My beginning math ed was founded on “New Math” (circa 1963, and it WAS new). Set theoretic principles taught me both algebraic principles and abstraction skills. At university, I studied math for fun since I could apply it to fulfil requirements “appropriate to major” as a science student. My coursework included: both differential and integral calculus of both algebraic and transcendental functions of both single and multiple variables (three courses), sequences and series, advanced calculus (start with the definition of a field and derive the rest), ordinary differential equations, matrix theory (linear algebra), Boolean algebra, mathematical statistics, linear regression and auto-regressive, integrated moving average models and methods, linear programming, queuing theory, and operations research. For about a decade, I used lots of my math training in the contexts of my employment. For my entire life since learning these topics, I’ve employed aspects of the knowledge and critical thinking skills daily.

Perhaps it’s a difference in volume of study, but I see programming (my art, craft, and trade since 1986) as applied mathematics – Boolean algebra. I’ve worked with hundreds of programmers over the course of nearly three decades of professional experience. Those who were math-illiterate were on average less capable than those with degree work that included extensive training in math topics. Yes, your experience may vary – you personally may be god’s gift to programming without the capacity to recall the quadratic formula, but that makes you an unlikely event in the universe of my experience; it also doesn’t mean you’re not doing math – simply that you’re unaware of the fact…programs are proofs ( http://en.wikipedia.org/wiki/Curry-Howard_correspondence ).

Math SHOULD be the easiest thing to teach/learn due to its perfect consistency, i.e., lack of exceptions. However, we have shrouded the discipline with elitist arguments that excuse teachers when they perform poorly and permit the ill-educated to pretend they are not deficient in adult skills. Mathiness is not genetic beyond the sense of “genetic” meaning “human.” Whether an individual student is more predisposed to learning by intensional methods or extensional ones, the same concepts CAN be imparted. The failing of our schools in the main part is the attempt to enforce that ALL students learn almost exclusively by intension since it’s faster…when it works. We aren’t very good yet at tailoring education for individual students. We mass-produce an inferior product since it has historically been deemed mostly, sort of, good enough.

When I hear claims like “I’ve never used it,” “I can’t imagine what good it is,” etc., I recognize victims of our pathetic education system, their intellectual lives less rich than mine for having been short-changed by our schools.