The only problem is that the latter calculation requires that students do old-fashioned "long division" whereby they end up with a quotient and a remainder -- NOT a fraction, NOT a decimal value, but two whole numbers. Needless to say, calculators do not do this correctly!! Does that stop students from trying to use their calculator? You tell me...
I'm used to that, and I am normally perfectly happy to give those students a whole lot of rope with which to hang themselves. But last week produced a shocker:
Ditzy Dana (up to my desk for the third time, the first being only two minutes after the problem was handed out to say "I'm so CONFUSED!!"): Is this right?
Professor SnarkyGeekChick: No, it's not. How did you get that answer?
Ditzy Dana: I did what you told me!
Professor SnarkyGeekChick: It doesn't look like it. Check your arithmetic. You should have both a quotient and a remainder here.
Ditzy Dana: But that's the answer the calculator gave me, see? *shows calculation on fancy graphing calculator*
Professor SnarkyGeekChick: Um, you can't use a calculator for this; it doesn't give you a remainder for division. Your answer shouldn't have the .5 in it, it should be a whole number *still incredulous that she has to use the term "whole number" instead of "integer" for college students*
Ditzy Dana: But that IS the remainder!!
Professor SnarkyGeekChick: Nooooo, it isn't. *looks sideways at Visiting Evil Minions to see if they are hearing the same words she is*
Ditzy Dana: You mean POINT FIVE isn't the SAME THING as a remainder of FIVE?
Visiting Evil Minion #1: *insufficiently smothered explosive snicker*
Visiting Evil Minion #2: Not unless you're dividing by 10, which you aren't!
Professor SnarkyGeekChick: *rendered speechless, thinks to herself "fifth grade, damn it, fifth grade" *
Visiting Evil Minion #1: *muttered aside* I knew I saw her not paying attention...
Ditzy Dana: *flounces away in a ditzy huff*
And my math colleagues wonder why I think the pervasive use of calculators in the teaching of mathematics is an Abomination From Hell...