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!

National Curriculum howler

Oh dear! There are two embarrassing statutory requirements about 'time' in the proposed Key Stage 1 Mathematics curriculum, which have led me to send the following message to the Department for Education:

There are two requirements in the Key Stage 1 Mathematics programmes of study for Measurement for pupils to be taught to 'draw hands on clock faces'. This is totally out of place as a statutory requirement. It might be a teaching device adopted by some teachers, but the objective is surely that children should learn to read the time from the hands on a clock face. My experience is that for many children the drawing of the hands on a clock face is much more difficult than the interpretation of it, so it is not even a good teaching method – because it is harder than the skill being taught! It would be embarrassing for these statutory requirements to remain in our national curriculum. 

While I was about it, I took the opportunity to request one other piece of editing (see my previous posting):

The notes on the Year 2 requirements for Addition and Subtraction state: 'Recording addition and subtraction in columns supports place value ...'. I am not aware of any evidence to support this assertion, although there is evidence to the contrary. Again, it would be an embarrassment for an unsupported assertion such as this to appear in our national curriculum. Please consider removing the words 'supports place value and' from this sentence. It would be acceptable to say that 'Recording addition and subtraction in columns prepares for formal written methods with larger numbers.'