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  Distinguished University Professor
'Making believe in math' topic of lecture

How does one come to believe a claim is true? Each field — law, history, medicine, physics — has its own methods for producing conviction. Mathematics has a unique answer to this question: deductive proof.
(Photo by Mike Gould)

Most people never encounter proofs until high school geometry, and Hyman Bass believes that's too late. He will discuss these concepts in an upcoming Distinguished University Professor lecture.

Bass is the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education, the Roger C. Lyndon Collegiate Professor of Mathematics, and a professor in the Department of Education.

His March 25 lecture is titled "How Do You Know that You Know? Making Believe in Mathematics." It takes place at 4 p.m. in the Rackham Amphitheatre. A reception will follow.

In the lecture, Bass will talk about the concept of proof, and about how it relates to the practices of proving in which mathematicians engage. He will further argue that, as a primary source of mathematical knowledge, proof should be part of the learning of all students.

"The practice of proving in mathematics is so fundamental that its learning has to be developed over time. It's like learning a language," Bass says. Students should begin acquiring the language and tools necessary to perform proofs as early as elementary school.

He proposes an approach similar to the teaching of literature.

"When you teach literature you want kids to learn more than word recognition," Bass says. "You want sense-making. You want to convey the idea that the literature is significant and means something in their life, and that has to happen developmentally. It's similar in math, and that's why the teaching of proofs should begin quite early."

Bass will show a video of third-grade students proving claims about even and odd numbers. The students also evaluate each other's claims, another important part of the learning process. He says proofs can be taught with almost any mathematical activity.

"The important thing is not just the answer," Bass says, "but the disposition to ask the questions and the resources to validate them and critically evaluate the answers of others."

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