Please Think of the Children

I've recently started teaching KS3 maths (pupils aged 11 - 14) and I must say I'm not a fan of the way probability is taught. For example one practice question is "Alice flips a coin 100 times. How many times would you expect her to get a head?" with the possible answers being 50, 25, or 100. My objection to this is that without the words 'on average' in the question I have no expectation for the result of her trial. The problem can be illustrated without even doing much maths because in order for exactly 50 heads and 50 tails the after the second to last flip their must either be 49 heads or 49 tails and the probability that the next coin flip brings us up to exactly 50 is a half. Doing the maths we find that there is only a 7.96% chance that Alice will actually record 50 heads.

Another question "John and Julie are both strong badminton players. Is it more probable that Julie will beat John in four games out of seven or five games out of nine?" First we must assume that by saying both are strong players that there is a 50:50 chance each will win. When I first saw this question my gut reaction was to say 5 out of 9 because it is closer to the 50:50 average. However, when we do the maths we find that Julie will win 4 out of 7 games 27.3% of the time and 5 out of 9 games only 24.6% of the time.

The question I had the biggest dislike for was "Helen and Christine play noughts and crosses 20 times. Helen wins 12 of the games. Estimate the probability that Christine will win the next game." My objection is not that the sample size isn't large enough to make the estimate from, but rather that they chose the game noughts and crosses, which as I have explained in an earlier entry should always result in a draw, and I would hope that after 20 games the players would have worked this out, so my estimate for winning the next game is 0. This assuming that the dataset is large enough shows up again in the following question "2 netball teams played 10 games. Team A won 2, B won 5 and 3 were draws. If they played 20 games, how many might A win?" With the options being 2, 4, or 10. Ignoring the fact that draws in netball are very rare, and also the lack of information about the victory margins, it is possible for all three of those options to occur, team A might win 2, or 4, or 10 of the next 20 games but answer that gets you the tick is 4 because if they won 2 out of 10 they might win 4 out of 20.

I realise that this post has been a bit different to usual but teaching this maths course has helped me to gain a better understanding of why some people struggle so much with playing risk/reward style games. So please think of the children and teach maths better, otherwise they won't grow up to be world class game players!