Anne D Cockburn on the difficulties young children face understanding the workings of clocks.
Why is it that few four-year olds can tell the time and few adults can't? The mathematical nature of the concept of time presents cognitive problems:
* Time is not a single concept - at a minimum it can pass and it can be told.
* Telling the time involves a range of bases (none of them 10), 60 seconds in a minute and 60 minutes in an hour but 24 hours in a day and seven days in a week.
* It requires a knowledge of fractions - which can be tricky for young children just getting to grips with halves and quarters.
Potential psychological problems also exist:
* Time is a highly abstract concept that cannot be touched. It can - you could argue - be seen. But how can you explain how 20 minutes watching your favourite television programme seemingly passes far more quickly than 20 minutes in a dentist's chair?
* Young children have limited experience of time passing - although they may have been living for six years they can probably remember only half of them.
* Analogue clocks require the reading of two pointers rather than just one, as with measurement of length. Then there is the perennial problem of remembering whether the minute hand is pointing to or past.
Finally, common experiences:
* "In a second" and "in a minute" are common phrases - but how often do we mean them literally? "In a couple of minutes" in practice means five or 10.
* Young children rarely need to tell the time - it is done for them, with waking, going to school, mealtimes and so on.
* Sometimes props for teaching time may confuse. For example, hands-on model clocks do not move unless we move them, and teachers may not remember to nudge the hour hand on a little when they move the minute hand. Thinking about mathematical concepts in terms of the problems that might pop up when teaching them encourages consideration of ways to reduce the likelihood of those difficulties occurring.
For example, awareness that the experience of time passing can vary dramatically according to what you are doing can become an issue of amusement and challenge for children.
And knowing about the potential problems of dealing with two-handed clocks and the difficulties of "past" and "to" could lead to the introduction of a one-handed hour clock and discussions of whether the hand is just past the three, nearer to the four or half-way between.
With the introduction of the Numeracy Hour and pressure on schedules, this proactive approach to likely errors is increasingly attractive. In time, of course, someone may well attempt to analyse the school mathematics curriculum in terms of potential problems and possible solutions, with clear explanations as to why it is more difficult to teach time than addition or length. Then teachers will be key devisers of solutions unique to the problems of each individual and class.
Anne D Cockburn lectures at the School of Education and Professional Development, University of East Anglia, Norwich and is the author of 'Teaching Mathematics with Insight: the identification, diagnosis and remediation of young children's mathematical errors'