# Re: [xmca] a minus times a plus

Related to the question, we have a recent publication in the Journal of the Learning Sciences. Watch the question in red. Following Husserl, we can see in the analysis the objective, transcendental nature of mathematics emerge from the embodied, sequentially ordered talk that makes the lessons. Michael
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The Emergence of 3D Geometry from Children’s (Teacher-Guided) Classification Tasks
```Wolff-Michael Roth & Jennifer S. Thom
University of Victoria

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Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the work of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the planned outcome of the curriculum or lesson. The fundamental question of the present study therefore is this: How can a lesson in which children are asked to participate in a task of classifying regular three-dimensional objects be a geometry lesson given that the participating second-grade children do not yet classify according to geometrical properties (predicates)? In our analyses, which have been inspired by ethnomethodological studies of work, we focus on the embodied and collective work that leads to the emergence of the geometrical nature of this lesson. Thus, we report both the collective and the individual work by means of which the lesson outcomes—the complete classification of a set of “mystery” objects according to geometrical (shape) rather than other properties (color, size, “pointy-ness”)—are achieved. In the process, our study shows how geometrical work is reproduced by second-grade children who, in a division of labor with their teachers, produce a particular set of geometrical practices (sorting 3D objects according to their geometrical properties) for the first time.
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On 29-Apr-09, at 9:22 AM, Ng Foo Keong wrote:

Is Mathematics _merely_ socially constructed, or is there something
deeper and inevitable?

I think this deserves a new thread, but I couldn't manage to start one.
Let me try to draw out and assemble the line of discussion that spun
off from the "a minus times a plus" thread.

In her inaugural post to xcma, Anna Sfard about talked "rules
of the mathematical game" among other things.

Then Jay Lemke said:-
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```...
I think it's important, however, to see, as Anna emphasizes,
that there is a certain "arbitrariness" involved in this, or
if you like it better: a freedom of choice. Yes, it's
structure-and-agency all over again! Structure determines that
some things fit into bigger pictures and some don't, but
agency is always at work deciding which pictures, which kind
of fit, which structures, etc. And behind that values, and
culture, and how we feel about things.
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Then I (Ng Foo Keong) said:-

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```regarding structure and agency, arbitrariness:-
i think now it's time for me to pop this question that has been
bugging me for some time.  i am convinced that mathematics is
socially constructured, but i am not so convinced that mathematics
is _merely_ socially constructured.  if we vary across cultures
and different human activities, we might find different ways
in which patterns and structure can be expressed and yet we might
find commonalities / analogies.  the question i am asking is:
is maths just a ball game determined by some group of nerds who
happen to be in power and dominate the discourse, or is there some
invariant, something deeper in maths that can transcend and unite
language, culture, activity .... ?
```
```
Foo Keong,
NIE, Singapore

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Then Ed Wall said:-

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```Ng Foo Keong
constructed, I'm not entirely sure what you mean by
mathematics or what kind of evidence would convince you it wasn't.
Suppose I said that there was evidence for innate subtizing.
```
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