08/06/2012 11:54 am ET Updated Dec 06, 2017

MathFest: Teach Meaning or Procedure in High School Mathematics?

Last weekend a near-record 1500 mathematicians gathered in Madison, Wisconsin, for the summer meeting (MathFest) of the Mathematical Association of America (MAA). That 1500 included over 200 undergraduates; the majority gave talks on their own research. My three students presented their new discoveries about tilings of the plane, tilings of space, and a calculus formula.

Karen King, Director of Research for the National Council of Teachers of Mathematics and MathFest's 17th Falconer Lecturer for the Association for Women in Mathematics, explained that high school teachers and students need to focus on meaning rather than just procedures. It's one thing to know you cannot divide by 0; it is more to know why. (The official reason is that x = 1/0 means that 0x = 1, which is impossible. The intuition is that 1/a, as a gets small, grows without limit. And what if a is negative? Actually mathematicians have a special number system in which infinity ∞ is a number, -∞ = ∞, and 1/0 = ∞.) King emphasized that searching for understanding is a good habit that has to be learned and relearned for real education. A high purpose of education is to develop such mental habits. We need to explain that to future teachers, students, parents, client disciplines, and government.

Karen King, Director of Research for the National Council of Teachers of Mathematics

My old friend Sylvia Bozeman of Spelman College and 14th Leitzel Lecturer spoke on the importance of mentoring, especially for minority women. One needs good mentors and a culture to support them. Historically black colleges, which provide such a culture, enroll just 10% of African-American students but award 30% of all African-American baccalaureate degrees in mathematics and statistics.

Sylvia Bozeman of Spelman College

John Ewing, President of Mathematics for America, told me of the importance of a community of excellent mathematics teachers in our high schools:

John Ewing, President of Mathematics for America

Mathematics itself is always growing. Robert Ghrist of the University of Pennsylvania, in his invited address, presented algebraic topology as the new mathematics which will revolutionize education and society. To a mathematician, all interconnections and relationships can be viewed geometrically and then understood algebraically.

Robert Ghrist of the University of Pennsylvania

Student talks are a highlight of mathematics meetings. A student team from the University of Colorado, Boulder -- Christopher Corey, Stephen Kissler, and Sean Wiese -- talked about their winning entry in the Mathematical Contest in Modeling. They designed a plan to get the maximum number of rafting trips through the Grand Canyon.

Stephen Kissler, Christopher Corey, and Sean Wiese

Another winning student team from Cornell, Dennis Chua and Alvin Adrian Wijaya, explained and predicted the shapes of trees and leaves.

Alvin Adrian Wijaya and Dennis Chua

Everyone deserves to feel the joy of discovering and understanding some new bit of mathematics.