I am teaching a lower level class this year for the first time, and am very surprised at some of my students’ inability to grasp the concept of integers. I had to have them use + and – to visually show integer addition. 3 + -4 would be expressed as +++ and – - – -. Since each pair cancels out, there is one negative left over, and therefore the answer is negative one. We did this for several days, and then moved on to bigger numbers. I thought that the students could visualize 23 – 31 as drawing 23 positives and 31 negatives. Since there are more negative signs, I thought they would be able to understand that there would be some negative signs left over, and that the answer had to come from subtracting the two, which would be -8. But they won’t take the time to think the problem through, nor do they want to take the time to draw so many positive and negative signs to find the correct answer the long way.
At any rate, I do not want to teach the rules (2 positives = positive, 2 negatives = negative, opposite signs = take the absolute value, whichever is greater, that is the sign of the answer then subtract the two). I know that is what they’re doing when they draw positive and negative signs, but if I teach it explicitly in that manner, then the students will confuse those rules with the rules of multiplying and dividing integers when we study that section. Does anyone have any good ideas? I did try the money analogy: -3 + 5 means you owe three dollars, but you have five dollars. Since you always pay off your debt, then you have to give 3 of your dollars to pay off your debt, which leaves you 2 dollars (having money is a positive thing). Likewise, -6 + 2 means you owe six dollars, but you have 2, so you give your two away and you still owe 4 dollars (owing money is a negative thing). Does anyone have any better ideas?
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