Through a Linkedin discussion I came across an interesting blog offering an advice of how to handle the situation where "words have different meanings in academic subjects than they have in everyday language." There is a couple of nice examples:
... reducing a fraction to lowest terms has no effect on its value (e.g., 6/8 = 3/4). And where we borrow a "1" when subtracting even though we're not going to return it.
I absolutely agree with the notion that changing the terminology is not a solution and
might create more confusion than it prevents, since students are sure to encounter the confusing language in various resources and other classes.
So rather than replace confusing words, be sure to proactively discuss with students how their meanings in your class are different from their meanings in other contexts.
One issue I think that is worth being emphasized is that potential confusion due to different meanings the words have is not restricted to mathematics. It is encountered in every field of human endeavors and even in everyday, common language - as such. Even the concept that ""words have different meanings in academic subjects than they have in everyday language" presupposes that words have definitive meaning in everyday language. Some words do but many don't. For example, the word "number" appears in practically unrelated contexts:
- The crowd was small in number.
- David Copperfield's number was the pinnacle of the show.
- The South had leaders, the North numbers.
- The suspects will do their usual number - protesting innocence - and then confess.
- Mosquitoes without number filled the yard.
Two books with similar titles have been published in 1996:
- Christa Brelin (Editor), Strength in Numbers : A Lesbian, Gay and Bisexual Resource, 1996
- Sherman K. Stein, Strength in Numbers : Discovering the Joy and Power of Mathematics in Everyday Life, 1996
In his Mathematician Reads a Newspaper, John Allen Paulos gives a superb demonstration of the inherent ambiguity built into the common language:
You write to ask me for my opinion of X, who has applied for a position in your department. I cannot recommend him too highly nor say enough good things about him. There is no other student of mine with whom I can adequately compare him. His thesis is the sort of work you don't expect to see nowadays and in it he has clearly demonstrated his complete capabilities. The amount of material he knows will surprise you. You will indeed be fortunate if you can get him to work for you.
Not that long ago, English speaking people in the US and elsewhere were treated to a question of the meaning of word IS. Naturally, in mathematics the meaning of that word is rather dependent on the context.
As a follow-up to the advice to "be sure to proactively discuss with students how their meanings in your class are different from their meanings in other contexts," I would suggest that a general introduction into equivocal nature of spoken languages might sharpen students appreciation of an exceptional accuracy of the language used in mathematics. The fact that communication in mathematics employs many words borrowed from the everyday language does not affect that fact, even though those words in mathematical discourse may have meanings different from the common ones - whatever that may mean.
As every other language, mathematical language has to be learned in order to be used effectively.
- J. A. Paulos, A Mathematician Reads The Newspaper, Anchor Books, 1995