(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!
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5 comments:
I have to admit, that notation would give me pause, too. I knew the rule, but it's been a long time since my last math class, while I use these symbols every day in computer programming -- where parentheses, brackets and curly braces all have distinct meanings.
I once got marked down in a science lab when I wrote an expression something like: f(x) = (2+x)*(3+y) / (4*(5+z)), rather than with more traditional mathy syntax. It was the same formula as what other people had, but I think the TA simply didn't grok the syntax. The programmer notation is so intuitive to me that I didn't realize why I had been marked wrong until a non-programmer friend asked me what the equation meant.
One of the kindest features of Excel (and the Vim development environment, and many others)is the coloring of parentheses pairs. As my eyes get older, parentheses, brackets, and braces increasingly start to resemble each other, but I can still tell red from blue.
I suspect fairly few of Zeno's students can claim my excuse, though.
But brackets and curly braces take so long to write! I much prefer having ten thousand layers of parentheses, with outside layers successively larger in size than inside layers.
That's a horrible joke, btw.
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