teaching the concept of negative numbers

Below zero temperatures might work.

Have you used number lines? That would be my approach.

Nancy

A long long time ago I posted some long and detailed outlines on teaching negative numbers. If you search under victoria, victoriah, or negative, or signed numbers, you may be able to find the posts (three or four of them). If you can’t find them, maybe some nice person has saved them. I’m still having computer hassles, but as a last resort email me at [email protected] and I’ll see if I can get the outlines to you.

I was tortured all the way from grade 1 to grade 12, in every math classroom….now, 35 years later, I found out what was wrong with me. Now I can answer when somebody says, what’s wrong with you ? why can’t you figure that out? Are you stupid? You just don’t try hard enough! you aren’t paying attemtion! Stop daydreaming and listen.
Nope not add, dyscalculia. It’s real and real horrible. I was 30 before I finally understood that negative numbers were on the left, the “wrong hand” side, thus negative in themselves, then I met a bookkeeper, who fixed it all. She explained that negative numbers are what you owe out, what you already spent. I can make change but I can’t count the back to you. Just give me a paper bag and I can and will get lost in it. Still have no way to remember my west from my south, etc. I know the NEWS thing but it doesn’t work for me. I can do simple geometry and basic math if I study really hard but after that I am lost, I cannot remember the formulas or the order of the processes. The best I ever did in that was to recall that in the order of operations you always do what;s in the parenthisis first? wait now I seem to have forgotten…not joking. Rats, that was one I knew for a long time, oh well, gone now.
I’m 48 and I still have a huge fear of numbers, I will do many things to avoid interacting with them.
One of the MOST IMPORTANT things to remember, for teachers, is never raise your voice one little bit and don’t hover over the kids at their desks like a monster, that IS how it feels. I had a basketball coach for my junior year math, he screamed and yelled at me like he did his players…so I, being a little smarty pants anyway, gave it back in spades and we went through the year like that. He never put me out of the room but I know he despised me. And no man was going to speak at me like that and see me sit still and be quiet or dominated….I’d have rather died right there. I learned one thing from him, I totally hated math.
Somebody needs to tell me why there is such a need to force this on kids who can’t manage it. Test them and give them a calculator to go through life with so they can be normal.

I collected strategies & approaches for negative numbers and put them here:
http://www.resourceroom.net/math/integers.asp

Thermometers, sea level, football fields, number lines, mineshafts, tides and tidewater marks, bank accounts, credit and debt, even lost sheep—they’re the negatives—and sheep that are not lost. Visually, graduated cylinders or measuring cups of water, or koolaid or fruit juice for colour.

What I found most beneficial is: 1. simplify the number of rules, 2. get integer rules all in one place (i.e. a recipe card easily tucked in between pages), and 3. practice saying the rules being used out loud or explaining which rule used was chosen or how it was used.

We synthesized the rules down to five:
1. Zero is not negative or positive
2. Addition:
* If the signs are the same, that is the sign of the
answer. Then you really add.
* If the signs are different, the sign of the biggest
number is the sign of the answer. Then you really
subtract. This is where it begins to boggle their minds!
3. Subtraction: use which ever wording works:
-Add the opposite value (7 - (-4) becomes 7 + (+4))
Then follow the adding rules.
-Change the sign of the number being subtracted and the minus sign to a plus. Then follow the adding rules
Either way, the operation sign changes to addition and the sign of the subtrahend changes.
4. When multiplying or dividing two integers, if there is
only one negative sign, the answer is negative.
Otherwise, it’s positive.

Don’t teach the rules by symbols (i.e - + - = -, - x - = +) Students try to memorize symbols only, and I can guarantee confusion between addition and multiplication rules. Use words.

Teach guidelines:
1. Read the question—properly! -5 - (-7) should be read as negative 5 minus (or take away) negative 7, NOT minus 5 negative minus seven or some such combination. It really helps!
2. Determine the operation and sign symbols.
3. Determine the rule that applies.
4. Determine the answer’s sign.
5. Calculate.

I never found a concrete example for division. After some research, I found a mathematician who stated that it doesn’t make “practical sense”, but works in a mathematical context. I use the fact that division is a reverse of multiplication. If -2 x 6 = -12, then when you divide -12 by 6, the answer has to be negative because 2 x 6 gives a positive 12. Or use the underline symbol for division and cancelling. To divide -12 by -6, write -12/-6 (vertically— not a slash / ) and you can see negative signs cancel.

For most integer questions, it’s easier to determine an answer’s sign first. An exception is addition and subtraction of signed fractions. Then determine common denominators before determining the answer’s sign.

Practice one set of rules until it is being used comfortably before you introduce a new one; then after practicing the new rule, combine the two. Sometimes they are OK until you mix them up, and that underlines the importance of discerning the operation to be done and which rule applies first.