- #36

dkotschessaa

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UsableThought said:This is exactly the position taken by the guy who wroteA Mathematician's Lament, an essay and later a book by Paul Lockhart, a math teacher at St. Ann's School, a K-12 school in Brooklyn Heights, NY. I assume most here know of at least the essay, given that it was publicized back in 2008 by Keith Devlin in his MMA column. The essay is here as a PDF and the book is available on Amazon and elsewhere. Book & essay attack traditional teaching along the lines given by @dkotschessaa, and suggest play as a far more suitable approach, e.g. treating math more like art class than history or science. He also has a more recent bookMeasurement, which is a self-teaching guide for adolescents or older; the reader is invited to "play" with math via geometric patterns such as symmetry, rotation, etc. I started that book but found it a bit daunting, plus it doesn't meet my current goals (re-learning high school algebra) so I put it aside.

In response to a couple of comments saying that learning mere calculation (as we are supposed to in grade school & secondary school) will never be anything but tedious - I disagree; I think it depends on your circumstances and attitude. If you are re-teaching yourself high school algebra, as I am for example, you can go at your own pace; and you can concentrate on those things you find interesting. This is similar to what I've read about the concept of "flow" as espoused by psychologist Mihaly Csikszentmihalyi: almost activity can support an enjoyable state of flow so long as the person doing it able to take charge of how they do it, can set their own goals & receive immediate feedback, and engage in it as if it were a game.

I admit I kind of keep wanting to go back to some of those "mental math" books and learn all manner of tricks for arithmetic. But mainly my goal is a kind of brain training, and secondly I think the tricks use some neat "number theoretical" types of ideas to get the answer. I don't think arithmetic is that useful as a skill anymore but it would be fun.

I will add that in my case, my ability to guide my own learning is probably much greater as an adult than it was when I was very young; and although I no longer have the full measure of wonder that everyone misses from childhood, I can understand certain difficult subjects better now than I could then. Also, I have been heavily influenced by a MOOC I took early on, Keith Devlin'sIntroduction to Mathematical Thinking, that taught predicate logic and simple proofs; quite a few of the proofs involved number theory. So now when I do my simple algebra problems in Gelfand and Shen, or Brown et al, I often go beyond the problem as stated and do a proof; and also look for interesting patterns. It's actually good that I've been so bad at math most of my life, because now even high school algebra is rich territory for me!

Oh, I think algebra (high school level) is beautiful stuff. It is really ones first exposure to mathematical thinking since it requires some kind of manipulation of objects, and there is more than one way to get from one place to the other. There's also all manner of "tricks." Even last year as a master's student I watched a fellow TA teach an algebra class and learned new ways to factor.

-Dave K