Does anyone have any good resources for my 12 dd who is a gifted dyslexic going into Honors Algebra next year? Her class started the Algebra book the last quarter of this school year & she is doing okay except for the whole concept of positive & negative integers. She just cannot wrap her brain around it. She also has difficulty when someone tells her to move to the left or right, so I'm not entirely surprised. But I've tried a number of different methods of explaining (I'm an Algebra teacher) & she is going to her teacher for tutoring. But she is so frustrated!!! And I hate to see her like this.
Thanks!

Hi ginger234
I know your daughter's pain - I was not diagnosed until college when matricies became my downfall - rows and rows of numbers, it was horrible. And while I am great at navigating from maps, I often say right while pointing left - my body gets it correct - I meant left but said right. So frustrating to know what you mean and get it wrong anyway or to not get it because your brain just goes a different way!

So I am so glad that you and she are able to identify what the trouble is and seek help for it! That said I only have a teensy bit of help which someone here offered on some other thread - or maybe it was in the Basher math book I got for my son - not sure but anyway - think of an apartment building. The lobby is zero, all the positive numbers are the floors up - the basement, subbasement, cellar, etc are the negative numbers, the floors down below the lobby. Might help with the brain wrapping - operationalizing of course will be another story.

HTH

DeHe

I wonder if she has seen the explanation used in Jacob's Algebra, where the positive numbers are particles and the negative numbers are anti-particles. It isn't directional, and might not confuse her as much.

My financially-minded but spatially-challenged kiddos grasped the concept of negative numbers as debts or bills and positive numbers as assets. This made the rules about signed operations a little more intuitive for them: taking away a debt naturally means that you are adding to the money you keep, for example. I've also seen students use the concepts of ladders and holes, with the zero point being ground level, too. A vertical number line might be more helpful for grasping this concept than one oriented horizontally. Presenting it this way ties in with talking about numbers being "higher" or "lower", which she is probably already familiar with.

HTH

Ditto on ground level-- I was going to suggest sea level! Anything that lets her consider the negative numbers as simply numbers on the same old number line, instead of instances of some new strange thing opposed to numbers somehow, may help.

My son is getting his first regular math instruction now, but when I initially assessed him some time ago to see how much math he intuitively knew at the time, I was able to teach him about negative numbers within several minutes. The way I did it back then was to start explaining about how zero (which he already knew) was like the other integers he knew, just one point in the middle of the infinite continuum of numbers. I made a simple hand-drawn paper widget with a horizontal number line, with some positive numbers labeled above the line in green, and the corresponding negative integers labeled in red below the line. I also labeled the back of the positive side and negative side. Then I cut out the top half of the left-hand negative side; cut out the bottom half of the right-hand positive side; and folded the paper vertically down the middle, so that the positive side could flop behind the negative side and vice versa.

I then explained to him how negative numbers were opposites of positive numbers, to the extent that they'd cancel each other out if added together (the flopping demonstrated this concept neatly, so that he was able to also see how the left over bit after an uneven cancellation would be the new non-zero result). I showed him how easy subtraction was too, by just thinking of it as distance between two points on the number line.

With that demonstration he picked it up quickly, definitely in less than 2 minutes, to the point of being able to do simple arithmetic in his head with positive and negative integers. The demonstration and explanation just clicked with him. (He has his share of conceptual foibles, so I don't know how well this particular demo would work with other kids yet. I had my reservations afterward about focusing him too much on a particular mental model that might not be the best, but I was in the moment at the time.)

I don't know if your DD plays the piano or not, but when I was a kid I always thought of middle C as zero, and anything to the right of that was a positive number and anything to the left of that was a negative number. I also thought of the white keys as whole numbers and the black keys as decimals or fractions (although looking at it now, obviously the black keys don't have an exact correlation to fractions or decimals). Anyway, it was just the way my mind made sense of negative numbers when I was a kid. I really like the sea-level and ground-level explanations others have mentioned.

Does it help to imagine a magical land where the king's just loves the number 34, and now all of his frustrated subjects must refer to everything in relation to this favorite number, such as:

I have 34 plus 12 sheep.
I have 34 minus 30 children.
I am getting married in 34 plus 100 days.

In a way, Zero is sort of arbitrary, and we all may as well be using 34.

I also wonder how she is with sense of time. I sort of think of my body as a number line, with zero near my left ear, and the positive numbers streaming foward into the future, and the negative numbers streaming back in time. I learned in a ASL class that the sign for the past was to push air behind the left ear, and made the connection. So in this scheme, today is Zero, tomorrow is One, and yesterday is Negative one. Of course, I'm terrible with time, so this wouldn't help me at all!


Smiles,
Grinity

I feel as though you're getting a lot of ideas here and not much in the way of resources, but resources are a bit tricky without knowing more about what your DD needs. You could try Murderous Maths: The Phantom X, although she might find it a bit childish if she's not into its rather cartoonish humour. Or, going to the other extreme, you could consider getting her a university textbook on introductory algebra (as you may know, algebra really means something quite different at university level than at school level, but a possible approach is to go deeper to understand the school stuff - sometimes it's the school's "just don't worry about that dear" that actually makes things hard). I love Cohn's Algebra Volume 1 (and 2 :-); his Classic Algebra seems to be essentially the same book; neither seems to be readily available as new printings, but there are lots of second-hand copies around.

One thing that I think might be confusing about negative numbers, especially for someone inclined to think deeply, is that there are two really quite different things going on: the ordering ... -2 < -1 < 0 < 1 ... and the addition, i.e. that -n is defined to be the thing which, when you add it to n, gives 0. You DD probably doesn't want to go quite as far as Euclidean domains but you never know! At least, it might help to let her know that there is deep theory associated with this stuff: if anyone is telling her things should be obvious and she thinks they aren't, she may well be the one who is right.

Thank you all...so many great ideas! I never expected this many replies! And some things I honestly have never thought of before. I will be able to use some with my students as well as with my daughter! I'll post again to let you know how things progress; for now I wanted to say THANKS!
Oh, so true!

DD was able to make it to the end of the year and made an A in her math class. I really think the pace was too fast for an introduction to Algebra. She memorized the rules for -/+ integers & their operations so that she could do the work; I told her that it would eventually make sense. One explanation that helped some (besides all these GREAT ideas--thanks again!) was to think of the negative sign as "the opposite of" whatever operation is given. So 3*-(-4) would be "three times the opposite of negative four, or three times positive four." It might break down as an effective process eventually, but by then I think she will have had a light bulb moment & not need it any more.