Teachers' Math Circle Talk at Math Fest

Photo Credit: Rusty Rogers

I'm excited to announce that I'll present the demonstration Teachers' Math Circle Class at MathFest!

For those not in the know, MathFest is the biggest and best national summer math conference, organized by the Math Association of America (MAA). There will be many activities sponsored by the Special Interest Group on Math Circles for Students and Teachers (SIGMAA-MCST) including two contributed papers sessions, a math wrangle and demo classes for students and teachers.

My demonstration class will be my talk on Nim and Jim, which I blogged about here in April. Every time I presented this activity about impartial games it gets better and more interactive. So if you've seen it before, you'll have a lot of fun, but if you've never seen it, then you're guaranteed to have a great time!

MathFest this year is August 4-6 in Lexington, Kentucky.

Always be Prepared

Back in April, I wrote about Math Circles and Safety, and a large part was inspired by Brandy Wieger's presentation at the Math Circles on the Road 2011 conference in Houston. You can now watch her talk here:



This is one of the videos recently posted by The National Association of Math Circles. Check out their YouTube channel here: MathCircles.

Jim and Nim

I presented my talk "Jim and Nim" yesterday at the Bard Math Seminar, and managed to fill the house.


My introduction actually extended over two days, as I visited math and CS classes on Wednesday and Thursday and personally invited students to my talk. This was really fun, and I got to meet some of Bard's amazing undergraduates. I teased them with the Magic Birthday Trick:

Have you seen this?

1. Identify the boxes that contain the day of the month that you were born. (For example, I was born on the 18th, and the number 18 appears only in the two boxes on the right.)
2. Add up the numbers in the top left of each box that includes your birthdate. (For me, that's 2 + 16.)
3. The sum is mathemagically your birthdate.
4. Share in the amazement!

Here's a picture that I used to explain why this trick works. I'll leave it to you to puzzle it out!

Another teaser I shared is the game I call 21-Nim. Start with 21, and on your turn you subtract 1, 2 or 3. The first person to reach 0 is the winner.  (My MAT student Kristen used this at our Pi Day Celebration for the students at 345 Brook Avenue in the Bronx.) What's interesting here is the set of losing numbers, and I challenged the Bard students to find them. In a losing position, the next player will lose, if her opponent plays correctly. Can you find the losing positions?

We didn't play 21-Nim during my talk, but we did play the classic game of Nim, with Teddy Bears:

Here's a picture of me, getting ready to hand out the teddy bears.

(This amazing photo is by Rusty, who was visiting Bard with his son Kyle the day of my talk.)

The Game of Nim

This is the real game of Nim, whose winning strategy was first described and proved in a math research paper published in 1901. The game starts with several piles of counters. Players alternate moves: on your turn, select a pile and remove at least one counter from that pile. You win if you take the last counter from the last pile. That is, the last player with a legal move wins. If you know the set of losing positions, then you know the winning strategy! 

Strategy

I had the participants play a few games of Nim, just to get the feel of the game and to start identifying the losing and winning positions. The amazing thing about impartial combinatorial games is that in each game position (with a finiteness condition) there must either be a winning strategy for you, or your opponent has a winning strategy. I call these two possibilities Winning and Losing positions (the standard notation from Winning Ways is N and P positions), which brings up a natural opportunity to use quantifiers:

• If you are in a Losing position, then EVERY move you make leads to a Winning position for your opponent.
• If you are in a Winning position, then there EXISTS a move that leaves your opponent in a Losing position.

I represented this in the following diagram:

Jim

Did I mention that I invented a Nim-type game that I call "Japheth's Nim", or Jim for short? One day in February 2011, I was running around Prospect Park in Brooklyn and thinking about how to motivate the strategy for Nim. Halfway around the park, I realized that a visual representation of the binary number strategy could be described independently of its connection to binary numbers and exclusive OR. I used the rest of my run to figure out just how to describe a Nim move visually in binary, which resulted in the game of Jim.

A Jim game starts with  several rows of red and yellow tokens. Players alternate moves: select a row, and change one or more tokens (yellow to red or red to yellow). The first token to be changed (from the left) must be yellow (but does not need to be the leftmost yellow token). The last player with a legal move wins. Equivalently, if you only see red tokens, then you’ve just lost! 

Here's a 3-row Jim game:

Can you explain why this is a Losing position?
One of the most exciting parts of the talk was at the end, when I revealed the connection between Jim and Nim with this slide:

Well, you might have had to be at my talk for this to make sense. Please leave a comment below to describe how Nim and Jim are related!

Bard Math Circle in the News (bring your kids!)

Dear Friends,

The Bard Math Circle made the front page of today's Daily Freeman with a story about our math outreach activities at the Kingston Library. COUNTING ON FUN: Math Circle at Kingston Library takes middle school kids beyond boring basics (video) (Monday, January 17, 2011) http://dailyfreeman.com/articles/2011/01/17/news/doc4d33674c5f430298712442.txt 

The Bard Math Circle meets twice per month at the Kingston Library with a program of math and logic games, problem solving and hands-on math activities, designed for middle school math students. Everyone is welcome! The next meeting will be on Saturday, February 12, 1-3pm.

The Bard Math Circle was previously featured here:

Las Noticias: Por el amor a las matemáticas (Wednesday, October 06, 2010)

http://www.lasnoticiasny.com/articles/2010/10/06/comunidad/doc4cacee4f1d7bd487053172.txt

and in our La Voz: Círculo de matemáticas en Kingston (Agosto 2010)

http://lavoz.bard.edu/archivo/archivo.php?id=10568

What is the Bard Math Circle?

The Bard Math Circle, which targets middle school and elementary school students in the Mid-Hudson Valley, was formed in 2007 by Bard College Professors Lauren Rose and Japheth Wood. The Bard Math Circle is run jointly by students, under Bard's Trustee Leader Scholar Program (http://inside.bard.edu/tls/), and math faculty at Bard College. Student leaders have included Shelley Stahl, Ezra Winston, Elias Halloran and currently Jackie Stone. Outreach activities have focused on Kingston and Tivoli.

In the summer of 2010, Bard hosted the New York Math Circle's Summer Workshop 2010 for teachers (http://nymathcircle.org/2010workshop). I brought (primarily NYC) middle school math teachers to Bard for a week-long residential math immersion experience. The workshop sessions were led by Bard math professors, and instructors from the New York Math Circle and the Albany Area Math Circle. The 2011 workshop, which is scheduled for the week of July 25-29, will welcome both middle school and high school math teachers to Bard.

The New York Math Circle was featured recently in the news on NY1, "NYC's 24-hour Newschannel on the web":

Bonus Curriculum Is Greatest Common Factor For Local Math Masters (12/26/2010)

http://manhattan.ny1.com/content/top_stories/131224/bonus-curriculum-is-greatest-common-factor-for-local-math-masters?ap=1&MP4&r=4320001457

Please let me know if you would like to participate in any of these activities!

Thanks,

Japheth Wood, PhD

Mathematics Faculty

Bard MAT Program

--
"If you can't solve a problem, then there is an easier problem you can solve: find it."
-George Polya

NY1 News Article about the New York Math Circle

The New York Math Circle was recently featured on NY1 ("NYC's 24-hour newschannel on the web"). Check out the video here:

Bonus Curriculum Is Greatest Common Factor For Local Math Masters

Many thanks to TV reporter Shazia Khan for pursuing this topic! She got in touch with the New York Math Circle (NYMC) and I helped coordinate the filming. What came out in the video was filmed in late October, and shows an amalgam of the middle school and high school classes that day.
I learned a lot about how much effort the parents make to get their children to these high-quality math enrichment classes. Some devote their entire Saturdays to shuttling their children from activity to activity, and see it as an investment in the future.
There was one notable exception that truly impressed me - one of the middle school students takes the subway train all the way from the Bronx for class on his own. He was clearly having a great time at the class, and it completely shows in his interview. Can you spot him in the video?
The TV news reporter, Shazia, also had a lot of fun visiting the New York Math Circle, and is interested in covering further stories in STEM (Science, Technology, Engineering and Mathematics) Eduction. You can see more of her videos here: Shazia Khan news clips
If you know of a good story for Shazia, please leave a comment, and I'll make sure your idea gets passed on!

Canada/USA Mathcamp article

Here's a wonderful article I just read about (Canada/USA) Mathcamp:

Finding Nirvana in Numbers

https://simonsfoundation.org/mathematics-physical-sciences/news/-/asset_publisher/bo1E/content/finding-nirvana-in-numbers?redirect=/mathematics-physical-sciences/news

Mathcamp is a summer math enrichment program for high school students that boasts an incredible alumni base of mathematicians, whose instructors are also something of a dream team. They move campuses from summer to summer, and are able to roll out each summer's program flawlessly. The program seems to be so successful, that I suspect it is now run completely by alums.

One wonderful thing about how Mathcamp is organized, is that this flexibility makes it replicable to some extent. Take for example Mathpath, a similar program, but for middle school students. Also, the Summer Program in Mathematical Problem Solving (SPMPS) for underserved middle school students. In some sense, both these programs "spawned" off of Mathcamp.

In high school, I attended a similar program: The Hampshire College Summer Studies in Mathematics or HCSSiM. The Hampshire program, run by Hampshire College math professor David Kelly, has raised generations of mathematicians and also has an incredible group of alumni. Honestly, you can't swing a dead cat at a math conference without hitting a HCSSiM alum. (Please don't bring your dead cat to the next math conference. Bring a yellow pig.)

The HCSSiM program seems less replicable, but that hasn't stopped alums who are recently getting started in the growing Math Circle movement. Take, for example, the New York Math Circle (NYMC), which has programming for high school and middle school students (and also teachers; more information on that soon!) and in Chicago, the soon-to-arrive Payton Math Circle. Another fairly recent math enrichment program started by an HCSSiM alum is the Math Prize for Girls contest. The Math Prize for Girls is working hard to encourage girls to achieve at the highest levels by offering incredible cash prizes. Check out their new blog! These efforts all involve HCSSiM alumni.

Out of curiosity, if you know of other math enrichment groups run by HCSSiM alums, please leave me a comment.

All of these math enrichment opportunities are wonderful, but still out of reach for most students who show interest, motivation and potential in mathematics. The Math Prize for Girls is a step in the right direction, and an even more ambitious project is the Summer Program in Mathematical Problem Solving mentioned above.

How can the math community provide enrichment opportunities to underserved students who are just out of the loop? (Please leave me a comment if you have an idea). Is the notion of mathematical talent, so often mentioned, actually damaging, as my friend Ben Blum-Smith suggests in his blog? How could mathematical resources best be used to offer high quality math enrichment to interested students? What about students are apathetic or traumatized by math?

I plan to come back to these topics and more, so stay tuned!