In the wake of our previous article “Algebra is essential in a 21st century economy” (see Math Drudge blog and Huffington Post article), one of the present bloggers (DHB) participated in a “televised” interview with Andrew Hacker, the author of the New York Times article in question, together with several other respondents, organized by the *Huffington Post*. This transcript will be made available here when ready.

Here are some other “talking points” to consider on this issue:

- Our economy is moving inexorably to information-age, high-technology careers, many of which require mathematics backgrounds. In a ranking of the top jobs published in the Wall Street Journal, based on income, working environment, stress and job outlook, all of the top five jobs (software engineer, mathematician, actuary, statistician, computer systems analyst), and 11 of the top 20 jobs, are math-intensive. Mathematical skills are becoming increasingly critical to many white-collar professions. Marketing and public relations persons, for example, have to understand rather sophisticated statistics in order to analyze data on ad campaigns. Blue-collar workers need to understand trigonometry and think through abstractions in order to ensure that products are shaped properly and fit together upon assembly. Many blue collar workers (including a friend of DHB) now work with high-tech CAD-CAM systems.
- Mathematics is well known for being valuable for instilling critical thinking and problem-solving skills. The logical, axiomatic method learned in high school geometry, for example, is recommended for those seeking careers in law.
- Mathematical skill is unique in that it relies on a sequence of courses. Numerous college-level science and engineering courses require calculus; calculus requires trigonometry and analytic geometry; these require geometry and two years of algebra. If students don’t start this sequence until college, because well-meaning high schools did not require these subjects, even for college-bound students, then for the vast majority of students it will hopelessly too late to catch up once in college. Talented or not, these students’ future lives will have been decided by the “system”.
- Learning mathematics is very much like learning a foreign language — the earlier one becomes comfortable with these concepts, the easier it is to learn. Other than that, there is no “royal road” to mastering these topics. For example, in spite of centuries of tinkering, textbooks today still generally follow the outline prescribed by Euclid in 300 BC. When Ptolemy I (ruler of Egypt from 323 BCE – 283 BCE) grew frustrated at the degree of effort required to master geometry, he asked his tutor Euclid whether there was some shorter path. Euclid replied “There is no royal road to geometry.” Indeed, and there is no royal road to algebra either.
- Hacker is opposed to “tracking” students, especially not at an early age. But if some students must start algebra beginning at the 8th or 9th grade, to prepare them for STEM fields in college, how do we decide which ones, except by some system of evaluation that amounts to tracking? Hacker suggests that we make all mathematics courses “electives,” but this is wildly impractical — how can students in middle school and early high school possibly be expected to make ultimate career choices on their own?
- Why pick on algebra (or mathematics)? Yes, a knowledge of calculus may or may not help one negotiate through traffic or connect one’s computer to the Internet, but the same could be said for many other disciplines. How does knowing whom Hamlet killed accidentally help one be a better consumer? Does knowing the history of the Spanish-American War help one complete one’s tax return?
- Algebra is necessary even in everyday life: Consider a very common, simple question: You bought an item at a store, and although you didn’t keep the receipt, a charge of $173.15 was posted to your credit card account. The sales tax (or VAT) rate is 8.25%. What was the pre-sales-tax price of the item? With algebra, it is easy: x + 0.0825x = x(1 + 0.0825) = 173.15, so x = 173.15/1.0825 = 159.95. How can you possibly solve such a problem without at least a rudimentary mastery of algebra? As another example, if you get a 20% pay cut, followed by a 20% pay increase, will you be better off, worse off, or the same? (Answer: worse off).
- We certainly agree with Hacker that reforms must be made to education. But at least one change is clear: As authors William Schmidt and Curtis McKnight point in their recent book, most 8-10 grade U.S. mathematics courses are now being taught by persons with neither a major or minor in mathematics. How can a student learn to “love” mathematics, if it is being taught by someone weak in mathematics, or for whom math is at best a chore? As Biddle points out, out of 63 elementary mathematics programs surveyed by the U.S. Department of Education, only one was rated as having “potentially positive” effects on student achievement.
- Defacto tracking or “dumbing down” the mathematics curriculum does not do any favor to disadvantaged students. The universal experience of those who actually teach and work with these students is that they require “more opportunities in later grades than other students.” And dumbing down course materials only leaves these students even more hopelessly behind their more privileged peers.
- Other nations outside the U.S. are not standing still. Finland for example, has ranked at (or near) the top of European nations in educational performance for ten straight years, due in large part to its strict requirements for teacher training (all teachers must have at least a masters degree) (certainly not because, as Hacker suggested, they persevere more). Australia, Taiwan, Singapore and Korea are significantly upgrading their mathematics education, and these trends are widely credited with their economic rise. Is the U.S. going to just fall down and surrender?
- Hacker points out that unemployment among computer programmers, for instance, is currently 8%. But this is because many programmers’ skills have become dated, and they (like many other mid-career people in our economy) need some retraining. Fresh-out computer science graduates, particularly at the MS and PhD level (which require significantly more mathematical sophistication) have no trouble finding employment. A colleague at the University of Maryland reported that even in the past month, long after most MS and PhD graduates have accepted positions, employers are still calling to ask if there are any graduates available for employment. And this is in a recession!
- A 1996 study by two psychologists and a prominent computer scientist found that drilling on how to solve specific problems (such as rates of inflation) does not transfer to skill in other areas, such as interest on investments. Thus converting all mathematics education to everyday “quantitative reasoning,” as Hacker suggests, does not bode well for instilling general problem-solving skills. This was attempted a number of years ago in the Netherlands, with disastrous results. For further analysis, see Dillingham’s article in the Washington Post.