Re: [xmca] Math Question

From: Janet Frost (
Date: Tue Jan 02 2007 - 19:59:34 PST

It seems to me that this perspective is based on the traditional way that
most of us learned mathematics ­ by being taught and expected to follow
certain rules or algorithms in order to work with numbers. However, newer
approaches to teaching mathematics, based on a problem-solving approach,
allows children the opportunity to be very creative in their approaches to
working with numbers.

Boaler and Greeno suggest that the traditional non-creative approach is what
drives many creative and divergent thinkers out of mathematics, to the
detriment of the field. (Fortunately, the strongest mathematicians ­ like
Einstein ­ maintain their sense of creativity.) Unfortunately, they suggest
that the math majors who prefer ³received knowing² - meaning the memorized
algorithmic kind ­ are often the ones who go on to become math teachers and
perpetuate the idea that math is not creative but instead is a repetitive

Boaler and Greeno (2000) Identity, agency, and knowing in mathematical
worlds. In J. Boaler (Ed.) Multiple Perspectives on Mathematics Teaching and
Learning (pp. 171-200). Westport, CT: Ablex Publishing.


On 1/2/07 7:12 PM, "Michael Glassman" <> wrote:

> Are we talking about two different mathematics. I have been told that
> mathematics doesn't start getting really creative until you stop using
> numbers. Not being a mathemetician I can't grasp this at all - but I have
> gotten this from two sides - the successful mathematician who said to really
> work on math you have to move beyond the use of numbers, and to a fellow who
> flunked out of the Courant Institute (sp?) because he could not get past the
> use of numbers. I think this is true of writing - that really great writers
> are past the use of words as symbols, what they are writing is what is
> happening at the moment for them - the characters takes on lives of their own.
> I think in reading you can always tell who has gotten past this point and who
> hasn't. Some people simply write words down on a piece of paper, and for some
> writers the words are only residue - what is left over from the experience. So
> perhaps mathematics and writing are in many ways the same process along
> different trajectories.
> Michael
> From: on behalf of Cathrene Connery
> Sent: Tue 1/2/2007 9:54 PM
> To:;
> Subject: [xmca] Math Question
> Hi Ed and everyone,
> What an interesting question. It is true that so many writers and artists as
> well have stated that they felt the ideas they mediate cross a line in the
> creative process where mind and activity and object seems to blurr and the
> work seems to create itself so to speak. Michelangelo wrote that his
> sculptures spoke to him as he carved the marble. Sometimes when I am
> painting, the same phenomenon occurs. From a Vygotskian perspective, this
> experience has interesting appeal when considering the inner voice. Vera
> John-Steiner's Notebooks of the Mind and Creative Collaborations document this
> psychological activity.
> To apply it to mathematics is a fascinating question. Being someone who can
> barely balance a checkbook, I am not sure how it would apply.......however, I
> suspect different domains in mathematics would reflect variations of this
> experience as they each depend or are derived from various forms of cognitive
> pluralism. have you looked at Reuben Hersh's work?
> Best,
> Cathrene
> M. Cathrene Connery, Ph.D.
> Assistant Professor of Bilingual & TESL Education
> Central Washington University
>>>> >>> Ed Wall <> 01/02/07 5:06 PM >>>
> Mike and all
> This is not quite on the topic (and, thus, I have held back a
> bit), but given the amount of expertise that people are bringin I ask
> a question I have asked elsewhere (I apologize for how it is phrased,
> but something like this was appropriate in that particular community):
>> > I had a question and wonder if you might point me in a useful
>> >direction(s). The situation is such: It has been argued of late that
>> >the work mathematicians do - proof and the such - proceeds within the
>> >mathematics being created. That is, without going into a lot of
>> >detail, the mathematics one does is both circumscribed and supported
>> >by the mathematics one is doing. This is not exactly a matter of
>> >prior knowledge or the hermeneutic circle per se although it might
>> >have something to do with being an 'expert.'
>> > The reason why I am asking is that, the other day in a somewhat
>> >philosophic discussion around a novel, a participant noted that some
>> >authors describe the authoring process as open-ended in the sense
>> >that what finally takes place may differ from what was originally
>> >intended. That is, in a certain sense, the writing writes itself. As
>> >this sounded somewhat parallel to the phenomenon I mentioned in
>> >mathematics, I was wondering if you knew of someone(s) who makes
>> >remarks about a similar phenomenon re writing.
> Ed Wall
>> >Hi David--
>> >
>> >There is a LOT of material on the topic of writing systems.
>> >Two interesting places to start are:
>> >
>> >D. Schmandt-Besserat, Before Writing:. U of Texas Press. 1992 (two volumes)
>> >
>> >R. Harris. The origin of writing. Open Court. 1986.
>> >
>> >David Olson has written extensively on this topic, primarily from secondary
>> >sources.
>> >
>> >I am unsure of best sources that delve into origins of writing in China
>> >which were more or less co-incident with
>> >events in Euphrates area.
>> >mike
>> >_______________________________________________
>> >xmca mailing list
>> >
>> >
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