Mathematics is used as a hoop, a badge, a totem

Quote of the Day for Sunday, July 29th, 2012:

Andrew Hacker, in today’s New York Times, asks: Is Algebra Necessary?

Peter Braunfeld of the University of Illinois tells his students, “Our civilization would collapse without mathematics.” He’s absolutely right.

Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.

What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.

Many of those who struggled through a traditional math regimen feel that doing so annealed their character. This may or may not speak to the fact that institutions and occupations often install prerequisites just to look rigorous — hardly a rational justification for maintaining so many mathematics mandates. Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever 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 in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.

It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better.

math1Interesting essay, and at first blush I’m inclined to agree with the author that advanced math requirements in schools sets an artificial barrier to success that ultimately does more harm than good, because of the effects on otherwise-skilled learners who end up being alienating from success in the broader educational enterprise – though I wouldn’t call basic algebra and geometry advanced math. I also agree that advanced math skills are of little to no use in most career vocations, including most professional vocations (though I doubt many philosophers, unlike poets, would see such skills as extrinsic to their craft). math2In fact, I’m inclined to think that the modern emphasis on math and science in education is a large part of the problem with contemporary education, and not part of its solution. And Hacker gets the difference between education and training, sees that advanced math skills acquisition is really more the latter than the former, and laments the lack of truly educational components in the typical math curriculum.

But Hacker’s view is too utilitarian for me; too focused on the value of advanced mathematical training for job performance or for the works of citizenry. I think there is more intrinsic value in the exercise of intellectual rigor than he seems to want to allow. It seems to me that the real problem is that our approach to credentialing (not our approach to education, per se) creates this albatross, which would be avoidable in a system with a more finely organized and meaningful process for tracking and articulating the abilities and accomplishments of students, whether at secondary or post-secondary levels. A degree system that could identify, on an on-going and not a static basis, student accomplishment levels across a range of potential subject areas would not only be much more useful both personally and socially, but would also allow institutions to establish much more meaningful minimal accomplishment requirements in various disciplines, as well as more sensible degree requirements.