Our regular feature highlighting an article or research paper that will, we hope, have a helpful bearing on your teaching of mathematics
In this issue we consider Children's understandings of probability: a literature review by Peter Bryant and Terezinha Nunes.
The paper first identifies four "cognitive demands" that pupils need to understand in order to make sense of probability in mathematics, and then explores how these areas are taught in school. They are:
- Understanding randomness: to understand the nature and the consequences of randomness, and the use of randomness in our everyday lives.
- Working out the sample space: to recognise that the first and essential step in solving any probability problem is to work out all the possible events and sequences of events that could happen. The set of all the possible events is called ‘the sample space’ and working out the sample space is not just a necessary part of the calculation of the probabilities of particular event, but also an essential element in understanding the nature of probability.
- Comparing and quantifying probabilities: probabilities are quantities based on proportions, and one has to calculate these proportions to make most (but not all) comparisons of the probabilities of two or more events. These proportions can be expressed as decimals, as fractions or as ratios.
- Understanding correlation (or relationships between events): an association between two kinds of event could happen randomly or, alternatively, could represent a genuine relationship. To discover whether there is a non-random relation or not, we have to attend to the relation between confirming and disconfirming evidence and check whether the frequency of confirming cases could have happened by chance.
You can read a longer and more detailed version of this report, which is also available to download.
We think that, having read this paper, you will have a deeper understanding of why some pupils find probability difficult, and also have some ideas how to respond to this in order to help your pupils develop more secure conceptual understanding and procedural fluency. Let us know what you think.
And if your pupils find this xkcd cartoon as funny as we do, then you know you’ve taught them well!