 

So began our younger Math Circle today (after playing Function Machines for a few minutes to make sure everyone was comfortable adding numbers).  Immediately the participants began doing what mathematicians do:  clarifying the question.  (Can they throw the flashlight?  Can they carry each other? How much does the unicorn weigh? Can they get across without the flashlight?  Can one person go at a time?  Did they bring any tools?  Can the unicorn use magic?  And so on.)  They asked many questions beginning with those 2 magic words that spark mathematical discovery, “what if….?”  (What if Ginny made return trips with the flashlight?  What if Fred and Percy travelled together?)  Some were looking forloopholes in the rules (a skill that will come in handy for proofs) while others were adding up the numbersto see what is possible.  While stymied with every attempt, enthusiasm grew. 

  We struggled with the idea of combined rates (how long would it take Ginny and Ron to cross together?), so we shifted to a historical anecdote about the mathematician Gauss and some of his early childhood math-related experiences.  I was ready to return to Function Machines to work on the rate issue, but the ideas, excitement, and questions about the problem just kept coming.  With one minute remaining, 1 young mathematician jumped out of her seat and came up to the board to illustrate her solution idea.  We left the question open to play with more at home, with the instruction to email me with questions and ideas.  A hint to the parents in the room:  question your assumptions.

I asked the older group, “Can you predict the number of pieces you get when you connect the dots on the edge of a circle?”  I drew a circle with one dot on the edge and asked, “How many pieces?”  We added a few more dots and connecting lines to realize that the question needed clarifying to specify the maximum number of pieces and what our explicit goal was.  (In a Math Circle, initial questions are intentionally vague to foster skillful question-asking.)  One person soon noticed that the number of pieces was always even.  We added a fifth dot and line and another member of our group piped in the idea that “they are doubling.”  I asked what is doubling to elicit accuracy of description, and the pattern was named:  “The number of pieces doubles each time you add a dot.”   I asked for a prediction for 6 dots, and they all agreed that there would be 32 pieces.  I asked how we can be sure, and they said to draw and count.  So we did.  We counted 31 pieces.  The group decided to redraw and recount several times, with the process becoming more systematic each time.  Their claim of “the drawing is wrong” became “the rule is wrong.”

At this point I asked how many examples we need to prove a rule (“a lot!”).  I mentioned empiricism(conclusions that arise initially from observation, as espoused by Aristotle) versus rationalism (theory first, then experiment, as espoused by Desartes).  We discussed which they thought was better, and how both can be used in real life.  We then talked about the Ptolemaic astronomers who struggled with making predictions based upon their observations and in light of more and more evidence of a sun-centered universe.  We took a quick detour into the question of whether the astronomer Ptolemy might have been related to Cleopatra, then returned to our original question.

The group decided to count the pieces for 7 dots, and discussed which counting strategy is better: adding to the current diagram, or starting anew with each revision.  We counted 57 pieces from 7 dots. We stared.  We thought.  We presented and then rejected conjectures about patterns.  Frustration mounted.  (One goal of a Math Circle is to be able to tolerate higher and higher levels of mathematical frustration and hence greater future rewards of discovery.)   Time was almost up when one participant said, “Look!  3 dots, 3 lines, that’s times 1.  5 dots, 10 lines, that’s times 2.  7 dots, 21 lines, that’s times 3. Every other one is times another number!”  When asked what we could do with that idea, they all agreed that we should draw a circle with 9 dots and see if we got the predicted 36 lines.  Despite only having a few minutes left, the consensus was adamant that we start from scratch with our diagram to ensure accurate counting.  We applied our most systematic drawing and counting strategies and discovered that the prediction held:  36 lines!  Delight filled the room.

We ended with hope that with time and effort, we could probably test this pattern on larger numbers of dots, and also continue to look for a pattern in the number of pieces.  We talked about how mathematicians play with problems like this for years, and take breaks, and come back again.  I took a picture of the last diagram (attached), and look forward to hearing ideas from anyone who plays with this some more. 

Below are some references if you are curious about any of the topics we explored today:

·        List of notable astronomers with brief bios.  This list includes Ptolemy, and also 2 women of more recent times: http://www.starteachastronomy.com/astronomers.html

·        Geocentric view of the solar system:  http://en.wikipedia.org/wiki/Geocentric   

·        Ptolemy, including discussion of his ancestry: http://en.wikipedia.org/wiki/Ptolemy

·        Dark bridge problem:  http://www.coolmath4kids.com/math_puzzles/b2-darkbridge.html  (but please, play with this one first before looking here, and if parents can’t resist peeking at this, please give your kids the chance to work on this themselves over time!  Remember, our goal is for them to think like mathematicians, so revisiting this problem after the passage of time is valuable.  This link is reluctantly included for parents only.)

On Wednesday, September 21, our Math Circle leader will offer a free “try it” for those who might be interested in learning more about Math Circles. This will take place at our Whitemarsh location. At 3:30, Rodi will offer the “try it” for anyone 9 and under.  At 4:15, there will be a “try it” for anyone 10 and over.  Come check it out!  Please RSVP to this e-mail address so we know how many people to expect. 

Math Circles have existed for a long time in other parts of the world,especially Eastern Europe. Two Harvard professors — Robert and Ellen Kaplan — brought Math Circles to this country when they become very disappointed with math education. In a Math Circle, the facilitator poses a math related question to the group. For example, for younger kids, the facilitator might ask whether there are numbers between the whole numbers. The group would discuss the answer together, developing strategies for answering that might involve using manipulatives. A discussion of math history might evolve, as participants wondered how people long ago answered this question, and why it mattered then or today. If the group got excited about something that arises from this discussion, the facilitator would support them in taking the inquiry in another direction. A Math Circle is math as pure inquiry, joy, and play. Our facilitator spent a week this summer withe Robert and Ellen Kaplan, and is excited to be bringing the first Math Circle to the immediate Philadelphia area. You can read more about the Kaplans and Math Circles here:http://www.themathcircle.org/history.php 

Day Program     

for ages 4-13

9:00 to 3:00

Tuesday Session: September 13 - December 13 

Wednesday Session: September 7- December 7

Thursday Session: September 8 - December  8

Semester tuition is $602 ($532 siblings) for participants attending one day a week. 

Each session runs 14 weeks.

Participants enjoy activities including science experiments, art projects,

cooperative games, and imaginative interactions. We create obstacle courses and create crepe paper flowers, build forts out of natural materials, and explore math manipulates. We sew stuffed animals, explore meadows, do origami, practice yoga, sprout beans, and hold mayoral elections. 

Our rooms are abuzz with creative energy and collaborative spirit.

Adult facilitators provide resources, guidance, and ensure the physical and

emotional well-being of participants. Materials and educational supplies are

easily accessible, interactive, and open-ended. Events unfold organically

and opportunities to develop communication skills abound.

Self-Direction

Participants instigate activities which cover a wide range of interests. For exampling putting on a play may involve script writing, recruiting actors, set making, prop building, costume design, advertising, dancing, music, public speaking, and an immense sense of accomplishment and creative expression.

One individual might spend two hours weaving, one hour interviewing others

about their jobs, half an hour telling jokes, and hour and a half outside running, sketching pine cones, and having conversations with both youth and adults. Their afternoon could be spent reading to friends and taking a modern dance class taught by a peer.

Invention

One of our most used items is the “invention box”. We set out a container filled with odds and ends such as springs, film canisters, pieces of foam, string, feathers, and pipe cleaners. These items can be put together in endless combinations.

Reading

We read many books, either in small groups, one on one, or young people on their own. We bring books that have to do with changes in perspective, finding details in a larger picture (what’s different about these pictures, for example), and unexpected combinations of ideas.

Group Exploration

for ages 9-14

Wednesday Session: September 7- December 7

Thursday Session: September 8 - December  8

Tuition for one day a week is $602 and $532 for siblings, plus $20 materials fee.

Each session runs 14 weeks.

Group Explorations participants will begin the semester working together to pick an overarching topic that they would like to investigate further.  With the help of facilitators, participants will generate a list of possible topics, and work through a process to come to a consensus on one.  Although the topic could be anything that participants like, some examples may be the current economic crisis, the Tudor period of English History, sustainable agriculture, Norse Mythology, or oceanography.  Once a broad topic has been agreed upon, participants will work in small groups on sub-topics of particular interest.  

For example, some participants may want to research the cuisine of a historical era.  Others may want to experiment with hydroponics as a way to explore food cultivation or write their own fiction based on the topic.  Some participants may choose to interview homeowners affected by the mortgage crisis, or produce a short film on the topic. Others may want to produce artwork or theater pieces that relate to whatever subject has been chosen.  

Talking Stick facilitators will provide resources for research and supplies.  The semester will culminate in a presentation about our topic where we will share our projects with each other and with our families.  For example, if the agreed upon topic is the Renaissance, the presentation may include the performance of a madrigal, the reading of an original piece of historical fiction, a model of the Florentine Duomo, and a sampling of Renaissance pastry.

In addition to applying reading, writing, research, and math skills to the project, participants will also have the opportunity to learn negotiation, collaboration, and communication skills.  Group Explorations will be a self-governing group, working together to make decision on which area to study, and how to spend materials money.

Math Circle

Tuesday 3:30 to 4:25

Session 1 (for ages 7-8): September 27 - November 8.  

Session 2 (for ages 11-12): November 15 - December 20.

Tuition is $120 for a six week session. Sibling discounts are available.

There will be one week off during the first session. 

We plan to run more Math Circles for other age groups in the spring.

What is a Math Circle?:

Math Circles exists all over the country.  Talking Stick’s Math Circle is the first in the immediate Philadelphia area.  

A Math Circle is collaborative inquiry. These are some of its goals:

Confidence

Competence

Increased intuition

Love of the art and intellectual playfulness of math

Analytical thinking

Collaboration in the pursuit of revelations about structure

Comfort in contributing to class

Learning what questions to ask so that students can figure relationships and patterns out for

themselves

An understanding of the interaction between history and mathematics

Exposure to the etiquette of intellectual engagement, in which students learn to work in

community to explore interesting questions.

A Math Circle leader acts as a secretary, recording students’ conjectures and asking occasional clarifying questions. The Leader does not feed students facts and algorithms to be memorized, but instead facilities invention and discovery by presenting a question in which students find a need to look for structure and meaning themselves.

The Talking Stick Math Circle follows the model used in the Harvard-based program founded by Robertand Ellen Kaplan 18 years ago. 

Click on this link for a description of a Math Circle Session: http://www.themathcircle.org/kaplanamsarticle.php

For more information on research supporting the Math Circle pedagogy: http://www.scientificamerican.com/blog/post.cfm?id=the-educational-value-of-creative-d-2011-07-07

Math Circle Leader Rodi Steinig studied how to lead a Math Circle with the Kaplans. She has extensive coursework in undergraduate mathematics as well as a masters degree in education. She has been teaching math for The Princeton Review for the past 2 decades and homeschooling her children all their lives. Rodi has Pennsylvania State Certification to teach in Public Schools, but a Math Circle is nothing like you’ve ever seen in school.

Talking Stick Chess Club

Monday 12:30 to 1:30 

Session 1: September 12 - October 17

Session 2: October 24 - November 2.

Tuition is $60 for a six week session.  Sibling discounts are available.

This chess class is open to all levels.  If there is adequate demand, the class will have a beginner and advanced group.  

The chess club is led by Leteef Street.  Leteef has taught chess in over 10 schools in the Philadelphia area and is the coach of the local and state champions from the MasterMinds Chess Club.  Leteef has a master’s degree in education. If we have two groups, Leteef will be assisted by another coach.

Writing Workshop  

for ages 8 to 14          

Tuesday 9:00 to 12:00

September 13 - December 13

Tuition is $280 for a 14 week session. Sibling discounts are available. Tuition may be combined with the afternoon day program. 

The writing workshop is designed to help each writer develop his/her

own writing process.  Through language experiments, prompts, and short

exercises, we will explore poetry, descriptive and persuasive writing, and

short stories. Participants will draft several pieces and then choose one to

take through the steps of the writing process from revision to publication.

The final class will include a reading, and participants will create an

anthology of their work.

The workshop is led by Paige Menton.  Paige Menton received a BA in

comparative literature from Brown University.  She earned her Master’s in

Education from the University of Pennsylvania.  Before homeschooling, she

was an educational researcher and a third grade teacher.  Paige has been

homeschooling for the past six years and has taught several successful

writing workshops for Talking Stick.