The problem with mathematics education at Rutgers
Introductory-level mathematics education is a festering wart on this country’s nose. More locally, Rutgers — a university that touts some of the best researchers in applied mathematics, as well as a top-twenty graduate program — is doing nothing to heal the deep intellectual wounds incoming liberal arts freshman have sustained as part of their mandatory mathematics education in public school. Recall that if you place into pre-calculus or higher on the Rutgers math placement entrance exam, you have the option of taking a course called “Math 103 — Topics in Mathematics for The Liberal Arts” to satisfy the “QQ” and “QR” School of Arts and Sciences Core Curriculum. Many liberal arts majors enroll in “Math 103” intending for it to be the last math class they ever take. Let’s look at some of the topics for that class and use them as a stepping-stone to briefly discuss the problems of math education today. But first, let’s inspect why so many people hate mathematics.
Long story short: Public schools condition people to see math as this repulsive, unintelligible and difficult thing, primarily focused on computation, long-winded definitions and real-world application. This is compounded by the idiocy of requiring math teachers to have 5-year advanced degrees, effectively ensuring that no practicing mathematician or mathematically talented person will ever become a math teacher. There are more contributing factors, such as the Common Core, standardization, et cetera. For more information, I strongly suggest reading Paul Lockhart’s “A Mathematician’s Lament,” which is a highly inspired look at the failings of early mathematics education.
Returning now to our original problem: The Spring 2014 syllabus for “Math 103” provides a list of 13 things students who successfully complete the course will be able to do. I’ve provided a few for you below — completely unaltered. The rest of the list is available online.
— Determine winners of elections under different voting methods, and use these to rank the candidates.
— Compute the future value of assets and value of a deferred annuity.
— Analyze the feasibility of performing certain brute force computation.
— Be able to articulate their understanding of the above items, in clear English.
Now, let’s assume all liberal arts majors have devoted their lives to the pursuit of beauty, truth and aesthetic gratification. They want to know what it means to be alive and better themselves, both mentally and spiritually. Rutgers has a golden opportunity to show these starry-eyed romantics what math is all about — truth with a capital T, internal necessity, elegance, transcendence, fun and reason. But instead, they teach them about “the feasibility of performing certain brute force computations” and “rank[ing] candidates.” I’m not saying these topics aren’t interesting — of course they are. What I’m saying is liberal arts majors are being duped. They may think they know what math is, but they don’t. How could they? It’s never been shown to them. They’ve never been allowed to poke, prod and explore inside that pearly world of Platonic idealism. They’re being deprived of humanity’s most enduring intellectual achievement, sans written language.
How do we fix this? How do we teach math — real math — to a bunch of bright beauty-seekers, when they’ve been conditioned their entire lives to approach it as this unattractive, arcane and difficult thing?
The hyper-ultra-SUPER condensed boring version of the answer is to start teaching Euclid’s Elements to liberal arts majors again, as we did for centuries prior to the pedagogical brain fart of the 20th century. The Elements — a collection of 465 propositions from plane and solid geometry and number theory — is only second to the Bible in terms of cultural and historical influence. Euclid was one of the first to take a rigorous, axiomatic approach to math — to start from first principles and from them prove True (that’s true with a capital T) geometric properties.
Students should feel like they’re partaking in something that connects them to their cultural and philosophical heritage — something that brings them back to the dawn of mankind’s intellectual rebirth. Something that places them right in the middle of Alexandria, circa 300 B.C., surrounded by brown scrolls and bearded geniuses muttering in Egyptian and Greek. Let them explore a branch of math that is predominantly visual and uses just the most basic operations — and by doing so, put their general faculties of reason against the best whetstone there is.
Leo Kozachkov is a School of Arts and Sciences sophomore majoring in physics. He is a staff writer for Applied Sentience, a Rutgers humanist blog.