Tuesday, August 07, 2012

An unconvincing case to X-out algebra

I had a bit of a long commute yesterday, driving from south-central New Jersey up to Starbase Cambridge.  In general it's a dull ride, having been done too often.  Still, it was the perfect time to absorb the magnificence of a George Washington Bridge crossing, followed by a great sunrise-lit view  from the loop ramp onto the Henry Hudson Parkway, and similar snippets of the Palisades also glowing in the early sun.  But, much of the time I was flipping through radio stations.  Due to this, I caught the tail end of a NPR interview with Andrew Hacker, who wrote a recent NY Times opinion piece calling for algebra to be removed from the required high school curriculum in the U.S., which has garnered letters both for and against.

In the Op-Ed piece, Hacker carefully constructs an argument that really has three key arguments.  First, algebra is uniquely difficult and a key contributor to high dropout rates.  Second, that algebra is critical to only a small number of jobs.  Third, he claims that arguments for secondary benefits of teaching algebra, such as engendering a sense of quantitative reasoning, ring hollow.

Hacker deploys a number of rhetorical devices, but to me these fail to convince.  He repeatedly claims that no studies support the general benefits of algebra (but never stating whether studies to test such a hypothesis have been made), but in support of his own contentions he cites only opinions of specific educators who frown on algebra.  It seems likely that other educators could have been found, ala Jaime Escalante

In the call-in portion of the show I listened to, Hacker displayed a curious attitude towards the subject.  One woman caller said that she hated algebra in high school, but later had to learn it for her graduate training in sports psychology.  Hacker first displayed incredulity that algebra could be used in "sports" (he ignored the psychology part) and then claimed that the caller was only using algebra because her academic advisers were required it.  This dove-tailed with an earlier comment that can be described as the math geek conspiracy theory: there are a bunch of algebra whizzes who are imposing this on everyone else.

Hacker also set up a true straw man argument against the claim that algebra is beneficial because it teaches quantitative reasoning: what good, he asked, would algebra be in solving the current crisis in Syria?  Of course, it's the wrong tool for that job.  he essentially claimed that all reasoning skills are equivalent, which is silly.  What he ignores is that the quantitative reasoning found in math is special (but not necessarily superior) to the reasoning found in many other subjects: in math there are provable truths. 

Hacker also completely avoids asking the question of whether algebra is a useful foundation for other studies.  he claims that employers, such as Toyota, have set up specialized math classes to teach their workforce the skills for their factories.  Untouched in this argument is whether prior math exposure aided in setting up such programs.

Hacker, but not several letter writers, also ignores the question of whether poor results in algebra instruction are really due to the material being truly impenetrable, or whether it is a deficiency in teaching methods.  Similarly, Hacker's insistence that the entire subject be thrown overboard, rather than trimmed and adjusted, does not speak to his credit.  Curiously, Hacker promises he is not after removing long division from school curricula, which in a day of ubiquitous calculators is arguably quite expendable and also a high hurdle for many students.

About the only place I can agree with Hacker is that math curricula, from my small sample of my own education and now TNG's progress, fail to expose students to the joy and scope of math.  Driven by standards and the tests which go with them, math classes too often only touch on the real world with the stilted language of word problems.  Too rarely also are students exposed to examples of math in nature, art and science, or to basic concepts of topology, graph theory, fractals and other fields that might spark imagination.  It need not be so; I have an old copy of a textbook called Mathematics: A Human Endeavor which rigorously tackles the subject but leaves room for cartoons and side excursions.  Judging from the reviews in Amazon of the current edition, this is still a wonderful book


Anonymous said...

Sounds as if Hacker could not memorize the formula for solving quadratic equations. :)

rdf said...

I agree, he has too much of a "throwing out the baby with the bathwater" approach -- better to modify the courses to incorporate tools such as Mathematica to do the grunt work, and let the students work on understanding the underlying principles.

Shocked speechless that he thinks teaching long division is a win. I think that reduces his argument to "I sucked at it, and I'm (smart &) successful, so it must be worthless"

Mark said...

Yes, the American school system is far too rigorous in math (and science)! Let's throw out the most basic of courses in those fields. I remember high school biology being quite useless too. When has knowing th Kreb's cycle helped me in my career as a computational biologist? Never! Let's kick that one to the curb while we're at it.

Todd said...

He seems to ignore that a high school education is a "general" education, originally intended to give citizens the skills to be reasonably contributing members of society.

Perhaps a large corporation like Toyota will educate its own workforce, but I doubt he would encourage Americans to rely even more heavily on corporations for their well-being and adaptability.

However, he does raise 2 important albeit rather incongrouous points: 1) mathematics is used a hoop, badge, or token; and 2) European-style "apprenticeships" are really useful for a society. I won't comment on the first, but concerning the latter...Currently many sectors of the American job market must draw from the university/post-grad pool of graduates because the university/post-grad pool is the only pool to choose from.