Worthwhile Canadian Initiative, an economics blog that consistently punches far above its weight, had a post from late May by Frances Woolley on the current state of mathematics learning/teaching and also it’s application to economics. It was VERY relevant for me currently as I’ve been digging out from a poor attempt at math learning from a couple of decades ago when I was last in school. I took intermediate algebra twice to get a B and never got any further. So when I went back to school last year, I went into college algebra but also spent a couple of months reviewing and studying from an old text on my own just to feel like I had some clue what I would be getting back into.
And though I’m glad that I did, I probably could have skipped it, since I ended up in an algebra class that spent WEEKS reviewing all the basics from the class that all the kids were supposed to have just passed out of. I mean adding fractions, y+mx+b, etc. etc. Our professor was a pretty great teacher once things shook out in the class and he managed to do a good job of having me pretty well up to speed by the end and probably dragged a few other under-prepared students through with me as well. But the remarkable thing from my current vantage point about this class (as well as the one I’m taking now, finite mathematics) is the profound lack of interest in anything but passing out of the class by about 80% of the students. My algebra prof. got the usual questions about “what would you ever do with this stuff?” which he answered with aplomb, citing studying the growth of bacteria, structural engineering problems, accounting, etc. etc. but he also (as a totally old school bonafide Greek mathematician who eschewed calculators let alone computers) stressed the concept of studying mathematics to improve your mind and your ability to think about other things. I think in addition to Prof. Woolley’s very valid points about why kids who can’t add fractions in their heads can’t necessarily understand things like this:
I’m still working on it myself and I’m applying myself with all the stubbornness that a late-blooming “non-traditional student” can muster. (Brad Delong likes to say in his lectures that economists like to use whatever symbol he is explaining at the moment to keep the sociologists out of economics, so I guess it’s not supposed to be easy to understand.)
I also had a conversation with my advisor last week who asked me why I was taking more math classes, as I had the requirements met after this semester and he seemed a little puzzled by my explanation that I felt that I really needed to understand a certain level of mathematics pretty completely to be able to be effective in my chosen area of study. Not like he was skeptical, but just more like he hadn’t heard anything like that in a while.
I too was a lazy uninterested student many, many years ago, so I try to keep my judgements in check on the absolute contempt that some students in my “cohort” (such as it is) display towards math (and other subjects to be fair). BUT, it ain’t easy. I often feel like, for the most part, college is wasted on the young, but obviously there are many exceptions that prove my rule in this case. I think that much of the decline in our nation’s math achievement is intimately related to the overall devaluation of academic achievement in the US (and ironically much of this is driven by the lowering of standards in the name of being able to meet those standards, in other words, if the goal is hard, lower the bar), but that’s too big a can of worms to open here! For my own part, I’m finding mathematics quite fascinating in its own right and that, coupled with my fear of showing up unprepared down the road for any kind of critical analysis of data or methodology, is ample motivation to try and do it up old-school. Now, back to some pencil and paper linear programming.