Paul Sally vs. Tiger Woods
My friend and U of C classmate pointed out to me an interview in a recent issue of the Chicago Maroon with Paul Sally, Professor of Mathematics and mentor to generations of mathematicians and mathematics educators. He has a few good words about the practice.
In response to the question of why people boast about poor math skills (whereas they would not boast about poor reading skills), Sally says:
[T]o actually be good at math you have to practice, you have to take it seriously, and you have to be willing to spend time working at it. And all of these are very difficult for students and for humans in general. And they don’t understand that you should never confuse activity with achievement. Many people spend a lot of time early in their math careers, early in their math days, in the classroom, working at it extensively, saying, “I worked three hours on math last night.” Well, if they didn’t achieve anything, that’s activity, that’s not achievement.... And if you don’t get it right, you have failed.
...If you’re working on a certain project in a lab, and you set up the protocol correctly, then whatever the results, you can publish them. “I did this in the lab, and this is what happened.” But see, in mathematics you can’t do that. You have to set out to solve a problem or prove a theorem, and by the time you get through, if you don’t have a proof, you cannot actually publish your results, making apologies for your inability to prove the theorem. You simply have to confess that you couldn’t do it.... [emphasis added]
That probably sounds scary, coming from a guy who looks like that. If I could dare to soften that a bit, I would say that some people are scared of math because they're afraid to be wrong. As a student of another colleague said, "You can look at my work, tell me I am wrong, and be right about that."
True, but why is that a bad thing? Although Sally is correct in asserting that which is not right must be wrong, not all that is wrong is worthless. At the last Legacy of R.L. Moore conference, educators nationwide explained how disproving conjectures is a form of progress. I'm sure Sally, an attendant at that conference and a a proponent of Moore's method along with other Inquiry-Based Learning methods, would agree with that.
Sally has said on other occasions that, in essence, hard work in mathematics does pay off...eventually. When I was an uppity senior in his graduate analysis class, he told us of his postdoctorate days when he struggled with getting results. "It's like I gotta work my a** off to get anything done!" he complained to his advisor. "Yes, hard work is necessary in mathematics," the advisor said, "soon you will find it to be sufficient."
I've often mused about attitudes towards sports and how different they seem to be from those towards academics in general, and math in particular. This ad is saying pretty much the same thing about a different subject:
Compare the headline from from the ad with the part of Sally's quote I emphasized. As an educator, I aim not to make mathematics easy, but to present it as a challenge worth undertaking, and to give my student the tools to undertake it.