I would add to what Jim says to highlight differences in such definitions between Maths syllabuses in different countries..... On 4 Feb 2014, at 22:59, James Propp wrote:
Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college. I'm sure there's a lot of variety here, with some students for instance thinking that squares aren't rectangles and others thinking that they are rectangles, and of course some thinking that 1 is prime and others thinking that it isn't. It could double as a book for first year college students, too, I guess, though I suspect that the two target audiences are sufficiently different that two different books are called for.
Jim Propp
On Tuesday, February 4, 2014, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
I'm sorry to boggle about a non-essential part of this anecdote, but was the "million dollar question" really list the factors of 6? Or was that a small part of a larger, more interesting question? It is really hard to believe a question so simple (but apparently not so straightforward) was really the apex of a struggle for 1 million dollars...
(Incidentally, about the "factor" vs. "divisor" question: when I was in elementary school factor and "proper divisor" interchangeably referred to integers that divided a number "equally", while "prime factor" meant exactly what you'd expect. (Divisor without any qualifier (just like dividend and quotient) could be *any* number --- well, other than 0).)
On 2014-02-04 10:22, Bill Gosper wrote:
I just failed to Google up any outrage over an infuriating TV quiz show I mistakenly watched several years ago. The contestant, (former astronaut Rusty Schweikart?) sailed right through to the million dollar question without even using his two "lifelines(?)", and then was sent home penniless for not listing 1 among the "factors" of 6. I wonder if, had he mentioned 1, they would have screwed him for confusing "factors" with "divisors".
Anyway, ("drill and kill") Saxon Math is apparently using "factor" to mean divisor, presumably because it has fewer syllables:
"Write the factors of 10 that are also factors of 15."
Sounds like they are expecting a "factor" of 1. (I should've checked if they think 1 is a prime.)
In the same assignment,
"Divide 20/9 <x-apple-data-detectors://4>. Write the quotient as a fraction." "Divide and write the quotient as a fraction: 25/6<x-apple-data-detectors://5> "
It would probably be less harmful if they signaled their intent with gestures and whistles, as in canine obedience school.
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