Making math fun: Students discover the subject’s playful side

  • From left, Christine von Renesse, her 8-year-old daughter, Alena von Renesse-Marti and Daniel Schultheis assemble a spherical puzzle (shown below) at Saturday’s Mad Math event on the Smith College campus. Staff Photo/Andy Castillo

  • Jim Henle stands in front of his model Klein bottle. When it comes to teaching math, part of his philosophy is getting away from the idea that there are right and wrong answers. Staff Photo/Andy Castillo

  • The completed geometrical puzzle, on loan from the National Museum of Mathematics, was one of the elements Henle planned in order to turn the campus “into a magical fairyland of mathematical events and amusements,” he said. STAFF PHOTO/KEVIN GUTTING

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    take part in "Math Madness" organized by Smith College professors at locations around the campus on Saturday, Oct. 20, 2018. —STAFF PHOTO/KEVIN GUTTING

  • Smith College students Natalie Mosher, Halley Haruta, and Quincy Webb put together a giant puzzle made from cardboard boxes at Smith College's Mad Math day on Saturday, Oct. 20, 2018. Staff Photo/Andy Castillo—

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    take part in "Math Madness" organized by Smith College professors at locations around the campus on Saturday, Oct. 20, 2018. —STAFF PHOTO/KEVIN GUTTING

  • Jim Henle stands in front of his model Klein bottle. Staff Photo/Andy Castillo—

  • Jim Henle sits in a classroom in Burton Hall at Smith College. Staff Photo/Andy Castillo—

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    take part in "Math Madness" organized by Smith College professors at locations around the campus on Saturday, Oct. 20, 2018. —STAFF PHOTO/KEVIN GUTTING

  • The completed sculpture outside Jim Henle's office at Smith College. Staff Photo/Andy Castillo—

  • ">

    take part in "Math Madness" organized by Smith College professors at locations around the campus on Saturday, Oct. 20, 2018. —STAFF PHOTO/KEVIN GUTTING

  • “If kids have fun, they’ll do more math, and if they do more math, they’ll get really smart. And if they get really smart, they’ll take over the world,” said Henle of his 3-D model Klein bottle. STAFF PHOTO/KEVIN GUTTING

  • ">

    take part in "Math Madness" organized by Smith College professors at locations around the campus on Saturday, Oct. 20, 2018. —STAFF PHOTO/KEVIN GUTTING

Staff Writer
Published: 10/23/2018 4:51:01 PM

At Jackson Street Elementary School in Northampton, 50 of the school’s 350 students come in an hour early every Tuesday to learn about math. By choice. 

“The only rule is that you have to want to be there,” said math teacher Mary Cowhey, who helps organize the club. “No one can make them come.”

She helped start the club in 2010 because she wanted to make math fun: engineering projects, coding, coins, bingo, checkers. 

“As kids are coming into the first grade, they need a good foundation in being able to count forward and backward and read and write numerals,” she said. Getting there isn’t necessarily easy. “It’s actually a complicated set of skills as children learn the sequence of counting forward and backward.”

If a child has big gaps in those areas, they might have trouble moving on to addition and subtraction, she says. With little kids, Cowhey says that using words like more, less, before or after — and asking at bedtime, “What do we do right before we brush our teeth? Or right after we shut off the lights?” — actually strengthens a student’s mathematical vocabulary.

And this lays the ground work for more complicated concepts. 

“I wanted math to feel cool for everybody,” she said.

At the other end of the educational spectrum, Smith College math professor Jim Henle shares the exact same goal.

His sole mission on Saturday was to “turn the Smith College campus into a magical fairyland of mathematical events and amusements.”

There were 7-foot-tall puzzles, 50-foot long balloons twisted into tetrahedrons and octahedrons, a mathematical magician performing tricks, mathematical origami, and a (theoretical) four-dimensional structure made of plastic sheeting that was large enough to climb into.

The idea behind the public event, which he dubbed Mad Math, was to “create an environment of wonder and play, to see mathematics as a source of fun, of imagination of joy,” he said.

At one station, featuring a metal geometrical puzzle on loan from the National Museum of Mathematics in New York City, Westfield State University math professor Christine von Renesse screwed together a few pieces with her 8-year-old daughter Alena von Renesse-Marti.

“It’s built out of pentagons and triangles. They’re all similar pieces, but rotated and shifted around,” said Daniel Schulteis, who teaches math at Smith College and volunteered to help participants put the sphere-shaped puzzle together. “Over the course of the day, people will stop by and build one (section), and then move on. In a few hours we’ll have this together.”

Nearby, Henle, wearing a hat made from balloons, flagged down walkers and passed out fliers about a model geometrical object called a Klein bottle that he made from large sheets of plastic. A true Klein bottle can only exist in 4-dimensions, Henle says. The 3-dimensional model that he made was intended to get people interested in mathematical possibilities.

“We didn’t actually go into the fourth dimension. No one has actually done that and come back,” Henle said.

Mad about math

For the last 40-plus years, Henle, 72, a recently retired mathematics professor at Smith College and author of several books on math, has employed a fun-loving, philosophical approach to teaching the subject in order to help students learn to think through problems.

“If you’re exercising your logical mind that way, you’re getting smarter — and that’s what people need today. If they’re smart, they can pick up the knowledge and they (will) know what to do with it,” Henle said.

He describes his Logic 100 course, which he taught for years, as a sort of “back door” into mathematical problem-solving for students who might not otherwise think of themselves as left-brained or numerically-inclined.

“I had one student who came here hating math, and she was never going to take another math class,” Henle recalled. “But she took logic and did very well. I worked with her, and she’s now a math professor.”

Henle recalls another one of his students “who had trouble with some mathematical problem in kindergarten or first grade, and the teacher kept her in from recess. She still remembers the angle the light made coming in the window on that day,” Henle said.

Part of his philosophy is getting away from the idea that there are right and wrong answers.

Many students who don’t initially understand math are told “’ok, you got that problem wrong, maybe you’re not smart enough. Maybe you just can’t do it.’ It’s like being told at a very young age ‘I’m sorry, you’re never going to grow more than 3 feet tall.’”

The key to overcoming this challenge requires a perspective shift, he says. Instead of thinking about math as a series of equations or written problems on a piece of paper, Henle describes math as an art form that fosters a mental framework centered on logic.

“If it is an art, then you can make choices, just the way you decide that you like impressionist to post-modern art, or rock to baroque,” Henle said.

Changing the way his students think about math, and making problem solving fun and engaging, is something that Henle takes seriously.

“My idea of mathematics is very broad. It includes games and puzzles, fun stuff — rubik’s cubes, Sudoku — there are lots of things that are mind-bending and dependent on logic. That is mathematics,” he said.

It’s a sentiment echoed by Cowhey.

“When parents think of their own childhood, they think of worksheets,” she said. “They don’t understand how their children are learning now.”

That's where coin counting, bingo and puzzles come in. And even games like hopscotch. Cowhey has students call out the numbers as they land on each square, all the way up to 12.

Learning logic

Over his four decades of teaching, Henle estimated he’s taught about 9,000 students.

During graduate school at the Massachusetts Institute of Technology, where he earned his doctorate degree in mathematics, Henle taught middle school. As a way to spark an interest in his students, he invented a fictional number system to challenge any preexisting associations that students had with numbers.

And in his logic classes at Smith, he encouraged his students to write arguments for and against an imaginary campus controversy on a public sidewalk in chalk. One year, the chalk-arguments — about making all the dining halls exclusively vegan — caused such a stir around campus that the Boston Globe picked up the story (the reporters were in on it, too).

“It was a way for them to get around the baggage of mathematics, the whole idea that ‘you’re not smart enough,’ and ‘you did lousy in this course,’ and ‘you needed this course to understand that one, and that one to understand this one,’” Henle said.

 

Growing up, Henle says he was first introduced to math by reading science and mathematics writer Martin Gardner’s column in the Scientific American.

“He made everything so attractive, and furthermore, he would always end his column with some puzzles or problems that other mathematicians perhaps hadn’t solved,” Henle said. “You felt like you were a part of this great community of mathematicians, where people were talking together and sharing ideas.”

That experience influenced the atmosphere Henle tried to create in his own classrooms. In addition to teaching creative problem-solving, he also encouraged students to see that it’s OK to be wrong.

Ultimately, children who are considered to be mathematic prodigies probably grew up thinking a lot about math because they enjoyed it, he says.

“I think that’s true,” Henle said. “And if that’s so, if you think about it, what should be the goal of any math teacher? It shouldn’t be to teach them this, that, and the other thing. It should be to make them fall in love with mathematics. Because if they do, they’ll take more mathematics, and they’ll think about it more.”

These days, with everything at the click of a button, knowledge is cheap, Henle says. On the other hand, intelligence that comes from dealing with mathematics “in the broadest sense” is invaluable.

“If you think of mathematics as fun, and if you do it, you might learn stuff. But that’s not important, because if kids have fun, they’ll do more math, and if they do more math, they’ll get really smart. And if they get really smart, they’ll take over the world,” Henle said.

Andy Castillo can be reached at acastillo@gazettenet.com.


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