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Mathematician James Arthur recognized by U.S. National Academy of Sciences

James Arthur. Photo by John Guatto.

James Arthur. Photo by John Guatto.

Ted Mossman Chair in Mathematics James Arthur, University Professor at the University of Toronto, has been elected into the U.S. National Academy of Sciences (NAS) as one of the newest 21 foreign associates out of 15 countries.

The NAS is a society of distinguished scientists, which was established by an Act of Congress and signed by President Abraham Lincoln in 1863. They provide independent and objective advice to the U.S. government on science- and technology-related matters.

“I am very honoured to have been elected, and to be able to represent U of T in this way,” says Arthur.

Arthur works in the area of mathematics called automorphic forms. This includes a series of fundamental conjectures proposed by Canadian mathematician Robert Langlands, which postulate deep and unexpected relationships among different streams of mathematics. He is working on the possible application of a powerful technique called the trace formula.

A&S News spoke with Arthur recently about why he has devoted his professional life to researching and teaching mathematics, and why effective teaching of math in elementary and high schools is so crucial. Below are some excerpts of the conversation.

What are the relative advantages and disadvantages of memorization vs. discovery math teaching techniques?

To me, discovery math as it is often practiced in Canadian schools seems to defy common sense. While it might appear reasonable to someone whose background is more in education theory than mathematics, I do not think that discovery math is something to fire the imagination of students. Both students and parents are often perplexed by it, and can be intimidated into thinking that it represents more than it actually is. In truth, discovery math often seems to lack real content.

According to the OECD, Canada’s 15-year-olds have dropped out of the top 10 and now place 13th out of 65 countries. Why do you think that is?

It is certainly a concern. The problems we are seeing in Canada appear to be widespread throughout the world. The only exceptions I see are in Asia, where students still learn math by working hard and perfecting their skills, and are consequently doing much better. There are many dedicated and talented teachers of mathematics in Canada. But I suspect they often feel constrained by illogical and rigid requirements from school boards and ministries of education.

The problem is magnified when, because of a shortage of strong math teachers, the job falls to someone who is not comfortable with the subject. It is then that the deficiencies of discovery math without any practice of skills really stand out.

Are teachers uncomfortable with mathematics because they don’t like it?

If teachers are not comfortable with math and do not really understand it, they are not going to like it. And if children don’t like it, they will certainly not want to think about it. Thinking about math is extremely important for students, not just in the half-hour or hour of a math class but at other times as well, just because it is interesting.

We need teachers who love math, and who are free to communicate it in their own way. In my opinion, this is by far the most important thing. Students love to be taught by someone with a passion for a subject. Mathematics can seem beautiful and mysterious and powerful to anyone, but especially to impressionable children. They might laugh at an eccentric teacher with a passion for something as arcane as mathematics, but that is part of the deal. Once students plug in, they will start thinking about math out of curiosity, and that is how they become strong.

Private tutoring services seem to be almost a regular “extra” for many elementary and high school students. Is this the case and if so, why is it happening?

If parents sense that their children are not learning the math they should in school, they will try to deal with the situation as best they can. Tutors are not substitutes for good teachers, but if they are the only way parents can have their children learn basic skills in mathematics, they are a pretty good investment. Parents understand that it is very important for children to grow up with quantitative skills and mathematical understanding if they are to do well in our increasingly tech-based economy, or even if they are to make informed choices as citizens, voters and consumers.