## Monday, 5 August 2013

### Zero hours

Another example of how a mathematical phrase can have more than one meaning has emerged in recent days.

For me the phrase 'zero hours' usually referred to a time of day, midnight, in the 24-hour clock system. But then in the press recently there has been coverage of the problems of employees with a 'zero hours' contract; that is, a contract that does not guarantee any hours work in any given week. Same words, but indicating two very different ideas, using the two different meanings of 'time': (1) a time of day, recorded time, indicating a particular instant, the answer to the question, 'Have you got the time, please?' and (2) a time interval, the amount of time that has passed, answering the question, 'How long did it take?'

This is an example of one of the reasons why learning mathematics is so difficult: that the same words or symbols we use are often connected to very different situations. Young children learning about number encounter this first when a number like 3 (three) is connected sometimes to a set of three things (for example, three children, three fingers, three sweets), but also connected to one thing that is labelled 3 because of its position (a house numbered 3, 3 on a number strip, Year 3, 3 August - and, indeed, 3 o'clock.) These are technically called the cardinal and ordinal aspects of number.

Zero is a particularly difficult concept because of its different meanings. Sometimes it means 'nothing', in the sense of an absence of something. A 'zero hours' contract is an absence of hours of work. Other occasions zero does not mean 'nothing', as in referring to midnight as 'zero hours'. Time does not disappear at 'zero hours', just as the temperature does not disappear at zero degrees!