There are a lot of misconceptions around negative numbers (see this post) and I sometimes wonder if this is down to confusion caused by the language we use when describing a number that is below zero. I know some maths teachers interchange between calling something negative or minus depending on the situation or the mood they are in. Outside of the maths classroom, the word “minus” is used frequently and almost always when describing temperature. Is it correct though?
I put a poll on Twitter to try and find out what other maths teachers think and the results were surprising for me. More than half of the teachers, it seems, have a different view to me..
Maths teachers: How do you say the number “-5”?
— Mo Ladak (@MathedUp) January 24, 2017
I know that I can be a bit pedantic but I argue that we should always use the word “negative” when we are describing a number below zero. For me it is a case of opposites. When talking about operations, the opposite of “add” is “subtract”. When talking about the operators themselves, then the opposite of “plus” is “minus”. So when talking about the property of a number, then the opposite of “positive” has to be “negative”.
So why does it matter? I find that there are many barriers to understanding the fundamentals of mathematics that stem from the language we use. An example is the fact that we say “half”, “third” and “quarter” rather that “twoth”, “threeth” and “fourth” when talking about fractions (all the other unit fractions seem to follow a more intuitive logic). I’m not sure if other languages have similar barriers so would love for anyone to let me know..
Anyway, when it comes to negative numbers, I have found that even some of the best mathematicians I’ve taught get themselves into a pickle with unhelpful phrases such as “two minuses make a plus” and struggle with the misconceptions this brings. It is much more useful, in my experience, to be able to separate the language and always use the words “positive” and “negative” to highlight a property that belongs to a number and add/plus or subtract/minus as an operation that we apply to a number. Being clear and consistent with the language removes this barrier and allows students to concentrate on getting to grips with the conceptual understanding.
Do you agree/disagree? Have you been convinced? Please comment below to let me know..