# It should be you;Mathematics;Subject of the week

It is somewhat alarming that the recently published Numeracy Framework has omitted the topic of probability from key stage 2. Probability has gone from a three-part objective in the national curriculum to a bare mention of the word, totally unsupported by the identification of concepts or suggested activities.

One would hope that any decisions about changes to the national curriculum would be based on a review of current mathematics research. If this were so, then the findings of several recent studies in England, Australia and the United States should have prevented the omission of probability from the Numeracy Framework and, maybe, the curriculum after 2000.

There are several strong arguments that demand the inclusion of probability in a modern primary maths curriculum. The thrust of these is that developing "normal" mathematical reasoning does not lead to the development of probabilistic reasoning. Indeed, it can be detrimental, as revealed in a study of students aged 10 to 14 that I have been conducting with Dr Paul Ayres from the University of Western Sydney.

When asked to explain their reasons for making various decisions during probability tasks, many students said that they were looking for patterns to follow. Looking for patterns is of course useful in most mathematics but misleading in probability. Unlike other mathematical thinking, reasoning in probability does not produce a guaranteed conclusion. Randomness prohibits pattern.

The problem is not that probability concepts are too difficult for young children to understand, but rather that they need assistance to integrate the separate concepts that combine in probability. These separate concepts, such as randomness, impossibility, ordering of likelihood, fractions and proportion develop naturally, but in most children will never fully develop without appropriate education.

Strikingly, our study also demonstrated that the 13 and 14-year-olds, who had received no instruction in probability, performed no better than the 10 and 11-year-olds.

A major finding of another research project I have been involved in through the University of Western Sydney and Cambridge University, using in-depth interviews of 74 children aged 5 to 12, was that the optimum age for probability education is around 9 or 10. This is the age when the children have intuitively developed the individual probability concepts, have acquired the supporting number skills and display a readiness to respond to instruction.

Professor Graham Jones and his colleagues from the University of Illinois have demonstrated the benefit that a small amount of systematic instruction can have on the development of probabilistic reasoning of children aged around 8 or 9.

All this research has shown that without appropriate instruction, probability intuitions lead to misconceptions which persist into adulthood and are then extremely difficult to correct. As there is little modern mathematics that does not require the application of probability theory, this has serious consequences for students intending to study medicine, engineering and psychology.

However, the impact of inadequate understanding of basic probability ideas is not limited to this relatively small proportion of the population. We are constantly making choices, the wisdom of which depends on our ability to assess possibilities. In a single day the probability skills we need could range from interpreting a weather report to making a large financial decision for the family.

Unfortunately, there are times when the public is misled by mathematically absurd information. For example, sometimes the televised National Lottery draw includes the computer-generated statistics on the frequency of numbers appearing in previous draws, with the implication that this might help people choose winning numbers next time. To make use of this information you would have to believe that the numbered balls could somehow demand that they had their rightful turn in the next draw.

Key stage 2 is the optimum time to teach probability. Are we going to miss this chance and disadvantage future citizens?

Jenni Way is lecturer in mathematics education at the University of Western Sydney

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