Strogatz ’80, Dehaene discuss learning, math in evening lecture

Neuroscientist Stanislas Dehaene, author of the book “The Number Sense,” and Steven Strogatz ’80, author and mathematician, discussed the relationship between mathematics and the human mind in front of a nearly full audience in McCosh 10 on Wednesday evening. Dehaene and Strogatz’s wide-ranging discussion touched on intuition, education and the nature of mathematical concepts.

Dehaene, who studies mathematical intuitions and “brain structures that allow us to learn mathematics,” such as the numerical sense that underlies the ability to compare numbers and identify parallel lines, described the findings of his research as well as the role of intuition in understanding mathematics.

Humans appear to be born with an innate ability for mathematics independent of culture or education, Dehaene said, noting that “babies behave in a manner that is consistent with a sense of number.” Dehaene further described the work of collaborators who showed that members of remote Amazonian tribes whose languages lacked precise terms for mathematics could nonetheless solve simple problems in Euclidean geometry. These results show that “not all of mathematics depends on education,” Dehaene said.

However, Dehaene explained, humans must learn the ability to connect symbols to numbers and relate numbers to space. He discussed a group of Amazonian tribe members who, he said, can only find approximate answers to simply computations, adding, “The sense of exact number seems to be missing in this people.”

After Dehaene’s remarks, Strogatz discussed his personal history of learning math, focusing on two particular experiences.

Strogatz said he was originally drawn to mathematics in high school, when a teacher mentioned a geometry problem he had been unable to solve. “I had never heard a teacher say that he didn’t know how to solve a problem before,” Strogatz said. “It was unthinkable.”

For six months, Strogatz said, he was immersed in the problem. “Someone would pass me the ball and it’d bounce off my knee because I was in bisector-world,” he said. In the end, he said, “it was very, very thrilling to have worked on this problem and solved it.”

Strogatz then described a contrasting experience, which came in a linear algebra course at the University designed to separate “the people who were good at math in high school from people who have the potential to be mathematicians,” he said.

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In the deeply abstract course, Strogatz struggled. “I started to understand, for the first time in my life, why people hated math,” he said. When, in another class, the instructor solved a difficult problem using a visual method, “I erupted into applause. I was the only student clapping,” Strogatz said.

Strogatz and Dehaene then discussed each other’s remarks and responded to questions from the audience. Much of their discussion focused on improving mathematical education.

Dehane said he thought teachers needed to appeal to students through puzzle-like challenges.

“What can be done to change the nature of mathematics education is to introduce loveable problems,” he said.

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“There’s a lot of different buttons that can be pressed,” Strogatz said, adding that teachers should follow “a very ecumenical approach” in order to “activate different types of people.”

Dehaene and Strogatz also discussed the perennial question of whether mathematical concepts have an existence independent of the human mind.

“I think we have largely revised the idea that mathematics is just a construction,” Dehaene said, adding however that such historical examples as the introduction of irrational and imaginary numbers to overcome conceptual hurdles show that mathematics “still could be a creation of the brain.”

Strogatz suggested a compromise. “The concepts may be invented, but the results aren’t,” he said.

Audience members had a mixed reaction to the event.

Michael Cedrone, a high school mathematics teacher who attended the talk, said he was interested by “the concept of intuition being an important part of math education,” noting that teaching intuitively may be part of successful math education in other countries. But, he said, he had hoped for “a little more interactivity” from the presentation.

“It was an interesting meeting of minds,” Stephanie Chan GS said, although she said she was skeptical that Dehaene’s study of basic computation could be brought directly to bear on more abstract concepts.

“I think that ... the type of math that Dehaene studies is very different from the type of math that mathematicians like Strogatz study,” she said.

The event was part of the Louis Clark Vanuxem lecture series.