```Date: Nov 30, 2012 6:51 PM
Author: Joe Niederberger
Subject: Re: Some important demonstrations on negative numbers

>Joe, numbers are not quantities. Quantities are physical, they include a number, a unit, a direction, if needed, and for goodness sake, a freaking context. My goodness. I was speaking of the good old world, as Dickens might say, not your personal universe.Here is Isaac Newton:"Algebraic quantities are of two sorts, affirmative and negative; an affirmative quantity is greater than nothing, and is known by this sign +; a negative quantity is less than nothing, and is known by this sign -."He follows up with a money example.Here is Euler:"The calculation of imaginary quantities is of the greatest importance."Lest you think taking number as "quantity" is merely archaic usage, check these:* http://oxforddictionaries.com/definition/english/mathematics* http://dictionary.reference.com/browse/mathematics?s=t&ld=1122* http://en.wikipedia.org/wiki/Mathematics* http://en.wikipedia.org/wiki/Quantity#Quantity_in_mathematicsI understand the distinction you are pointing to, though; nice as it is, it doesn't seem particularly germane in this context, that of understanding negative numbers and their rules.Saying that a negative number "is a mathematical concept" (well, by golly, its abstract!) does nothing to explain what it is. How are they different from the whole numbers a child already knows about? What good are they? Why are the rules (esp. the infamous one) such as they are?What's your lesson look like? What are the key points for a child?R.H. says:>Mathematics deals only with the number part of all that.And which part is that? Does your concept of number include separable components as well? What makes a real number real, but an imaginary number a figment of the imagination?And now, just for fun, some people who want to get real about math:http://web.maths.unsw.edu.au/~jim/structmath.htmlhttp://web.maths.unsw.edu.au/~jim/manifesto.htmlCheers,Joe N
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