A recent tweet, by the author and mathematician Rob Eastaway, requested important non-sporting occurrences of coin tossing. I got a little carried away and, half an hour of internetary later, had found a whole gaggle of stories, mostly very sad tales where the toss of a coin meant that another person subsequently died. Some were partly expected as in which soldier should make the trip across no-man’s-land to get a message through or the selection of aircrew for a particular mission or team. Other less so such as the presence of the young new star Ritchie Valens on the fatal flight with Buddy Holly and others.
Whilst rather less prosaic or life changing, I was reminded of the section on coin tossing in Ivars Petersen’s excellent book, Jungles of Randomness. Here, he writes about the human mind’s weakness with regard to likelihood of outcomes and particularly the probability of repeated events such as a series of just heads or just tails when tossing a coin. He shows the data in a number of different ways and I have used these ideas in lessons when dealing with probability. His main assertions are that when generating a random sequence, people are reluctant to go beyond five consecutive repeat events such as five heads or tails in a row but that in reality relatively small data sets are likely to produce significantly longer sequences.
One of the joys of teaching children at the ages of around 11 or 12 is that they are sufficiently developed intellectually, and mathematically, to tackle reasonably complex concepts that they have never come across or considered in an academic way before: genuine tabulae rasae (see, my Latin O-level wasn’t a waste of time after all!). So, when asked to pretend to be a coin and “flip themselves” a hundred times and write down the sequence of results, they have no preconception of what the task is about or where it might be leading, and so just get on and do it. I normally segue straight into doing the practical equivalent at that point so that they have not had the opportunity to do some analysis of the first set of data and start to make suppositions that might affect how they carry out the coin tossing. I do however take sufficient time to discuss ways of cheating and how one should generate a fair set of results.
[Down side with 11 or 12 year old boys doing this activity is that the word tossing can cause giggles; I try to use the word flip more often than not, and the worksheet is deliberately mis-spelt as Toin Cossing, a Spoonerism that the nice Mr Eastaway mentioned in a subsequent tweet].
After a little careful explaining, the pupils then convert their sequences into tally charts, showing how many of each length of sequence occurred. I then collate the class’ data into a larger spreadsheet; this gives a good opportunity to discuss validity and sample size. As with any experiment that pupils carry out there is the possibility of statistical anomalies outweighing the general tenor of the data. In the main I have found that the data produced support Petersen’s suggestions. Also that the children are initially surprised by the difference between the two sets of data but then able to discuss and explain why the discrepancy occurs and indeed might be expected.
This sort of experimentation is somewhat topical with criticisms of school science currently in the media, such as this article in the Grauniad. Here, however, the children genuinely discover things for themselves that they would not normally be taught or find out in class or at home. Being presented with the data will not have a worthwhile impact unless they have carried out this investigation themselves first otherwise the results may be quietly disbelieved or ignored by the pupils; cynicism is alive and well even at the age of eleven!