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Topic: Of Sequence and Success
Replies: 17   Last Post: Nov 4, 2012 11:22 PM

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Robert Hansen

Posts: 11,345
From: Florida
Registered: 6/22/09
Re: Of Sequence and Success
Posted: Nov 3, 2012 8:04 AM
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On Nov 3, 2012, at 1:52 AM, kirby urner <> wrote:

> On Fri, Nov 2, 2012 at 3:54 PM, Robert Hansen <> wrote:
>> On Nov 2, 2012, at 6:05 PM, kirby urner <> wrote:
>> To this day, there's a sense among mathematicians (many of them) that
>> "arithmetic" as we call it is a vocational skill that, if not
>> orthogonal to mathematics, is certainly not its essential core.
>> No there isn't. Lou is the first I have met. Even Devlin is firmly in the
>> times-tables camp. I so often must remind you about exaggeration.
>> Bob Hansen

> I have listened to Devlin in personal appearances, e.g. Oregon Math
> Summit ** as well as on the radio.
> His schtick when I saw him was "arithmetic" is basic numeracy like
> knowing how to weigh, use a fork, blow your nose, tie your shoes.
> All teachers in all subjects were equally responsible for imparting
> these basics, he was saying, as that would free the math teachers to
> teach what's really math, which isn't "the four operations".
> He ridiculed traditional schooling in the "four operations" as
> spending years making junior try to make himself a cheap imitation of
> a cheap plastic calculator, and still not being able to perform as
> well.
> These are necessary skills (add, divide, multiply, subtract), but so
> is buying toilet paper (alluding to Paul's obsession with "money" over
> "energy" when talking economics -- symptomatic of that discipline's
> out-of-touchness with reality).
> I'm surprised Lou is the first mathematician you've met with that
> attitude. I assure you Devlin somewhat shares it. I do not
> exaggerate. Plato shares it too.

Devlin on Video Games

"Yet whenever I have tried some of the math ed video games being produced, I have been significantly underwhelmed. For the most part, they do not teach mathematics at all, rather they test what has already been learned elsewhere. Moreover, that testing is largely restricted to automatic recall of basic number facts and rapid use of arithmetic skills. Nothing wrong in that. I wish I'd had access to an enjoyable video game to help me practice my multiplication tables when I was in elementary school. What has left me unsatisfied is that those games (and we are really still talking about first-generation mathematics education video games here), while succeeding in achieving their (modest) educational design goals, fall way short of the potential I, and many other, are sure the medium offers."

Devlin on NPR

"You cannot become good at algebra without a mastery of arithmetic," Devlin says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers."

Maybe you only hear what you want to hear.

> It's somewhat endemic in the culture, I'm surprise you haven't noticed.

What I have noticed is that people (mathematicians are people) tend to take arithmetic for granted. They have very little (usually none) experience with the processes that occur with children learning arithmetic. And I don't mean "scientifically how" (which is silly to even suggest that we are even close to that yet). I mean that they simply have not witnessed first hand (as a teacher) the phenomena (which occurs over a period of 3 to 5 years) of children learning arithmetic.

> The comic book math mensch can visualize hyper-dimensional topologies
> rotating with ease but can barely balance a check book, because mere
> addition is boring/tedious/error-prone and he never bothered to get
> good at it (too busy getting good at math).

> Being good at arithmetic means you're a well oiled machine, like fast
> with an abacus, maybe you have lots of mental tricks and can add the
> grocery bill in your head.

When have I, or anyone for that matter, described "being good at arithmetic" in that manner? Being good at arithmetic means knowing numbers, addition, subtraction, multiplication and division and how to apply them in context. You can't accomplish that without becoming familiar with it yourself. In that process, some people get very good at calculation, most get reasonably good.

> Good for you (applause!). But that's more
> under the heading of "salon trick" or "impress your friends at
> parties". Math means knowing lots of theorems and history and
> applications and...

And music must mean knowing lots of songs and the history of music. A million musicians would disagree with you, if they even bothered.

Bob Hansen

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