Absolute confusion
(Don't) [Fence] {Me In}
My prealgebra students were confused. It is their natural state. On this occasion, they were having an unhappy time with notation. What was the deal with all of these grouping symbols—parentheses, brackets, braces—and what are they for? I pointed out that it was customary in writing mathematical expressions to use difference “fences” when indicating groupings within groupings. If an expression already contains parentheses, one might choose to use brackets to indicate any higher level of grouping; for example,
[4(x + 5)]2,
in preference to
(4(x + 5))2.
I wrote the usual symbols up on the board: ordinary curved parentheses (), square brackets [], and the less common (except for set notation) curly braces {}.
Not all of the students were satisfied. One wanted to know the difference between −|−5| and −(−5). Why had I simplified the first expression as −5 and the second as 5? I reminded the class that the vertical bars were the absolute value symbol and had to be taken into account, while the parentheses were used for clarity rather than for functional purposes in the second expression (not, of course, that I phrased it in quite that way).
My perplexed student seemed to grasp the point, which she tried to confirm by rephrasing my remark, thus feeding me an irresistible gag line:
“So it's different when you're inside straight bars?”
“Well, certainly different from being inside gay bars.”
Ha!
