Math Teachers' Circle
Last Monday morning I was on a SuperShuttle from SFO to the Creekside Inn. But I was running a little late, so the driver took me straight to the American Institute of Mathematics (AIM). I was expecting a tall building with lots of glass windows — instead the driver stopped here.
I asked Erin, my next-door math colleague, to join me. She and I fulfilled the requirement for "two middle school math teachers" — we just needed to find "two mathematicians and one administrator or organizer" to make a team of five.
I contacted Brianna Donaldson, AIM's Director of Special Projects, to help us round out the team. Within the week, she hooked us up with Nate and Hala, both are math professors at Cal Lutheran. We still needed a fifth member, so I asked Melissa, another math colleague (there are only 3 of us at our junior high) — she graciously got on board.
Needless to say I was thrilled to hear that our team was chosen among many (like hundreds of thousands of teams) to receive full funding to participate in this workshop.
Below is a summary of my week in beautiful Palo Alto, California. (For some reason it's easier for me to write in present tense when I recount a story — maybe it's an ELD or ESL thing.)
Josh Zucker appears first on the agenda, "Introduction to Problem Solving." I've always wanted to meet Josh — his name appears on most of the cool math problems that I first encountered at the Julia Robinson Mathematics Festival in Los Angeles. Turns out he's the director.
He facilitates this classic problem:
I just want to post the problems here without further discussions on them so that you — the thinker, the mathematician, the teacher, the student, the problem solver — get to struggle with the problem and construct meaning for yourself.
I will say that this problem makes me crazy happy because I will try to see rectangles in almost every math problem, and although I am stuck with my rectangle drawn, Erin sees something from it and brings the problem home, and Nate concurs with her answer.
***
There are three things that happen consistently each day, so I'll just mention them once here:
Tatiana Shubin is a math professor at San Jose State University; she presents "Grid Power." I've always required my students to use quadrille-ruled composition notebooks to take notes and such, but after hearing Tatiana speak, I want my kiddos to do ALL their math work on grid paper!
Tatiana gives us this delightful problem:
Tom Davis is a retired math professor; he walks us through "Conway's Rational Tangles." I don't even know how to begin to explain and illustrate this problem. It requires four students and two long ropes — each student holding one end of a rope. The task is to do two (and only two) commands of "twist" and "rotate" to tangle up the ropes — the challenge then is to untangle the ropes in a systematic way that involves arithmetic with positive and negative fractions. Okay, my explanation is as clear as mud.
The point is it is a wonderful activity that kids and teachers will absolutely love to get their hands on, literally.
The other point is I'm better than you because I have the two ropes. See?
Here is our awesome team.
I asked Erin, my next-door math colleague, to join me. She and I fulfilled the requirement for "two middle school math teachers" — we just needed to find "two mathematicians and one administrator or organizer" to make a team of five.
I contacted Brianna Donaldson, AIM's Director of Special Projects, to help us round out the team. Within the week, she hooked us up with Nate and Hala, both are math professors at Cal Lutheran. We still needed a fifth member, so I asked Melissa, another math colleague (there are only 3 of us at our junior high) — she graciously got on board.
Needless to say I was thrilled to hear that our team was chosen among many (like hundreds of thousands of teams) to receive full funding to participate in this workshop.
Below is a summary of my week in beautiful Palo Alto, California. (For some reason it's easier for me to write in present tense when I recount a story — maybe it's an ELD or ESL thing.)
Monday
I meet the other two members of our team for the first time, Nate and Hala. I've seen their pictures online, and they look the same — thank God!
There are six teams: 2 from Texas, 1 Kansas, 1 New York (Rochester), and 2 California.
There are six teams: 2 from Texas, 1 Kansas, 1 New York (Rochester), and 2 California.
Josh Zucker appears first on the agenda, "Introduction to Problem Solving." I've always wanted to meet Josh — his name appears on most of the cool math problems that I first encountered at the Julia Robinson Mathematics Festival in Los Angeles. Turns out he's the director.
He facilitates this classic problem:
The numbers 1 through 100 are written on the board. You choose any two numbers x and y and erase them, writing xy + x + y in their place. You continue to do this until one number remains. What are the possible values for that remaining number?
I just want to post the problems here without further discussions on them so that you — the thinker, the mathematician, the teacher, the student, the problem solver — get to struggle with the problem and construct meaning for yourself.
I will say that this problem makes me crazy happy because I will try to see rectangles in almost every math problem, and although I am stuck with my rectangle drawn, Erin sees something from it and brings the problem home, and Nate concurs with her answer.
***
There are three things that happen consistently each day, so I'll just mention them once here:
- We get two hours (TWO HOURS!!) for lunch as the nearby restaurants are about a 15-minute walk away.
- After lunch, we work within our group on logistics and fundraising to run our own math circle.
- "Happy Hour" greets us at the end of each session, if we wish to stay.
Tuesday
Tatiana Shubin is a math professor at San Jose State University; she presents "Grid Power." I've always required my students to use quadrille-ruled composition notebooks to take notes and such, but after hearing Tatiana speak, I want my kiddos to do ALL their math work on grid paper!
Tatiana gives us this delightful problem:
How many squares are there in a 7 x 7 square?
***
Paul Zeitz introduces us to "Mathematical Games." He's a math professor at the University of San Francisco and is taking a sabbatical this year. I've ALWAYS wanted to buy the book The Art and Craft of Problem Solving — lo and behold, Paul is the author! But Paul doesn't once mention his book (I made the connection after the workshop was over), instead he recommends James Tanton's Solve This. I need these books.
Two of the games we work on:
Takeaway. A set of 16 pennies is placed on the table. Two players take turns removing pennies. At each turn, a player must remove between 1 and 4 pennies (inclusive). The winner is the last player to make a legal move.
Puppies and Kittens, aka Wythoff's Nim. We start with a pile of kittens and puppies. Two players take turns; a legal move is removing any number of puppies or any number of kittens or an equal number of both puppies and kittens. The winner is the last player to make a legal move.
I really like how Paul keeps track of winning/losing moves as oasis/desert points on a horizontal line. So with the two variables like in Puppies and Kittens, we use a coordinate plane instead to record.
Wednesday
Diana White is a math professor at the University of Colorado Denver. Diana facilitates us through the "Exploding Dots" problem. (James Tanton owns the dots.)
Diana White is a math professor at the University of Colorado Denver. Diana facilitates us through the "Exploding Dots" problem. (James Tanton owns the dots.)
***Say you have a machine that holds ping pong balls. If you put three balls in the far right slot, they'll explode and two balls will move one space left into the next slot. Like this:
This happens with any set of three balls in one slot, therefore the explosion continues until there are fewer than three balls per slot. Thus, starting with 9 ping pong balls, the result looks like this:
Tom Davis is a retired math professor; he walks us through "Conway's Rational Tangles." I don't even know how to begin to explain and illustrate this problem. It requires four students and two long ropes — each student holding one end of a rope. The task is to do two (and only two) commands of "twist" and "rotate" to tangle up the ropes — the challenge then is to untangle the ropes in a systematic way that involves arithmetic with positive and negative fractions. Okay, my explanation is as clear as mud.
The point is it is a wonderful activity that kids and teachers will absolutely love to get their hands on, literally.
The other point is I'm better than you because I have the two ropes. See?
Thursday
Paul Zeitz is back this morning with "How to Gamble If You Must." We play a few dice games, then we work on Two Lottery Tickets:
It costs a consumer $1 to buy a Klopstockia lottery ticket. The buyer then scratches the ticket to see the prize. Compute, to the nearest penny, the expected profit that the state of Klopstockia makes per ticket sold, given the following scenarios for prizes awarded. (The state will make a profit if the expected value to the lottery ticket is less than $1.)
Friday
There is no math activity on our last day. Each team has 10 minutes to present the how/what/where/when of their own future Math Teachers' Circle. We each get a T-shirt and our team pictures taken. We bid farewell at noon.
**********
I'm grateful to everyone who made this workshop possible. And I love my team!! So I lied about us being chosen among hundreds of thousands.
I had never drank so much wine in one week. I took two wine corks home to practice a trick Josh had taught us —
Please consider joining a Math Teachers' Circle in your area. Our team leads the Thousand Oaks MTC and would love to have you. (I'm working on our website.) We owe it to our students to make math engaging and accessible.
Added 07/03/2012:**********
I'm grateful to everyone who made this workshop possible. And I love my team!! So I lied about us being chosen among hundreds of thousands.
I had never drank so much wine in one week. I took two wine corks home to practice a trick Josh had taught us —
Please consider joining a Math Teachers' Circle in your area. Our team leads the Thousand Oaks MTC and would love to have you. (I'm working on our website.) We owe it to our students to make math engaging and accessible.
Here is our awesome team.
Nate, Fawn, Melissa, Erin, Hala
June 29, 2012 at AIM, Palo Alto
Posted by fawnnguyen at July 2, 2012 2:31 PM 
Categories: Teaching, Problem Solving, General Math
Tags: math teachers' circle AIM Joshua Zucker Creekside Inn Julia Robinson Mathematics Festival James Tanton Solve This Paul Zeitz The Art and Craft of Problem Solving Takeaway Puppies and Kittens games Diana White Tom Davis Conway's Rational Tangles Brianna Donaldson Tatiana Shubin grid power exploding dots ropes Palo Alto American Institute of Mathematics
Categories: Teaching, Problem Solving, General Math
Tags: math teachers' circle AIM Joshua Zucker Creekside Inn Julia Robinson Mathematics Festival James Tanton Solve This Paul Zeitz The Art and Craft of Problem Solving Takeaway Puppies and Kittens games Diana White Tom Davis Conway's Rational Tangles Brianna Donaldson Tatiana Shubin grid power exploding dots ropes Palo Alto American Institute of Mathematics
Wish I could have joined you there! My math circle fun starts on Sunday. I love that rational tangles game. (The first time I saw it, Kate Nowak figured it out while I was still totally bewildered.)
Reply to this
One of the first questions I asked Joshua was if he knew you. He said, "Of course." It was as silly as asking him if a circle was round.
Reply to this
The Math Circle Teacher Training Institute is at Notre Dame, in Indiana, so I traveled farther than Kate did.
I think the hardcore part is how much math we did in the evenings. :^)
Reply to this
I forgot that MTC takes their show on the road too because they'll be in DC this summer for another training. I had every intention to do math in the evenings, but the chatting and wine glasses got in the way. I forgot to mention the Tuesday whole-group dinner. So much fun. The math jokes --
Reply to this
Lots of great stuff here I will need to check out in a few days. It sounds like a fantastic experience and maybe one day I will partake. Question: what have you found useful about using composition notebooks with your students? What's not useful and why the change to grid?
Reply to this
You would love it, Andrew. I'm also thinking about forming a Math Circle (no 'Teachers' in the name) in the future -- there isn't one near me at all; so this one would be for kids to participate in.
Composition book because it's bound; kids aren't tempted to tear pages out of it. I've always required the ones with grids, so it's not a change. I'm constantly telling kids in class: make a table, draw a picture, line things up, graph and see, etc. -- so grids are crucial.
But from now on, I want all math work outside of their journal/composition work to also be on grid paper. Graph paper is more expensive, so I'll definitely spend my room fund to get a large supply for kids who aren't able to get their own. Actually about a third of the kids already use grid papers regularly for math. There are certain lessons, of course, that I do not want the kids to rely on grids due to whatever concept I want them to explore.
Thanks for dropping in, Andrew! (Giving you a high five on my tippy toes.)
Reply to this