I don't want to hijack this thread, but I've been puzzled by the supposed need to decide whether mathematics is 'objective' or whether it is a 'social convention.' One of my pet peeves about the way that people - both lay and academics - talk about 'social construction' is that it is assumed that what has been socially constructed is insubstantial, maleable. 'Oh, gender is just a social construction!' as though this implies that we can change it tomorrow if we want to. Introducing the term 'convention' seems to me to make matters worse, because we all 'know' that a 'convention' is, well, merely conventional.
Surely we live in a social world in which there are many things that have been socially constructed - I would prefer to say socially constituted - and that as a consequence are objective, that is to say actual, matters of fact. It is a fact that Obama is US president, but this is equally a social construction. Want to change that fact? A whole lot of work - social work - is needed to do so.
The same with mathematics, I would suggest. Math is a social construction. And as a result it is objective. Math has a history: it has been constructed in different ways at different times. At each point is has been a matter of fact. Different cultures have invented different mathematics, each of which has been a matter of fact for that culture.
It seems to me that we need to stop opposing what is 'social' to what is 'objective.'
On Nov 6, 2014, at 1:10 AM, anna sfard <firstname.lastname@example.org> wrote:
I have not been aware of this super-interesting (for me) thread, and now, when I eventually noticed it, I cannot chime in properly. So I am doing this improperly, simply by attaching my own paper. Those who are interested enough to open the attachment will see the relevance of its theme to the present conversation. And although I mention Davydov only in an endnote, he is very much present. The theses I'm arguing for seem to substantiate his request for taking the quantitative discourse, rather than the numerical, as a point of departure for the process of developing child's mathematical thinking (we cannot help it, but in our society, these two discourses appear in the child's life separately and more or less in parallel, with the quantitative discourse free from numbers and the numerical one innocent of any connection to quantities; at a certain point, these two discourses coalescence, thus giving rise to the incipient mathematical discourse; but at the pre-mathematical
From: email@example.com [mailto:firstname.lastname@example.org] On Behalf Of HENRY SHONERD
Sent: Thursday, November 06, 2014 3:11 AM
To: eXtended Mind, Culture, Activity
Subject: [Xmca-l] Re: Objectivity of mathematics
Ed and Andy,
Just a little while ago, while I was finishing the Moxhay paper, which seems to have produced an AHA! moment” regarding object-mediated action for Andy, I had my own AHA! moment, and it is this:
Some years ago, after teaching Intro to Linguistics many times, I decided that the most important property of human language that clearly sets it apart from what we know about other species’ ability to communicate is what is called DISPLACEMENT: the ability to use language to refer to things removed from the here and now, including imaginary happenings or things. The Davydov tasks in the Moxhay article give children the same problem of displacement by requiring that they figure a way to compare two objects removed from one another in space, and, effectively, in time. And I am wondering if this touches on the other threads I have been following: L2 and the Blommmaert/Silverstein. Does the need for standardization in measurement of the objects in the world today find its way into L2 teaching and language policy? The blending of qualitative and quantitative research methods come to mind, to my mind at least. Moxhay’s article ended with a comparison of Classroom A and B th