mathbabe

This is a guest post by Allison Pacelli, a Professor of Mathematics at Williams College. She got her Ph.D. in Algebraic Number Theory at Brown University in 2003, and has been at Williams ever since.  Allison is an award-winning teacher, and author of numerous research papers in mathematics as well as the book Mathematics and Politics: Strategy, Voting, Power, and Proof with Alan Taylor of Union College. Allison is the founder and director of Williams College Math Camp (WCMC), a camp aimed at mathematically talented high school students. She is also the co-founder and director of PZ Math, an organization aimed at promoting mathematical literacy. She also does work in K-12 Math Education, working with elementary and high school teachers.

I met Cathy at UC Berkeley in the summer of 1996. I had just finished my junior year of college, and I was accepted into this 6-week summer program for women in math. Cathy was the TA for my course in elliptic curves, a branch of number theory, which I absolutely loved. I’m now an algebraic number theorist at Williams College. One of the things I remember most about Cathy was how honest and open she was about math being hard, and how other grad students she knew at Harvard pretended they knew what was going on when, in fact, they did not.

Math is hard. Very hard! No matter how intelligent someone is or how amazing their past accomplishments, math eventually becomes difficult for anyone. This should not be a surprise, but it is to most people I know. It’s perfectly acceptable for someone in society to say, “oh I’m not a math person.” Personally, I think, that with the right teacher or materials, everyone can enjoy and be successful with math.

What I most love about math is how useful it is. Yes, of course math is useful in engineering, building, accounting, etc. but that’s not what I mean. Math makes you smarter. It makes you a better problem solver. It makes you better at persevering and trying new ideas until you find a solution. It even makes you a better writer in your English or political science courses. Learning how to approach mathematical problems improves your logical and reasoning abilities. When one method doesn’t work, you try another. You start to build up an arsenal of methods for approaching a difficult situation, in any field. Mathematical thinking also requires that we be very precise and clear. This precision and clarity translates into better arguments in any paper or debate.

So why doesn’t everyone love math? Unfortunately, far too often, math is taught in schools as a bunch of formulas to memorize and rules to use. When I first took Calculus in high school, I did very well and got a 5 on the AP exam. But I didn’t truly understand it. I was just good at knowing which rules to use when, and I was good at algebraic manipulations. When I teach Calculus now, either at Williams or the PZ Math Calculus Prep Camp that I run, I spend a lot of time helping my students actually understand calculus.

What is a derivative? What does it mean? How do you find it? What is it good for?

In a one week camp, we can’t teach our students all of calculus of course. But we do give them all the big ideas and an understanding of what the subject is about, including the Fundamental Theorem. We also delve into the details of the first third of the course material, as well as strengthen students’ algebra and trig skills that are so critical for calculus success. The result is that students know what to expect when they begin their Calculus courses in the fall. The pace of the course doesn’t feel so rushed. They understand the ideas, and they have time to hone their skills with the calculations that do come their way. Most importantly, students feel more confident in their problem solving abilities and are ready to take on challenges, not just in their calculus courses, but with any obstacles that confront them.