So....here I am driving down the road and thinking about how we learn to count and when different number concepts were incorporated into arithmetic and mathematics. Which gets me to negative numbers. You can conceptualize the natural numbers and fractions (rational numbers), but how do you conceptualize a negative number? When numbers are thought of as quantities, what is a negative quantity? Any ideas out there?

If you have some uncontrollable desire to read about Peano's axioms, there is a good description here at Wikipedia.

## 10 comments:

"how do you conceptualize a negative number?"

"I owe you $10".

Harvey - Do you need my address to mail the $10?

After I finished laughing over the $10, I realized that's how I see it too - as something that is being "taken away" or "owed".

Hmmmm...

Nell - I suspect that most people see negative numbers in the way you do and it's a good way of visualizing negatives.

Mathematically, they're simply integers less than zero, an extension to the set of natural numbers in order to allow equations like x - y = z to have meaningful solutions for all values of x and y.

(Wikipedia http://en.wikipedia.org/wiki/Negative_and_non-negative_numbers)

I guess those darn mathematicians just had to try and make it more difficult for students to understand the concept. *bg*

Oddly enough I have always visualized it on a ruler or number line if you prefer with 0 in the middle and the positives on the right and negatives on the left. But really I don't actually "think" too much about them - so far as I'm concerned... they just "are". You do a mathmatical formula and end up in the negative numbers... do a different one and end up positive. (You know this is much harder to explain than it is to simply accept *grin*)

Teresa - I have the number line mental model. I wonder if this is a result of studying math? Might make an interesting research question. hmmmmm......

Future Master's Thesis?... Doctoral Dissertation? LOL!

Why does everyone suggest master's thesis or doctoral dissertation everytime I ask a question? Sheesh

I'm more like Teresa, I see charts and graphs in my head with negatives and postives. I think this has something to do with classes I took in college(That you continue to give me flashbacks to, and not the good kind!).

As for the thesis, I think it's just due to the nature of the question. Most people I've met don't think in math.

I tend to visualize negative numbers along a numberline, too. Mostly because that's how they were first presented to me in school.

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