Ditto on ground level-- I was going to suggest sea level! smile 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.)


Striving to increase my rate of flow, and fight forum gloopiness. sick