I can’t decide whether to be annoyed or amused by the opinion piece by Andrew Hacker entitled “Is Algebra Necessary?” in the New York Times on Sunday*. Annoyed because it is such an obviously flawed piece of writing, essentially saying that since (in the US) the system is failing to teach lots of people basic mathematics in school, the solution is to stop teaching it rather than figure out what is going wrong with the teaching process, while at the same time very lamely trying to make the case that it has no use anyway. Amused because it’s obviously flawed, and hopefully anyone reading it will laugh – one’s first thought has to be that it is not a serious article, given that it it is published in a respectable newspaper with reasonably educated editors.

But one can’t – shouldn’t – laugh, since there are (sadly) many people (lots of whom were educated in the very system under discussion) who might well take the whole thing seriously. Part of the problem is that the writer really does not seem to understand what Mathematics actually is, or what it is for, which I suspect reflects a lot of the flawed teaching that lies at the root of the issue. (Update: I recommend, for a change, browsing through some of the reader comments – at least the first few pages worth that I looked through – since the responses are interesting and at times amusing.)

Anyway, happily, I can also point to an excellent (and funny) response by Mark Chu-Carroll of Good Math, Bad Math, who has done a good job of getting angry enough to write something, but not too angry, thank goodness.

-cvj

*Thanks Moh!

Depressing similar to the arguments that are put forward for not teaching musical notation in schools. I like the response by Mark Chu-Carroll, especially where he substitutes algebra for literacy. It nicely illustrates the flaw in the original piece in the NY Times!

The article is clearly absurd overall, and less math is not the solution to any of our problems.

However I would agree that the teaching of algebra specifically is a weak point of the curriculum. It could be broken into segments and intermixed with elements of “precalculus” which are easier to motivate, e.g. trigonometry, probability, financial math. This would be better than an entire year of manipulating low-degree polynomials for no apparent reason other than to solve very artificial word problems. I can’t imagine that “solving for x” really would present such a big conceptual problem to most students, if the equations they’re directed to solve seem to actually have some meaning or point.

Plane geometry might be due for similar treatment. My memory is that this occupied a whole year, and I personally loved the formal proofs, but I think the typical student would benefit a lot more from a treatment less oriented towards formal proof and more towards understand properties of plane geometry through whatever tools are most useful (Euclidean proof, analytic means, trigonometry….)

Algebra and plane geometry together constitute a huge block of the student’s early exposure to “real” mathematics, at least on the U.S., and it seems to me that both are still following rather antiquated lesson plans. Of course, this is my memory from 3 decades ago now.

I loved math and became a math major, and then went into physics. After all was said and done I felt that my formal training in mathematics, even going back to plane geometry, was very heavy on the proof side and weak on the “practical understanding” side. Typically in math courses one immediately proves the most general form of any theorem, and spends little time understanding various special cases which might actually benefit the student more. An example would be Lie groups, which definitely can be understood more readily from a physicist treatment than from a formal math class. Looking back, it seems to me that the same sort of deficiency can be seen even in the algebra/geometry courses which are students’ first exposure to real math.

The article, well as much of it as I could read before I was overcome by something akin to revulsion, was horrible (and not that atypical, particularly in the wake of the ‘it’s the mathmoes who f***ed the world’s financial system scam): an example of the crap put forth by the bien pensant ‘cultured’ folk who dominate so much that purports to be intellectual discourse these days. Sad to say, we on the mathematically enabled side of the fence are quite as guilty in our ill thought out dismissal of soft science and the arts. Deep down creativity should provide some common ground: the wholly self indulgent act of bringing into being something that had previously not been, and the subsequent altruistic dissemination of the fruits of ones solipsistic strivings to ones fellows. Then everyone benefits – it’s fun and accessible too. Win-win, as it were

I must admit I stopped at the title, but even that was remarkably foolish. I am a biologist and not someone whose science is particularly quantitative, but I have always thought Algebra was (after simple computation) the most practically useful thing i learned in math. If you want to figure out how to make a 0.2M solution of CaCl2, it comes in mighty handy.

I also think math is intrinsically beautiful, and am sad all the math I learned in college has dissapated from lack of use, just when quantitative approaches in my field (cell biology) are becoming central to all we do.

I never “liked” math. My greatest accomplishment was remembering to use a pencil until I was in college. I had an excellent algebra professor at that point and did quite well in the required math classes on the way to my nursing degrees. Algebra is so much more than “math”. It’s critical thinking and analysis – of course, that’s just coming from a layperson! π Critical thinking and skills in analysis are qualities that EVERYONE benefits from!

Respect the math! Use a pencil! π

Thanks All!

Gleanne Marie… What was the rationale behind the insistence on pencil usage? Was it to encourage the freedom to make mistakes, which are more easily correctable in pencil?

-cvj

I wish that the pencil usage was to promote freedom to play with the numbers and experiment! That sounds like so much more fun. Sadly, my own personal edict was self-imposed due to my proclivity to produce so many not-quite-right answers! I think it takes great confidence in one’s abilities to tear through math problems with a pen. π Sorry if I’m not making much sense – I’m quite jet lagged and am still on San Francisco time… I bet you do math with a pen… π

Hi,

I do, but I still make my share of mistakes. The trick is not to worry about them. They can be corrected whether you wrote in pencil or pen.

Best,

-cvj

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