"There's outright hostility in the mathematics community toward
constructivist/psychological discourses about mathematical objects that
don't start and end with the canons of mathematical theory (which, of
course, only encapsulate the object/process relations). So, there are
limits to how much mathematical enculturation one wants to encourage in
future mathematics teachers." David Kirshner
I thought it was, somehow, interesting link that "outright hostility" to Vygotskii's idea of that there are different ways of development of "scientific concepts" and also different weight of each one of them (these different developmental processes) in the camp or area of distinct objects of knowledge - like in arithmetic and language, by one side, and sociology and natural sciences. by the other.
According to him "In arithmetic the child assimilate a certain method of thinking with no dependence from the material she/he uses to solve a task. In sociology and natural sciences the material is the concrete reality that the concept reflects. So, it seems to me that the ways of scientific concepts development in arithmetic and sociology can be someway different" (In an attached chapter titled Scientific and everyday concepts development in school age of the Portuguese version of EDUCATIONAL PSYCHOLOGY)
dkirsh@lsu.edu
Department of Curriculum & Instruction
Louisiana State University
Baton Rouge LA 70803-4728
"Julian S Williams" <mewssjsw@fs1.ed.man.ac.uk> on 10/16/2001 05:35:25 AM
Please respond to mewssjsw@man.ac.uk
To: xmca@weber.ucsd.edu
cc: (bcc: David H Kirshner/dkirsh/LSU)
Subject: Re: anxiety about the 'ontologic math anxiety'
Im feeling very uncomfortable with the way this conversation has been
going.
First, let me say I spent a lot of time developing maths teaching
based on 'reality', 'applications' and 'modelling'. So I am
sympathetic with much of what martin and bb and others are saying.
And John Holt's thinking about this appealed to me, too.
Yet, the notion of 'reality' needs some thought: whose reality? Dont
teachers have 'real world' skills? What world do they live in then?
I guess maths belongs to communities of practice, and there are many
different 'maths languages/genres', many different 'maths realities',
including maybe 'school maths', 'street maths' and maybe
'nursing maths', etc, etc. Im not sure if any one version
is any more 'real' than any other, though professional mathematicians
generally privelege their own version (and Ive often heard engineers
privelege theirs too.)
Some of these communities are more engaged in working ON mathematics
(is that what you mean by 'pure') and others in working 'WITH'
mathematics (is that what we mean by 'applied'?) But as we know,
breakdowns often occur which force us to switch our attention from
the 'with' to the 'on': (I usually cite Leont'ev for bringing this to
attention, but I think I 'knew' of it before I read it n
Leont'ev... hah hah). In addition,almost all pure mathematical
activity can be considered to be 'applied' in the above sense:pure
maths uses itself recursively to build new
knowledge.
However, when a child plays at counting Im not sure I want to call
this 'pure' or 'applied'. And Im not convinced that the 'pure'
version entails 'understanding' while the 'applied' doesnt. Im
thinking of the CAD/CAM worker who uses the command G90 to set the
coordinates back to absolute reference coordinates: the worker may
not 'understand' the subroutine called, but they certainly know
and 'understand' coordinates, and how to use this to programme the
machine intelligently. The application requires a kind of 'external'
understanding of the maths and its relations with other objects,
perhaps without a complete internal understanding of the math, its
relations to its mathematical parts.
Generally the internal and
external understandings go together, and need each other, like the
child who playfully counts, also counts things playfully.
Surely the problem we need to address is the relative 'encapsulation'
of school maths.The child's first playful counting experiences can
too easily be replaced by and undermined by formal school learning
practices. We need to help the two to articulate: the 'street maths'
and the 'school maths' practices need to come to make joint sense.
I suppose most teachers speak some kind of 'school maths' and maybe
'street maths' and maybe some other dialects and genres. Maybe we can
say it would be helpful to pedagogy if we as teachers have a better
understanding of our pupils 'street maths' and 'school maths'.... and
the relations between the two which might help joint articulation
well? what do you think?
'> Date: Tue, 16 Oct 2001 09:25:26 +0100
> Subject: Re(2): ontologic math anxiety
> To: xmca@weber.ucsd.edu
> From: "Martin Owen" <mowen@rem.bangor.ac.uk>
> Reply-to: xmca@weber.ucsd.edu
> xmca@weber.ucsd.edu writes:
> >Shouldn't teachers be expected to actually
> >possess real world skills before they are sent into the classroom?
> But then why should we expect teachers to have had a better experience
> than anyone esle. The real world skill seems to be not very good at
maths.
> Maybe I should re-phrase:
> "the world is full of people who have not had a good experience of
> mathematics"
>
> Martin Owen
> Labordy Dysgu- Learning Lab
> Prifysgol Cymru Bangor- University of Wales, Bangor
>
> "How do you explain school to a higher intelligence?"
>
>
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