Maths Moment of the Day: A Hearty Defence of Algebra
An article, interesting at best, called "Is Algebra Necessary?", was recently featured on the opinion pages of the New York Times. I read it thoroughly twice - once to understand the content being presented, and the second to wonder at the impact of author Andrew Hacker’s words (and, most notably, opinions) being printed in an eminent and well-respected publication - a literary pinch, if you will.
As usual, I felt the need to respond; I think Blake Stacey said it best:
Although I would strongly encourage you to read the article, its basic premise is that mathematics above “simple arithmetic” - notably long division - is useless for the majority of students, and making it a requirement is to our detriment as we are “misdirecting precious resources.”
Bill Nye (The Science Guy!) was asked, on Reddit, what he would choose if he had to do a profession that did not involve science. His answer was: “You stumped me. What profession doesn’t involve science? Lumberjack? Plenty of science. Bus driving? Hope you have a sense of momentum, torque, traction, and the passage of time. For me, science rules.”
Mathematics gives science constraints. It distinguishes between the possible and the probable, the infinite and the finite. It’s the methodology we use to interpret science; if science rules, so does maths. The universe is their happy dominion. And if we ever hope to continue to increase our understanding of the universe (which, after all, is what science is all about) we should probably learn to speak it’s language. Yes, that’s right, I’m talking about maths - and not long division, either.
In fact, I would argue that knowing how to do long division out on paper (although it was the highlight of fourth grade) is less important then, say, understanding that pesky “Fermat’s dilemma.” (I’m going to assume you were going for ‘Last Theorem’, Mr. Hacker, although that’s giving you a pretty wide error margin).
My first problem with this article is that Mr. Hacker tells us algebra is wholly unnecessary, and then proceeds to give statistics (oh, the irony) about dropout rates and graduate employment before having the audacity to state, “What we need is not textbook formulas but a greater understanding of where various numbers come from, and what they actually convey.” An “understanding of where various numbers come from” is achieved through algebra - the study of the functions that generated those numbers, as well as those statistics he keeps using.
While I believe that Mr. Hacker is wrong to blame every statistic he quotes on algebra and calculus, my bigger problem with the article is his apparent lack of understanding of how fundamental mathematics is. While he does stress that thinking quantitatively is important (phew), he does not detail how, exactly, a groundwork for quantitative thinking can be established using only basic arithmetic. Even worse, he states: “Certification programs for veterinary technicians require algebra, although none of the graduates I’ve ever met have used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure into the clinical curriculum, let alone subsequent practice.”
Of course they require calculus! Mathematics is not about memorising formulas; it’s about learning to think and understand the world a certain way. When Harvard and Johns Hopkins M.D. graduates read clinical studies, they’ll be able to have a healthy skepticism about the statistics presented - because they can understand where they came from and see how they were obtained. Biology is becoming increasingly quantitative, and research biologists are beginning to rely more and more on their understanding of mathematics. For example, I’d pity anyone trying to use MatLab without an understanding of algebra - I imagine it would be pretty difficult. Not understanding algebra is a road block, not something that should be actively encouraged - especially not for our doctors.
I am very proud of my understanding of algebra, calculus, and beyond, and firmly believe that a strong understanding of mathematics has been my biggest asset as a scientist and a biologist. In fact, I find Mr. Hacker’s “simple arithmatic” a bit useless - for that, I can just use a calculator. My understanding of “vectorial angles and discontinuous functions”, however? (Seriously, are those the best “scary maths words” you could come up with?) Priceless.
In conclusion, is algebra necessary? Well, in a word… DUH.
Image: A representation of data storage in molecular biology, showing the construction of a generic, microcircuit neural network model. Made possible through a decent understanding of algebra…and probably calculus, too.