News

Old texts inspire new thinking about math teaching

By Katherine Long, The Seattle Times
August 24th, 2015

University professor is turning to early math scholars in research focused on using primary math sources.

math-teachingCentral Washington University math professor Dominic Klyve is pioneering a novel new way to teach math — by relying on some of the oldest mathematical texts ever written.

Klyve has been awarded a $1.5 million National Science Foundation grant, which will be shared among six other universities and will be used to test whether teaching math using primary sources will make it easier for college students to grasp math concepts.

Klyve believes that studying the struggles of early math scholars, like Euclid and Archimedes, can help give college students insights that are missing in most college textbooks.

“Over generations, as the original author’s ideas are copied and recopied, transcribed and interpreted, we end up with a modern textbook that is stripped away of all context,” he said.

Modern textbooks are filled with the equations used to solve math problems, but rarely do they explain how and why the equations were developed, Klyve said.

As an example, Klyve says that an influential Swiss mathematician, Leonhard Euler, wrote a paper on prime numbers and factoring that is easy for even a first-year math student to understand, yet clearly shows Euler’s struggle to come up with a theory to explain the concepts he was exploring. “There are some things he writes that make little sense, there are some things that are brilliant,” Klyve said. “By the time you finish reading it, you understand the basic concepts. But you can also get a sense of what it is to do mathematical discovery.”

Klyve is a strong believer in using many different ways to understand a mathematical concept. “Being able to think about anything in more than one way is really helpful,” he said. “We usually don’t do that well in math.” He joked that he tells his students that if they ever say there is just one way to solve a math problem, “I will hunt them down and fail them retroactively.”

Klyve and other math professors participating in the grant will write lessons that can be downloaded and distributed to a class, and will be available for college instructors and high school teachers alike to use. He and his fellow instructors will also travel to regional and national conferences to share the work, and they have already received commitments from instructors at 40 universities across the country who say they will write materials or use them in class.

The idea of using historical sources to teach modern math was first developed by David Pengelley, a professor at New Mexico State University, Klyve said.

As part of the grant, a Florida State University assessment expert has been tapped to design tests that measure whether this type of instruction makes a difference in students’ understanding, and if it changes their attitudes about math. The project will take about five years.

CWU will receive about $400,000 of the $1.5 million grant. The other six universities involved are: New Mexico State University, Colorado State University-Pueblo, Colorado University at Denver, Ursinus College in Pennsylvania, Xavier University in Ohio and Florida State University.

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