1202579308:::Mike Hardy:::hardy@math.umn.edu::::::Putting too much credence in a correctly functioning calculator is also a dumb mistake that it can be hard to talk students out of. A very simple example: Suppose you want to multiply

(14/3) * 13 * 6.

A student divides 14 by 3, gets 4.6666... with the "6" repeating.

(A calculator will usually not tell you that the "6" repeats forever, but there is an easy way to tell by doing long division by hand---just the thing that students using a calculator as an anesthetic want to avoid.)

Now say the student rounds this answer to 4.66, then multiplies by 13 and then by 6. He gets 363.948. When you write three digits after the decimal point, it's supposed to mean that the answer is either exact or rounded to the nearest thousandth.

But now notice that the "3" and the "6" cancel each other so that you get

14 * 13 * 2.

With _NO_ fractions. If one can multiply integers the way I was expect to do in elementary school, one need not actually do so in order to know that there will be nothing after the decimal point. One quickly gets 364. Now in some cases the bottom line is supposed to answer the question "How many...?", and that in itself ought to make anyone suspicious, to say the least, of "363.938".

Stuff like this happens. 1202642849:::Adrian Hester:::adrhester@yahoo.com::::::"Putting too much credence in a correctly functioning calculator is also a dumb mistake that it can be hard to talk students out of."

Heh.

http://www.xkcd.com/217/ 1202859674:::John Dailey:::Phyrm_1@hotmail.com::::::~ I remember reading 2 decades ago an article by I. Asimov about the 'new' calculators replacing slide rules; their ease-of-use resulted in too many discovering that way too often users found themselves 'automatically' (in the midst of an ongoing calculating problem) wasting time by dividing 9 by 1, adding 3 plus 8, or multiplying 231 by 0, via their being 'machine-mesmerized' into mere button pushing.

~ This sounds like an advancement on that retrogression of letting a machine do one's 'thinking' for one.

~ Electronic machines are great...until one UNthinkingly accepts that they can do one's thinking for one. -- All users should 'think twice' about presented results which even slightly raise a suspicion-'flag', yet, are counted upon.

LLAP
J:D