Colley says ‘math is an essential human activity’ — and also joyful

Interviewer note: Kara Shane [née Relyea] Colley is a native of Voorheesville. She was graduated from Clayton A. Bouton High School in 1994, Dartmouth College in 1998 as a physics major, and Columbia University Teachers College in 2004 with a master’s degree in math education. For years she taught math at the college level and remains devoted to making life easier for younger students to master the elements of mathematics.

The title of her forthcoming book is “ My Hundred Friends, ” published by Natural Math. It is illustrated by Coley Nielsen and advertised as designed for children ages 7 to 11 or for anyone learning about factors, multiples, and primes.

AE: Good morning, Kara, thank you for agreeing to be interviewed by The Enterprise, your hometown paper when you were growing up in Voorheesville. I had planned to start by speaking with you about your math book that comes out next month but, an event just occurred in the math world that I think requires immediate comment especially by you, a schooled teacher and writer of mathematics.

The problem, if you will, was reported on last month in an article by Kenneth Chang, science reporter for The New York Times — the Sept. 10 edition — titled. “An N.Y.U. Mathematician Clashed With OpenAI Over a $1 Million Proof.” The sub-head reads, “Tristan Buckmaster was on the path toward an important proof when one of the A.I. giants used its staggering resources to get there first.”

Buckmaster, a professor of Math at NYU, had been long-working on a long-standing puzzle in the math world — the Navier-Stokes equations, questions about how viscous fluids, including liquids like water and gases like air, move and change. Physics! The solutions are said to ease the workload of weather forecasters and aircraft designers among other professions.

You can see why (parenthetically) those who dedicate themselves to solving such problems, lead monastic lives.

The long and short of the matter is though: AI got involved in the solving-math-equations business. Chang says, “The list includes the Navier-Stokes puzzle, and in less than a week, OpenAI beat Dr. Buckmaster and all of the world’s other human mathematicians, announcing on Tuesday that it had found the answer.” A sub-sub head might read “Machine renders human mind obsolete.”

There’s all sorts of ethical and legal issues involved in what took place to win the race, but the point remains: AI can solve math problems faster — and more accurately — than humans. It means the death of math as we know it. In the Chang article it says Dr. Buckmaster and others called attention to the “human element” in solving math problems. But, if a problem is solved sooner than later, and all humankind benefits from knowing what it needs to know sooner, I say tomorrow’s headline will read: “Math is Dead!” With a sub-head: “All Math People (theoreticians especially) should start looking for other kinds of work.”

Sorry to take so long to introduce the issue but our readers will need some context for understanding. What does a young scholar, coming out with a new math book very soon, have to say about the matters laid out there?

KSC: It makes me sad and kind of angry. The AI models were trained on humanity’s output without the permission of humans. I, personally, view AI as theft. These tech companies scoured the internet for news articles, books, blogs, and hoovered it all up. Were the human creators asked permission? No. Were they compensated? In most cases, no.

The New York Times has sued OpenAI over copyright infringement. I am very interested to see the outcome of that case, but the wheels of justice move so slowly. I believe that the case was filed three years ago and they just started court filings a few weeks ago. Ugh.

But what does it mean for math? Look, I am not a research mathematician. Rather, I am a lifelong lover of math. I believe in math and its power for solving the world’s problems. We need math to build bridges and solar panels and we need math to make the correct dosages for medicines. We need well-trained engineers and nurses.

Math is an essential human activity. I think humans need to sit, think, and ponder. We need to measure, estimate, evaluate, calculate, conjecture, prove, disprove, draw diagrams, make models, and spot patterns.

But even more than that, like many other math teachers, I wish that I could help more people see math as joyful. Math is everywhere, in everything, and it’s a great travesty that so many people hate and fear math.

AE: You are talking to a man who got a minus 6 on the math section of the GRE [Graduate Record Examination]. I hated geometry in sophomore year of high school because the class forced the student to speak another language and I wanted to speak how I spoke, like poets do.

Nevertheless, I retain great respect for theoretical mathematicians and the work they do, especially physicists. They are, as you know, two of the four disciplines that make up what is known as STEM, technology and engineering being the other two.

I just found a statement on the www. that says, “These disciplines are often grouped together because they share a common emphasis on critical thinking, problem-solving, and analytical skills.” How, in your estimation, is that true? Do you have examples? Explain as well, if you would, what you just ended your remarks with “that so many people hate and fear math.”

KSC: One thing I noticed as a physics major in college was that there were times I spent hours working on problem sets and there were still problems that I couldn’t ever figure out. Whereas if I spent hours working on a history paper, I would reach the end of my paper. There was never a moment where I couldn’t “figure out” the paper. I wouldn’t leave a section of the paper blank. I would work through it and write something down. But sometimes on physics problem sets or math homeworks, I left whole questions blank.

Some math educators make a distinction between an “exercise” and a “problem.” An exercise is a math question that the student knows how to solve and they are practicing the skill. For example, let’s say that the teacher has shown the class how to add two fractions, like 1/6+1/12. After the teacher’s lesson on adding fractions, an exercise would be to add 1/5+1/15.

On the other hand, a problem is a math question that the student doesn’t know how to solve. They have to use critical thinking to figure out how to solve it. After the teacher’s lesson on adding fractions, a problem would be “Find two fractions whose sum is 1/20.”

Many students hate and fear math because, at some point in the math journey, they stopped understanding the logic behind what was going on and they had to just memorize or accept what their teacher told them.

Often, this happens when students reach fractions or when they reach algebra. Math students shouldn’t be forced to accept someone else’s reasoning. They should be given time to play around with math and develop their own reasoning.

First off, math students need time. And second, they need an opportunity to play. (And to be clear, I believe that math teachers should also lecture. But what’s often missing from math classrooms is time for playing.)

AE: Which brings us to your friends, your hundred friends, the title of your book “My Hundred Friends,” which is so beautifully illustrated. I am sure you have considered how your friends might become the friends of all young people taking math across the country, say, in grades 1 through 5. That is, not just helping students deal with “math anxiety” but showing them a way to love math by, as you say, “understanding the logic behind what [is] going on.”

Publishers always want prospective authors in their book proposals to say how their work differs from what else is out there. Might you say a few words on how your approach, your friends, will make things better for young people by encouraging them to play in the “fields of math” with joy?

KSC: As part of the editing process, my publisher asked me to take my manuscript and read it with children. I took my story — at that point, a 100-page artist’s sketchbook with my illustrations — to a Montessori classroom of 4th-, 5th-, and 6th-graders in Portland, Oregon. The teacher gave me a corner of the room and set me up with pairs of students.

The kids took the sketchbook into their laps, while I sat nearby and listened as they read it out loud to each other. In “My Hundred Friends,” each number from 1 to 100 has its own page, and on that page, readers meet jellybean-shaped number-characters who romp around and play.

The kids interacted with the drawings in ways that I didn’t expect. They reached out to trace the path of a jumping number-character. They giggled when a number-character exclaimed, “It’s me!” when it saw its own number on a page.

The children touched the pages, brushing their hands over the number-characters, almost like they were petting them. This early feedback made me realize that I was on the right path with my story and my jellybean-shaped number-characters. The kids were connecting with the book, connecting with numbers!

Many of the pairs just read the book straight through, starting at page 1 and going forward. One pair of children, Theo and Pascale, reached page 24 and noticed that the number-character Twenty-Four had one strip of brown at the bottom. Pascale, a 4th-grade reader, asked, “What’s brown?” She paused and then wondered, “Is it 12?” as they flipped back to page 12. Pascale guessed, “6?” as they flipped back to page 6. “No, it’s 3!” she exclaimed as they landed on page 3.

They were on to something. They had picked up some sort of pattern with the colors. From that point forward, Theo and Pascale started reading with an eye towards what was going on with the colors. I didn’t explain the role of colors in the book; they were having fun trying to figure it out.

This was such an exciting and proud moment for me. I had created a world where kids were exploring and asking themselves math questions. They were playing with the number-characters, playing with math.

AE: Wow. Thank you, Kara, for taking the time to speak to The Enterprise about the state of math in the world these days and how your new book, “My Hundred Friends,” will improve the lives of young people. Thank you, thank you.

I might add editorially that I have studied the lives of people in the town of New Scotland and the village of Voorheesville for 40 years, including the goings-on at your alma mater, Clayton A. Bouton High School in Voorheesville. I can think of no other instance where a student — even a teacher — in the district’s school system — going all the way back to the 19th Century when Voorheesville was New Scotland School #10 — has written a book dealing with an academic subject they took while growing up. Congratulations are due you indeed.

Colley says ‘math is an essential human activity’ — and also joyful

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