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My question is about the reading "negative five" sometimes used for $-5$, instead of "minus five."

It's a follow-up to this question: "Negative" versus "Minus"

Putting together all the answers given there, it seems that the original reading of $-5$ was "minus five," but sometime in the 1960s there was a trend in math education to start saying "negative five" instead, supposedly in the belief that it better distinguished the unary operation from the binary one in "$8-5$." Based on the answers, it seems this trend never caught on in the U.K. and Ireland, but it did in the United States, to such an extent that "negative five" now strongly predominates among the younger generations in the U.S. Nothing is said in the answers about other English-speaking countries, such as Canada or Australia.

My question is: How did this trend originate? Was there a specific, identifiable proposal made at some point that was particularly influential, or did the change spread "organically," so to speak? Which textbooks were most responsible for popularizing this phraseology in U.S. schools?

If there are any well-researched articles that discuss this issue from a historical perspective, I'd appreciate a reference.

Incidentally, I am Canadian and was born in the 1970s, and I had never encountered anything like "negative five" until I started teaching people born in the 1990s.

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user404961
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    Interesting question! It's on-topic here (IMO at least), but you may have better luck at Math Educators SE. – pjs36 Jan 07 '17 at 19:56
  • ... or "history of Science and Mathematics". I am french and we still not have this second notation (we say "moins 5" and not "negatif 5"), although the 1970s' big turmoil in secondary school mathematics teaching here has brought a lot of oddities, maybe even more than in the US system... – Jean Marie Jan 07 '17 at 20:15
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    A remark: I had one professor who insisted on saying "minus" instead of "negative." At first I found it funny, but it really makes more sense to say "minus," esp. if you're dealing with abstract concepts (which choice of square root of $-1$ is negative?). I think pedagogically it can also be helpful, as reading "$-$" as "negative" can be confusing, especially when it comes to something like $-x$, where $x$ is an indeterminate. I've had more than a few students who were confused by signs when writing something like that when $x$ itself is less than $0$ (esp. when dealing with absolute values). – Stahl Jan 08 '17 at 01:07

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Two good places to look would be the texts produced by the School Mathematics Study Group (SMSG) under Edward Begle and those produced by the University of Illinois Committee on School Mathematics under Max Beberman. Fifty-plus years ago I had copies of both, but I got rid of them in a move many years ago and can’t check them myself, and I fear that they may be hard to come by. I do clearly remember, however, that at least one of them made quite a point of the difference between unary and binary minus, writing ${^-4}$ for the additive inverse of $4$ and writing the binary operation in the usual way, e.g. $3-4={^-1}$.

Both series actually saw some use in schools. The Illinois project got an earlier start, but I have the impression that the SMSG books were used more widely and had more influence.

Brian M. Scott
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