Posted: Nov 09, 2021 2:46 am
by don't get me started
Evolving wrote:I once encountered an interesting example of the difference between the scientific and the normal use of language, when my eldest daughter was doing a maths exercise and was asked whether a particular statement "was true" ("stimmt"). The statement was numerically close to the correct statement, so she wrote "es stimmt fast" (it's almost true). Since it was a maths exercise, this was, naturally, marked wrong.

This brings to mind a chapter in a book I read some while back. (See reference below).

It is well known that in mundane spoken interactions speakers often prefer to use vague expressions for numbers, times, amounts, etc.

'Oh, I dunno, like ten, fifteen, something like that.'

'Yeah, I should be there about sevenish.'

'It's probably gonna cost around 3,000 yen.'

It is assumed that in mathematics, precision is the key and vagueness is to be avoided. However, in the research carried out by Rowland, it seems to be the case that in mathematics classrooms, vagueness is a key interactional resource. Rowland quotes a pamphlet (pp. 17-18) by the Association of Teachers of mathematics. (p.79)

"Because it is a tolerant medium, everyday language is necessarily ambiguous... Now, mathematising is also a form of action in the world. And its expressions, however carefully defined, have to retain a fundamental tolerance...Because it is a tolerant medium, mathematics is also necessarily and ambiguous one."

Rowland goes on to note,

"As a 'product' (polished, final), mathematics may be presented, particularly in writing but also in speech, as though it lacked ambiguity, representing truths about the world - or at the very least, about itself - in a sure, exact and unequivocal kind of way. By contrast the 'process' of mathematics production (mathematising) is characterized by a number of forms of vagueness." (p.80)

The rest of Rowland's chapter gave detailed accounts of how language is used in 'Mathematising'. (The title of the chapter says it all, really.)

Rowland, T. (2007). Well maybe not exactly, but it's around fifty basically? Vague language in mathematics classrooms. In J. Cutting. (Ed.), Vague language explored. Plagrave. (pp. 79-96.)

Once again, the mismatch between language use in science and daily life is highlighted.