Walter Whitely's article "Why You Should Learn Geometry" was a response to an LA Times article titled "Why You Should Learn Algebra" which brings forth the value of mathematics as a classical training of them mind. When I saw the title "Why You Should Learn Algebra," I was brought to remember a NY Times article that was essentially titled "Why You Should NOT Learn Algebra." I'll try to find a link to it and post it here.
Whitely elaborates on the unnecessary equivalence between that is often associated between algebra and mathematics. That is, if you excel at mathematical thinking, you excel at algebraic thinking. He brings forward the case of Michael Faraday, who was dyslexic. Although Faraday did not do his work algebraically, he was very geometrically and visually inclined. I have always considered myself to be a visual learner of sorts, but I have always had a great deal of respect for those who can "see" the answer; an ability I do not have. But, as Whitely notes, many students with a strong geometric intuition are often pushed aside for those who are algebraically competent. He argues that geometry and algebra both play significant roles in developing mathematical reasoning and warns that we should not narrow the mathematical landscape.
When I first started dating my boyfriend, one of the first things we talked about was our experience in school. Although I wasn't involved in the education field yet, I was particularly intrigued by the way mathematics was taught in British Columbia. In the United States, students typically study "algebra" in grade 8, "geometry" in grade 9, "algebra II" in grade 10, and the mathematics course of their choice in grade 11 and 12. During high school, I was under the impression that I was "better" at algebra than I was at geometry. Somehow, they seemed like separate quantities to me. My boyfriend, on the other hand, just saw the material as "math." He told me that he never thought "I'm better at geometry than algebra" perhaps because the material was not presented to him as such. It was just math class; all the topics were intertwined and played important roles in the development of his mathematical knowledge. So, I've since wondered if the majority of students who go through such a system feel this way.
As a side note, I was a little bit bothered during Whitely's mention of Faraday, when he stated that "he did not reason with formulae (algebra)." The term "algebra" as a mathematical field is not about formulae. I honestly do not understand why the term algebra was coined for purely arithmetic manipulations. Really, this "kind" of "algebra" is just advanced arithmetic. In fact, it's quite surprising how many students do not see this connection.
I found your response very enlightening. . .not that it isn't always enlightening ;) I had no idea that mathematics was taught so differently in the United States than it is here. In one respect I can appreciate focusing on one aspect of mathematics at a time, but on the other hand I also see the importance of creating intracurricular connections. I know of many people, including my brother, who in general did not experience much success in math, with the exception of geometry. He seemed to scrape each year, with the help of a tutor, but whenever the "geometry unit" surfaced he gained heaps of motivation, interest, and in turn, success. If only someone was able to take this motivation and connect it to other topics by bringing out the geometry in all other applicable math areas, perhaps he would have had a much more enjoyable mathematics experience in school.
ReplyDeleteI've often wondered what would happen if the courses were renumbered from "math 8" or "calculus 12", if the courses were just listed as "algebra I, algebra II, geometry I, geometry II", etc. Was there any value judgment associated with any level of math people were taking? Did people at a higher grade level have the option of taking a geometry I course if they had only focused on algebra?
ReplyDeleteAlso, I'd like to echo that algebra is not actually based on formula. Not the formal stuff, anyway. I was surprised at how few calculations I really did at higher levels - if any, they were very simple.