![]() ![]() What’s the opposite of “the opposite of happy”? What does make sense is a slight variant, less catchy but far more true: “The opposite of the opposite is just the thing itself.” In fact, “two negatives make a positive” doesn’t really make much sense anywhere. ![]() In fact, that’s one of my major complaints with “two negatives make a positive”: it is such a swift, over-arching generalization that students wind up applying it in places where it doesn’t make much sense. It’s not even true with negative numbers, where -10 + -30 does NOT equal +40 (although I have seen students claim that it does, citing “two negatives make a positive” as their justification). Rain on your wedding day plus grand larceny on your wedding day does not make for a winning combination, despite what “two negatives make a positive” would suggest. We can all think of many, many cases where two negatives don’t make a positive. “Two negatives make a positive” is one of those math slogans that drives me crazy, because it is so pithy, so memorable, so easy to apply… while also being so vague and non-mathematical that I’m amazed students find it useful at all. Then, if you listen carefully, you will hear something else: the low rumble of my teeth grinding together with tectonic force. They all know, for example, that 5 – (-2) = 7. ![]() My 6th- and 7th-grade students are pretty effective at calculating with negative numbers. ![]()
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