This post is inspired by a Science Friday interview I heard recently with Edward Frenkel. The gist of his argument (which is around 15 minutes and can be heard here) is that a lack of willingness to engage with mathematical concepts can set people up to be manipulated by others who do understand. Furthermore, by not trying understanding math, people are missing out on a particular beauty, every bit as spectacular as the masterworks of art and music.
I would argue that math is one of the last frontiers of cocktail party conversation. Bringing up mathematics can be an immediate conversation killer, but it doesn’t have to be! There are concepts and ways of thinking that are completely accessible to the curious mind. Most of what I’ve written here is most relevant to adults or college students. These tips probably won’t help a high schooler improve her SAT scores, but they might help that student cultivate a real appreciation for math that just isn’t present in most high school curriculums.
Sidenote: Frenkel has written a book that came out in 2013 called Love and Math: The Heart of the Hidden Reality. I haven’t read it yet, but if I get my hands on a copy of it soon, I’ll do a proper review.
1.) Realize that no one is born understanding math
I can’t imagine that an infant Tim Howard sat in his crib smacking away juice bottles and plush soccer balls with the same focus that he brought to the pitch during the 2014 World Cup, but a lack of innate ability for math is commonly cited as a reason that people don’t even try to study it. They may say “I just don’t ‘get’ it” or “Oh, I’m not really a math person.” The only problem? It is not true that great mathematicians are born with great mathematics ability. Like musicians and artists, they achieve understanding and comfort with the subject through practice.
It’s pretty easy to stop saying “I’m not a math person” (and you should!), but it can be more difficult to stop believing it. Great athletes have mental tricks like positive visualization and setting attainable goals that help them be great. These are the same kind of techniques that can work for you if you want to start to banish fear or discomfort with math. Examples of concrete goals might be:
- I will read a popular mathematics book this month.
- I will research a mathematical concept that interests me (What exactly is a fractal? How is e a number?) .
- I will do a little calculus (maybe find out what a Riemann Sum is).
When you’re crafting these goals, it’s absolutely critical that you take into account step number two…
2.) Learn it on your own terms
You’re out of school now (or if you’re in school, this kind of math improvement is an extra curricular activity), so don’t worry about trying to learn math the way your teachers taught it. When I was in college, I was enrolled in Calculus 2. The class was horrible. I felt like I understood the concepts, but when it came time to take the exams, I couldn’t remember all the tricks to calculate endless integrals by hand fast enough. Stressed and embarrassed, I decided to drop the class.
When I went into my advisor’s office to tell him, I was almost in tears. I felt like I’d failed him and myself, like there was no way I could ever be a “math person,” or, by extension, a good scientist. When I told him why I was dropping the class, he actually smiled.
“Greta,” he told me, “Have I ever told you that when I was in college I failed Calculus?” I was shocked. This professor is a scientist, perhaps the smartest person I have ever met in real life. He even had a reputation for having one of the most quantitative approaches in the department. And here he was admitting that there was a time when he struggled with math. “I didn’t have the sense to drop it like you are,” he continued, “but that summer I got out my Calculus book and started reading. I found some other sources too. It took a lot longer to get through each section than it did when I was in a class, but when I finally retook the class, I did well in it. From then on, I realized the importance of setting aside quiet time with myself to puzzle through exactly how an equation is operating.”
He went on to tell me that he wanted me to take his transport course the following semester. Calculus 2 was supposed to be a prerequisite for that class, but he was prepared to overlook the deficiency if I promised him that I would “take ownership” of the material and work hard in the class. The math in the transport class included not only Calculus 2, but also some multivariable work. It was the most complicated math I’d seen, but I thrived in that class. If you’re struggling with thinking about math, the only difference between me and you is that I had someone who believed in me and who took the time to help me figure out how to understand.
3.) Ground math in physical reality
Frenkel mentions in his interview that he really fell in love with math when he realized that it is the basis for physics. My story is similar. What really made the different in that transport class was that everything we learned was grounded in real life. Asking “wait what does ‘h’ mean?” was a totally viable question that could be answered with a sketch. (“h” was usually a height, perhaps the hight of a column of sand. And if “dh/dt” — the change in the hight with time — was positive, that meant that more sand was being added to the column than was being taken away during the time period. This simple little relationship ended up being the mathematical basis for my undergraduate research.)
There are fun (really!!) websites in subjects like fluid dynamics and statistics that can help provide you with something that you might like to see explained mathematically. If you find yourself reading a scientific paper, and the author has included an equation, don’t let your eyes slide over that without thinking about it. Take the extra time to figure out how each part of the equation is functioning. This might involve pencil and paper. Or even asking for help.
Bottom line: If you want to improve your mathematical literacy, you need to take ownership of the material. Read about math (popular articles — Frenkel has written some — and books will help you get a little more comfortable talking about and understanding it.) Finding illustrations of concepts is a great aid to understanding.
As always, if you have other ideas, leave them in the comments.