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Topic: Mathematics education on the arXiv?
Replies: 2   Last Post: Jul 30, 2013 9:00 AM

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Clyde Greeno @ MALEI

Posts: 220
Registered: 9/13/10
Re: Mathematics education on the arXiv?
Posted: Jul 30, 2013 2:22 AM
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"Dienes' view as it can be found in his writings was that children
learned through playing. Adults may learn but they sure don't play."
#Children internally develop their personal "theories" by thinking about
their experiments with whatever things they are trying to manage ... even if
adults call it "playing." Adults do the same, whether or not someone calls
it "playing."

"No. What is necessary is that the students be helped reading the
text---assuming of course that the book is honest."
# That depends on what you are trying to accomplish. If the goal is only to
equip non-readers with the mathematics of carpentry, reliance on a textbook
probably would get in the way. But if a concurrent goal is to prepare them
for higher levels of education, collateral instruction in reading is a
worthy undertaking."

"Yes, but arXiv is for research papers, that is assertions that are
either provable from previously established knowledge or reproducible
experimentally." [About teaching students how to learn mathematics.]
#It seems to me that there is much room for high quality research about at
least some "how to learn" tools ... such as "concept analysis: identify at
least 3 kinds of examples of that concept, and at least 3 *pertinent* kinds
of counter examples. I suspect that "pencil in hand" includes some such
particular tools.

" No. Mathematical processes are *developed as needed*. " [About MKTE in
arXiv dealing with "mathematical processes"]
# Whoa. It does make sense for students to become consciously aware of what
mathematical processes are called for *at the time*. But within the body of
research in Mathematical Knowledge for Teachers' Education, all of the
important processes should be aired and explored ... albeit the papers might
be read only "as needed."

Cordially,
Clyde


- --------------------------------------------------
From: "Alain Schremmer" <schremmer.alain@gmail.com>
Sent: Monday, July 29, 2013 3:31 PM
To: <mathedcc@mathforum.org>
Subject: Re: Mathematics education on the arXiv?

>
> On Jul 29, 2013, at 1:44 PM, Clyde Greeno wrote:
>

>> Responding to some of Schremmer's comments about a possible "Math ed"
>> space in arXiv:
>>
>> "(2) Unfortunately, there is just about nothing worth placing therein:
>> "math ed" is no more a science than, say, "economy". ...."
>> # Neither is the field of medicine a science, but the scientific sector
>> of that field is a crucial part, thereof. The field of "math ed" cannot
>> BECOME a science. But the search for its scientific components is
>> imperative. At best, those will constitute a learning-guidance science
>> of mathematics instructology, based on clinical research.

>
> This is a very clever distinction. I will have to think about it.
> Clearly, there are a few known truths such as lecturing does not work,
> cannot work. Yet 99.99% of us lecture. So?
>

>> "(3) The only work in mathematics education I respect is that of Z. P.
>> Dienes but it pertains only to children."
>> # Perhaps not. After a meeting of directors of NSF-funded teacher
>> institutes, Peter Braunfeld and I socially met for a while with Dienes
>> in his hotel room. My impression was that he perceived that children
>> construct their own, personal mathematical "theories" ... and that
>> adults do likewise. Its just easier to study in children. With adults,
>> the best way to study it is through clinical casework.

>
> Dienes' view as it can be found in his writings was that children learned
> through playing. Adults may learn but they sure don't play.
>

>> "(5) ... but the only known way for adults to learn mathematics is by
>> gaining "mathematical maturity" by experiencing the "compressibility of
>> mathematics" by "reading pencil in hand".
>> # Other ways now are becoming known ... depending on what one means by
>> "learn mathematics."

>
> Exactly! (When I was, a long time ago, in France, tutoring students for
> them to get the minimum passing score in mathematics on the state
> competitive exams, the meaning was entirely different. )
>

>> The challenge of guiding math-fearing, math-illiterate, poor reader,
>> impoverished "school dropouts" to "learn mathematics" up through high
>> school algebra

>
> This describes precisely half of my students for these past twenty years.
>

>> calls for minimum reliance on textbooks.
>
> No. What is necessary is that the students be helped reading the
> text---assuming of course that the book is honest. In other words, these
> students have no idea that knowledge can be drawn from a printed text.
> With a little bit of honest help (I should describe that somewhere) they
> can in fact discover that the printed stuff can sing to them. And THAT I
> find is enormous (But not publishable in arXiv)
>

>> Of course, there also is a level of "mathematical maturity" wherein the
>> learner must own personal abilities to digest post-secondary mathematics
>> textbooks.

>
> This is impossible as, by now, these are totally unreadable.
>

>> So arises the fact that American mathematics-educators badly fail to
>> teach students HOW TO LEARN mathematics.

>
> I badly fails to let student learn anything.
>

>> In my book, that void should be attended in any MKTE section within
>> arXiv.

>
> Yes, but arXiv is for research papers, that is assertions that are either
> provable from previously established knowledge or reproducible
> experimentally.
>

>> "(6) The difficulty in learning mathematics resides only in: -- the
>> degree of abstraction of what I am considering ..."
>> # Such is a major cause of students' difficulties in learning
>> mathematics from formal expositions about it: books, lectures, etc.

>
> The key here is your use of the term "formal exposition" by which I take
> it to mean the kind of books I alluded to earlier, the kind that is
> written for colleagues. That is why I try to use other terms, like
> "honest book" or, for my own stuff, "reasonable". Mathematical
> correctness does not imply "formal exposition"
>

>> Part of the problem is that too few educators have viable meanings for
>> "abstracts" or "abstracting" or "abstractions" ... or are aware that
>> mathematical abstractions are common-sensibly derived from generative
>> instances. Students' difficulties are not in learning mathematics, as
>> such, but in trying to learn it from how it usually is formally
>> presented.

>
> Yes. The little that is learned is usually learned in spite of the
> teacher. Which is why I present myself to the students as only a
> resource.
>

>> Consistent with Dienes and Piaget, Schremmer surfaces that, unless
>> students somehow are guided to personally do the abstracting, the
>> curricular formalisms truly are "abstract" only [and at best] to authors
>> and teachers. To the students, those same (educator- supposed)
>> "abstractions" only are mere formalisms ... which might or might not
>> later accrue some kind of exemplary meanings. Abstracting, generalizing,
>> exemplifying, etc. are crucial mathematical processes that must be aired
>> in an MKTE library.

>
> No. Mathematical processes are *developed as needed*. See Thurston's
> compressibility.
>
> Regards
> --schremmer
>
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