Roger Howe, a professor of mathematics at Yale University, gave two talks on April 19 in Snygg Hall, room 127.
The talks were a complement of the professor’s arrival set up by the math department and mathematics professor Victor Protsak.
“Howe was my doctoral advisor at Yale back in 2000,” Protsak said. “He is an internationally renowned mathematician and an authority on K-12 education. I’ve been so excited that he responded to my invitation to come (to Oswego) to talk about symmetry to our students and to present his thoughts on the ongoing reform of the K-12 curriculum.”
Howe received his Ph.D. from UC Berkeley in 1969. His research topics include representation theory, harmonic analysis, automorphic forms and invariant theory. Howe received the American Mathematical Society Award for Distinguished Public Service in 2006. In addition, Howe is currently a member of the National Academy of Sciences and the American Academy of Arts and Sciences.
His first talk delved into the topic of mathematical symmetry. To better illustrate symmetry, Howe projected multiple images of abstract paintings that displayed properties of balanced distribution amongst an axis. Along with these examples, he presented seashell models to illustrate his points.
The main point of symmetry in mathematics is to show a property that proves that something does not change under a set of transformations. Examples that could be found outside of art include the Leaning Tower of Pisa and the Taj Mahal.
Howe’s second talk dealt with how the topic of functions are taught in the primary and secondary education levels.
In the second presentation, Howe explains that functions are integrated in a great portion of our daily lives and play a big role in understanding the overall field of mathematics. He mentioned that functions cover a lot of mathematical subjects, from geometry and measurement to basic mathematical operations such as addition and subtraction.
With regards to improving on how to teach functions in a primary and secondary classroom setting, Howe recommended omitting certain techniques. He recommended moving away from general talks about functions outside their specific contexts. He also recommended avoiding references to mathematical variables and putting more emphasis on numerical values early on.
Howe said teachers should follow a principle of example sufficiency: when introducing a concept, use examples of such applications to get a concept’s point across more clearly. He recommended the solving of a few problems that are relative to the topic in order to better illustrate the significance of a taught concept.
Professor Howe said that he hopes the teaching of functions in elementary and secondary education becomes more consistent with a proper mathematics curriculum.