FOM: social construction?

[wtait@ix.netcom.com]

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.

>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?

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'?

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