I don't know of any research on this question specific to learning about mathematics. But the question opens up a big can of academic worms, outside of mathematics.
In linguistics, the Whorf hypothesis (sometimes called the Sapir-Whorf hypothesis) can be summarized as the notion that different peoples have different languages (syntax, lexicon, etc..), and these differences influence how they think about things. For example, different languages have different tenses available for use -- does this affect how speakers perceive time?
So, I'd say to start by looking up the Whorf hypothesis -- maybe it's been considered by some applied linguists studying education.
The other linguistic can of worms is the use of metaphor in mathematical language. Some words we use are directly visual, like "smooth" and "compact", some are strange (to me) analogies like "sheaf" and "flabby", and others are part of larger metaphorical systems like "consider a variety over a finite field" (the use of the positional word "over", to express dependence like a building resting on its foundation).
If you want to read up on these aspects of mathematical language, I'd recommend books by the Berkeley linguist Lakoff -- the classic "Metaphors we live by", and the application to mathematics in "Where mathematics comes from". Not that I agree with everything in the latter book, but it's an interesting read. I don't think you can address your question seriously without reviewing the linguistics literature.
No comments:
Post a Comment