My Understanding of Mathematics
Mathematics is a very fraught subject for many, many people, as you have just said, Nicole. And, it is embattled for good reason. However, to make an important point, as you have so well also said, it is an extremely important subject. To mathematicians, it is beautiful. But, I have never found it to be so. As children, too many of us have and have had no understanding of the mathematical minefield some of us will and have encountered in our mathematical educations. We need to be shown what mathematicians understand in order for mathematics to be beautiful for all of us. And, we all currently seem not to understand why this is so.
My husband is a mathematician/computer scientist. He remembers his calculus (a type of mathematics which is based upon algebra) really, really well. Obviously, he is one of the golden “chosen” for whom mathematics is inherently understandable and beautiful. Because of me, as an instructor, he has learned to teach all mathematical sequences in a down-to-earth, more understandable, more natural way. Nevertheless, I probably am his one teaching failure.
The point I am trying to make here is that some people are gifted in mathematical understanding while others are not. And, this mathematical ability has nothing to do with gender, as so many errant, sexist people have believed. I have known a good number of men and women who excel in mathematics, naturally. Yet, everyone desperately needs mathematical understanding in order to have better (in many ways) lives. Since science rests on the bedrock of mathematics, everyone who is interested in science needs to be able to understand and work with mathematics to a degree. But again, the more mathematical understanding one can attain, the better foundation one’s scientific endeavors rest upon.
Despite my general mathematical inability, I am a “soft scientist.” I have fought and struggled through numerous mathematics courses, and I have done well in a few of them. These are the courses that “seem” more logical to me…courses such as: trigonometry and statistics. I am strong in logic that uses words. Meanwhile, I’ve been blessed to have the most wonderful, gifted mathematics tutor possible…my husband. Through no fault of his however, I’ve never found through traditional teaching methods the cognitive connection to be able to understand and work advanced mathematical problems, such as calculus. I LOVE calculus, but it hates me. My ultimate downfall in calculus is algebra…that old bugaboo of way too many people. My husband says it’s because I never was taught algebra correctly. And, I’m guessing that means “algebra correctly for me.” A lot of people learn algebra well with traditional teaching methods. But, many of us apparently need a different approach.
Since mathematics is so important in the education of everyone, my husband and I have felt for a very long time that the teaching of mathematics teachers is crucial to the ablility of all people to learn the subject matter. Too many mathematics teachers have no idea that the teaching of their subject matter could be done in a variety of ways, and with a variety of approaches; thus, making it more understandable for everyone. And this is where I hold a lot of hope for children who are home schooled. They are taught many concepts through nature and a natural approach. In such a way, they get a feel for what it is that they are learning. And, it just might be the best way to teach mathematics, especially algebra…at least to some children.
(The old process that a number of college mathematics professors have employed, which is to use calculus to weed out those seeking to learn higher mathematics, is deplorable to me. It is subject matter for a different message.)
I am gifted with words; symbols carry no meaning for me. Therefore, I have approached trying to understand calculus through words. And, I now do understand what calculus is all about through the gifted teaching in Dr. Starbird’s Change and Motion: Calculus Made Clear, 2nd Edition course in The Great Courses. Meanwhile, this does not, at least yet, mean that I am able to work any of the calculus problems presented at the end of the course. I still am working on this. I simply have to struggle to inform my higher mathematical education in a way that speaks to me. And, so far, this method works. We need to find ways of teaching mathematics that work for everyone. If that means creating and using a variety of different teaching methods, especially for algebra, so be it.