Path: utzoo!mnetor!uunet!nbires!hao!husc6!cca!g-rh From: g-rh@cca.CCA.COM (Richard Harter) Newsgroups: comp.edu Subject: Re: Calculators in exams, was: Becoming CAI literate Message-ID: <24997@cca.CCA.COM> Date: 28 Feb 88 00:00:17 GMT References: <2032@ukecc.engr.uky.edu> <3900008@nucsrl.UUCP> <1988Feb24.224849.928@jarvis.csri.toronto.edu> <24954@cca.CCA.COM> <7301@tut.cis.ohio-state.edu> Reply-To: g-rh@CCA.CCA.COM.UUCP (Richard Harter) Distribution: na Organization: Computer Corp. of America, Cambridge, MA Lines: 62 In article <7301@tut.cis.ohio-state.edu> zwicky@pterodactyl.cis.ohio-state.edu (Elizabeth D. Zwicky) writes: > >I also calculate things in my head while people are still fumbling with >calculators. And I had quick arithmetic drills in school. The problem is >that the two are totally unrelated. I failed every single speed drill I >ever took; they regularly reduced me to tears. What gives me my speed is >the non-traditional but simple calculating techniques that I learned >from my mathematician father - you know, the ones they used to fail me >on math tests for using? All those math drills never taught me a thing, >and my husband, who had the drills but not the mathematician at home, >is utterly lousy at "routine mathematical calculations", even though >he likes numbers and I don't. (I stopped letting him calculate tips long >ago, having discovered that he was more often wrong than right. Now I >let him do it again, having dicovered that the reason that he screwed >up was that he was doing cross-multiplication, just like the books have >you do. That gets good scores on tests, because it looks right. I >was moving the decimal place to get 10% and then multiplying that, >which math teachers fail because the intermediate steps aren't "right" >but it sure works.) Interesting. I don't know what they teach in speed drills in school but, from what you say, it's a mistake. What I had in mind was more the sort of thing that your father taught you. I taught myself -- one of my sources was an 1890's handbook of practical calculating. Really. Some of the stuff (quick commercial calculations for example) was totally obsolete, but a lot of it was general, even if the wording was a little quaint. One question -- what did you mean by cross multiplication. To me, this means the following method. Example: 523 469 --- 245287 Steps: 3x9 = 27, write down 7, start 2 as a running sum 2 + 18 + 18 = 38, write down 8, start 3 as a running sum 3 + 45 + 12 + 12 = 72, write down 2, start 7 as a running sum, 7 + 30 + 8 = 45, write down 5, start 4 as a running sum, 4 + 20 = 24, write down 24, done expanded: 3x9 = 27 = 7 carry 2 2 + 2x9 + 6x3 = 38 = 8 carry 3 3 + 9x5 + 6x2 +4x3 = 72 = 2 carry 7 7 + 6x5 + 4x2 = 45 = 5 carry 4 4 + 4x5 = 24 Essentially, this is formal multiplication of polynomials carried out in numbers. If you can running totals in your head, this way of multiplying is actually quite easy -- if the numbers are written down and you can write the answer down. If everything has to be done in your head, it's not so simple because you have to keep track of the answer in your head while you are also running through the partial sums. -- In the fields of Hell where the grass grows high Are the graves of dreams allowed to die. Richard Harter, SMDS Inc.