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[Xmca-l] Re: units of mathematics education



I'm a bit stumped, Roger.
It seems that the "acquiring a social convention in manipulating text" unit of analysis reflects the current consensus of opinion in maths teaching. That explains why people are so repulsed by mathematics and why so many people have trouble learning it, but I am in no position whatsoever to do anything about that except observe. On the other hand, the Davydov approach has some merits, but if they never get past linear operations with constants, that is, the students never actually get to learn mathematics, we are hardly any better off, are we? And that's leaving aside (what I regard as) Davydov's misconceptions about the relation between everyday concepts and scientific concepts.
So that's it.
Full stop,
Andy
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*Andy Blunden*
http://home.pacific.net.au/~andy/


Tvmathdude wrote:
Andy,

You have identified the real problem in much of what is taught as mathematics. When I look at curriculum in schools or colleges, nowhere do I see "create an environment where the student asks "what if?" The study of Geometry lends itself to this kind of approach, but schools and colleges are more focused on "right" answers, than deviations from the norm.Yes, there is a very small percentage of the student population who do this on their own, but why can't we look to provide an opportunity for "mindful mathematics" rather than "rote learning" for a majority of the students? Are we locked into "social convention"?

All of our assessments of learning are about right and wrong, none are about "what do you think about this"?

Dr. DeBono took at look at thought when he described a process called "po-ing" (sp?), which is based on "what if".

Look at Project Zero out of Harvard. This is a real effort to encourage student thought. Legislatures seem so hung-up on accountability, but have no vision of what learning can be. I teach College Algebra to student right out of high-school. They are obsessed with "tell me what I need to know for the test".

When, after kindergarten, do students get to "explore and discover"?

Teaching is my passion. NLP is my tool set. I work very hard to open students minds to question and "play with" ideas, even when they don't realize they are doing it.

It is great to expand this discussion, but how do we help the student?

Roger


-----Original Message-----
From: Andy Blunden <ablunden@mira.net>
To: eXtended Mind, Culture, Activity <xmca-l@mailman.ucsd.edu>
Sent: Thu, Oct 30, 2014 8:34 pm
Subject: [Xmca-l] Re: units of mathematics education

Let's not let this thread drop, Ed.
To my mind, understanding that mathematics is constrained by objective relations, and is not just a social convention, and therefore *reveals* objective relations, quite distinct from relations discoverable by "experimenting" in the world beyond the text, and opens the possibility for students to *explore and discover*. Such an experience has a very different content from that of acquiring a social convention. So I think it is important that the unit of analysis reflect this.

Andy
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*Andy Blunden*
http://home.pacific.net.au/~andy/ <http://home.pacific.net.au/%7Eandy/>


Ed Wall wrote:
> Andy
>
>      Nice and important points. Thanks!
>
> Ed
>
> > On Oct 26, 2014, at 11:31 PM, Andy Blunden wrote:
>
> >> Well, I think that if you make a decision that mathematics is *not* essentially a social convention, but something which is essentially grasping something objective, then that affects what you choose as your unit of analysis. Student-text-teacher is all about acquiring a social convention.
>>
>> Remember that when Marx chose an exchange of commodities as a unit of analysis of bourgeois society, he knew full-well that commodities are rarely exchanged - they are bought and sold. But Marx did not "include" money in the unit of analysis.
>>
>> Andy
>> ------------------------------------------------------------------------
>> *Andy Blunden*
>> http://home.pacific.net.au/~andy/ <http://home.pacific.net.au/%7Eandy/>
>>
>> >