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
exercise.
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.
Janet
On 1/2/07 7:12 PM, "Michael Glassman" <MGlassman@ehe.ohio-state.edu> 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: xmca-bounces@weber.ucsd.edu on behalf of Cathrene Connery
> Sent: Tue 1/2/2007 9:54 PM
> To: ewall@umich.edu; xmca@weber.ucsd.edu
> 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 <ewall@umich.edu> 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
>> >_______________________________________________
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