Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Some important demonstrations on negative numbers
Replies: 70   Last Post: Dec 8, 2012 1:28 PM

 Messages: [ Previous | Next ]
 Joe Niederberger Posts: 4,657 Registered: 10/12/08
Re: Some important demonstrations on negative numbers
Posted: Nov 30, 2012 6:51 PM

>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_mathematics

I 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.html
http://web.maths.unsw.edu.au/~jim/manifesto.html

Cheers,
Joe N

Date Subject Author
11/27/12 Peter Duveen
11/27/12 James Elander
11/27/12 Robert Hansen
11/27/12 Joe Niederberger
11/27/12 Clyde Greeno @ MALEI
11/27/12 Robert Hansen
11/27/12 Peter Duveen
11/28/12 Robert Hansen
11/27/12 Joe Niederberger
11/27/12 Robert Hansen
11/27/12 Joe Niederberger
11/28/12 Robert Hansen
11/27/12 Joe Niederberger
11/28/12 GS Chandy
11/28/12 GS Chandy
11/28/12 Robert Hansen
11/28/12 Peter Duveen
11/28/12 Robert Hansen
11/28/12 Robert Hansen
11/29/12 kirby urner
11/28/12 Peter Duveen
11/28/12 syeds
11/28/12 GS Chandy
11/28/12 Joe Niederberger
11/28/12 Paul A. Tanner III
11/28/12 Robert Hansen
11/29/12 kirby urner
11/28/12 Joe Niederberger
11/29/12 Paul A. Tanner III
11/28/12 Jonathan J. Crabtree
11/28/12 Joe Niederberger
11/29/12 Robert Hansen
11/28/12 Joe Niederberger
11/29/12 Peter Duveen
11/29/12 Peter Duveen
11/29/12 Joe Niederberger
11/30/12 Robert Hansen
11/29/12 Joe Niederberger
11/29/12 Joe Niederberger
11/29/12 Peter Duveen
11/29/12 Joe Niederberger
11/29/12 Jonathan J. Crabtree
11/29/12 Robert Hansen
11/29/12 Jonathan J. Crabtree
11/30/12 Robert Hansen
11/29/12 Joe Niederberger
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Jonathan J. Crabtree
11/30/12 Robert Hansen
11/30/12 Clyde Greeno @ MALEI
11/30/12 Joe Niederberger
11/30/12 Clyde Greeno @ MALEI
11/30/12 Robert Hansen
12/1/12 Robert Hansen
11/30/12 Robert Hansen
11/30/12 Clyde Greeno
12/1/12 Robert Hansen
11/30/12 Jonathan J. Crabtree
12/1/12 Joe Niederberger
12/1/12 Robert Hansen
12/8/12 Clyde Greeno @ MALEI
12/1/12 Joe Niederberger
12/2/12 Jonathan J. Crabtree
12/2/12 Clyde Greeno @ MALEI
12/3/12 Robert Hansen