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Topic: "Learning to Work Like a Mathematician" by Douglas Williams
Replies: 116   Last Post: Mar 10, 2010 11:07 PM

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Bishop, Wayne

Posts: 2,881
Registered: 12/6/04
Re: "Learning to Work Like a Mathematician" by Douglas Williams
Posted: Mar 9, 2010 12:00 PM
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At 11:22 AM 3/3/2010, Jonathan Groves wrote:

>I have seen numerous articles addressing this issue that you have just
>mentioned--the problem that "reform math curricula" often do not contain
>any real mathematics content.

<snip>
>As of now, I don't have any way to really verify for myself how valid these
>claims are. Experiences with students don't tell me much; most of
>the students
>at Kaplan and the other schools I teach for are older students who never went
>through reform math classes. In fact, most of them had gone through boring
>math classes that reduce mathematics to memorization and recipes, the kinds
>of math classes that don't show any creativity or history behind mathematics,

<snip>
>"Because it's the rule. We're supposed to do it that way." So
>something works
>because it works or because it's the rule that tells us it works? That's not
>reasoning but simply regurgitating a fact in which the student has no earthly
>idea why it's true! These are the kinds of math classes I went through in
>K-12. The mathematical content is fine and useful for learning more advanced
>mathematics.


Exactly what you need to know in order to teach for Kaplan. Right?

>But it was taught without reasoning or motivation and was taught
>via memorization. In short, no creativity, no ideas of how
>mathematicians work,
>no idea of how the subject is developed, no idea of how new mathematics is
>developed, etc. No wonder such students have no earthly idea what
>mathematicians do or how they view mathematics! These are the kinds
>of classes
>that are the persistent disease in mathematics education. Regardless of
>actual mathematical content, classes that reduce mathematics to this kind of
>abhorrent crap cause far more harm than good.


Such speculation sounds beautiful, of course, but I have yet to meet
any mathematician who was taught in a full-blown "discovery"
environment. Many of us correctly believe that we should have been
taught more, and more quickly, but the idea of not learning as much
as possible (ostensibly, from knowledgeable teachers and/or
well-written mathematics books) before embarking on discovering new
and exciting mathematics is purely the stuff of ed school insight,
not professional mathematicians let alone (and statistically
speaking, more important) those who need a strong mathematics
background to pursue their areas of interest. For example, none of
the seminal group who created Mathematically Correct word is
mathematics per se (although some of us became involved very early).
Two were PhD's from Stanford, one of statistics and another in
genetics (later recruited as full professor with tenure to Brown),
another was a PhD in geophysics from USC, another was an independent
contractor electrical engineer, etc., united serendipitously one
evening with a single common thread; all were teaching their children
(and sometimes small groups of their children's friends as well)
mathematics to compensate for their school's use of one of the better
of the math reform curricula, CPM under the misnomer College
Preparatory Mathematics about which I have had some experience:
http://mathematicallycorrect.com/cpmwb.htm

Bringing this up to the present, one of this geographical region's
very expensive private schools - complete with an avid supporter and
sometimes contributor here with the same mathematics misconception as
yours - adopted the newer version of this curriculum that supposedly
has fixed those problems (that CPM never admitted that it had). Don't
believe it for a minute; its creators and proponents are true
believers. How's it working out at Chadwick? Here is the assessment
of one parent and attached is the school's: response to what it is learning:

"Disappointingly, she has gone from a child who loved math to one
that hates math."

>What teaching methods do you propose? Are the only kids doing well are the
>ones Wayne and Company, including you, label as the "mathy" ones? I highly
>suspect that these "mathy" kids are the only ones who do well under
>the programs of Wayne and Company. I see no evidence so far that suggests
>otherwise.


See the above and the attached.

Wayne




Date Subject Author
2/27/10
Read "Learning to Work Like a Mathematician" by Douglas Williams
Jonathan Groves
2/27/10
Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Robert Hansen
2/27/10
Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Haim
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Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Jonathan Groves
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Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Louis Talman
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Michael Paul Goldenberg
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Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
GS Chandy
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Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Robert Hansen
2/28/10
Read Re: "Learning to Work Like a Mathematician" by Douglas Williams
Robert Hansen
3/4/10
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