I was never taught how to take a cube root using a method that emulates long division, but I was taught how to take a square root. However, I am quite sure that given a pencil and paper, I could take a cube root using a Taylor expansion.
Having said that, I believe that kids use calculators at far too young an age - by the age of 8, 40% of children are using calculator! How many even understand decimals and the four basic functions at that age. Could this (along with non-metrication) be one of the reasons for the decline in numeracy in the UK. I cannot comment about the US - I do not have any experience of the US education system. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of James Frysinger Sent: 26 July 2008 18:47 To: U.S. Metric Association Subject: [USMA:41504] RE: Your sixty second lecture -- Down with fractions! Traditionally, the teaching of fractions in handling numbers provides the basis for handling fractions in algebra. All sorts of techniques carry over. This follows the Piaget line of reasoning of working from the concrete to the abstract. Some examples: 2/3 + 2/5 = 10/15 + 6/15 = 16/15 a/x + b/y = ay/xy + bx/xy = (ay + bx)/xy 4 3/5 = 20/5 + 3/5 = 23/5 x + a/y = xy/y + a/y = (xy + a)/y (2/3)/(3/4) = (2 x 4)/(3 x 3) = 8/9 (a/x)/(b/y) = ay/bx I have even taught "long division" in algebra by first reviewing "long division" with numbers. Recently I heard a horror story of public school systems no longer teaching long division of numbers. Argh! I am sadly certain that public schools no longer teach how to take square roots and cube roots of numbers by the method emulating long division! And as for checking one's arithmetic by casting out nines.... Jim Martin Vlietstra wrote: > Fractions DO have a role - in algebra when one is manipulating symbols, > but I agree with Pat, they do not have a role when one is manipulating > numbers. .... -- James R. Frysinger 632 Stony Point Mountain Road Doyle, TN 38559-3030 (H) 931.657.3107 (C) 931.212.0267
