FOM: social construction?

[Lincoln Wallen]

   Lincon Wallen (22/3)
   >Focus on the word "investigate" here.  In fact, an anthropologically
   >inspired view of langauge use and learning gives just this sort of
   >account of how we learn our native language: By observing the effects
   >our utterances have on the people around us we learn the meaning of
   >the utterances.  This type of "use and observation" seems good enough
   >to call "investigation" to me.
   If I focus on the word ``investigation'', I note that it is usually used 
   to refer to the case in which one is bringing to bear certain tools or 
   skills one already has. First language learning is not like that. 
   Learning a second language in the sense of learning to translate is.

I know what you mean here.  "Experiment" might be better here, but
that is a form of investigation.  Looking at my 2.5 year old son(!) I
would say that the tools one brings to bear begin as observations
about action which are gradually developed into associations with
words.  We get our students to calculate first, then teach them more
about the things they are manipulating.  The interplay between action
on paper and mathematical thought/reflection is on e of the areas
which bears further scrutiny in my opinion.

   >As a tutor of mathematics students one of the most important tasks is
   >to *react* to their mathematical utterances (marking, arguing etc) and
   >so provide a framework in which they can conduct similar
   >investigations.  In this way students learn to "speak" in the peculiar
   >way that enables them to do mathematics.
   The first sentence is about the tutor, not the student. But in ``similar 
   investigations'', I need to ask for clarification: similar to what?

Similar to the tutor.  The first sentence is about the tutor, but in a
conversation or exhange of ideas/scripts the behaviour of the tutor is
important, as is the behaviour of a fellow conversant in any
interative situation.

   As to the last sentence, maybe I need some clarification here too: Is 
   ``learn to `speak' in a peculiar way that enables them to do 
   mathematics'' the same as `learn to do mathematics'?

No.  But a major part of doing mathematics is communicating your
thoughts; to yourself as well as to others.  Other activities are
writing, calculating, drawing, correcting, elaborating, exemplifying,
modelling (not all distinct of course).

   I think that the first step and indispensible step in understanding what 
   math is is to learn some math---unless one is the anthropologist 
   investigating an alien culture. That kind of learning is primarily (as it 
   seems to me) obtaining a competence---learning to do things. The second 
   step will depend on picking out one of the many possible meanings of 
   ``what math is'' or `the nature of math''.

   Bill Tait 

I agree in the most part.  Again the point is that the anthropologist
is taking advantage of the fact that we articulate, to a certain
extent, our purposes and methods as we interact with each other
wihtint he profession. By observing these interactions some structure
of the practice can be discerned.  The depth of what is revealed
certainly will depend on the degree to which the anthropologist is a
mathematician.

Lincoln Wallen