In an effort to make teachers, and in turn their students, more enthusiastic about math, college mathematicians organized three nights of non-traditional “math circles” in Española this month.
A group of about 50 math teachers in the Española School District took part in the third and final math circle, June 21, at Anthony’s at the Delta, which is co-owned by Nancy Suazo, a math teacher at Española Valley High School.
James Taylor, director of the Math Circles Collaborative of New Mexico, asked them to place the cards “in order.” He did not say what kind of order.
Teachers spent about 30 minutes trying to figure out what to do with the cards. Each card had six numbers. Each number was two digits. Some numbers were colored red and others were black.
Teaching methods like this create a non-threatening, playful environment that allows people to talk about math and to think more like mathematicians instead of “algorithm-performing machines,” Taylor said.
Taylor then asked the teachers to make observations about the numbers, no matter how obvious.
After some discussion, Taylor asked teachers to take turns telling him the colors of the numbers on a card and to lie about one of the colors. He said he could use “psychic powers” to guess the number.
In reality, Taylor had memorized the pattern of the colors on the cards and their place values to determine the number.
Over the course of the remaining hour, the teachers investigated the relationship between the patterns of numbers to figure out how Taylor could so easily guess the numbers.
At one point Monica Sanchez-Lopez, a second-grade teacher at Española Elementary, walked up to the whiteboard and explained how she understood the place values of the numbers.
Sanchez-Lopez, who has spent her entire teaching career at Española Elementary, said she wants to use the exercise to teach her own students near the end of the school year.
She said the math circle was more complicated compared to other teacher training she has done.
“I could see, I’m always looking at upper-grade things, things that are more complicated, and trying to think how I can scale it down to kids at my level,” she said.
The teachers were frustrated but eventually enlightened on how to teach binary through the exercise.
As the session concluded, one teacher asked how they could have possibly followed Taylor’s original instructions to “put the cards in order.”
“The idea is that I give you the very vague instructions because what I want you to do is immerse yourself in the world of the cards, and get some sort of intuition, a feeling for what’s going on,” Taylor said. “You noticed all kinds of really useful information about the digits. But if you hadn’t had that, and I had just done the magic trick, it would have been kind of neat, but the cards wouldn’t have been part of your consciousness.”
Teachers received a $100 for every day they participated in the math circles, funded by the Los Alamos National Laboratories Foundation and the Española Tech Hub.
Teacher circles are about taking apart and investigating a problem seems mysterious but is solvable, Taylor said.
“The stuff that we do is accessible to wide range of grade levels, and different people will get different amounts out of it,” he said. “It’s not like a traditional curriculum where you expect everyone to master the same algorithm, and do a bunch of exercises to get that mastery. This is more, sometimes, open-ended problems.”
Math circles originated in the last century, in the former Soviet Union, he said.
Math circles were run by graduate students or university faculty who felt a responsibility to show younger students the joy of mathematics, according to “Mathematical Circles (Russian Experience)” by Dmitri Fomin, Sergey Genkin and Ilia Itenberg.
“It’s too alien,” Taylor said. “It’s a very different approach. ... The idea was that college-level mathematicians would bring their deep and rich knowledge to pre-college education.”
Taylor said the teacher training in Española School District and other districts would not be doing something like a math circle.
It is also a relatively new concept in United States education practice, where it did not take hold until 2006 in California, 15 years after the dissolution of the Soviet Union.
“Math is not a straitjacket of exercises in a textbook,” Taylor told the teachers. “This is stuff that can make kids think, ‘Huh, maybe there is something cool about this.’”
He offered to model the exercise in the teachers’ classrooms in the future.
“I want this to spread throughout Northern New Mexico, to get teachers and students to think like mathematicians,” Taylor said.
Taylor said he wants to continue the math circles in Española at the beginning of the school year in August and then every month from then on.