The Nuffield Foundation have recently released the result of their Childrens understanding of probability: an intervention study. When I was doing the Widening Participation Award at Manchester University I developed and gave a probability workshop to lots of primary school kids. I was interested to read what the Nuffield lot had found out.
They talk about 4 "cognitive demands": Understanding randomness, working out the sample space, comparing and quantifying probability, understanding correlation.
They believe that fairness, which kids have a better grasp of, could be used to teach randomness.
They highlight the common mistake of thinking that the opposite of the previous event will occur next, which they call `negative recency’. I've never heard this phrase before. They also called the opposite of this- believing the same outcome will occur, the hot-hand fallacy/positive recency. Adults and kids make these 2 types of mistakes in different proportions.
They refer to "aggregation" with the example of suming 2 dice throws. Generally this is a case of a function of multiple events which modfies the probabilities and is often not intuitive.
They think about how a child considers all of the sample space as all of the possible outcomes imaging all future states. Of course, there can only actually be one so these are hyperthetic, counterfactual, "other worlds". That is, this is in essence a philosophic thought experiment and not necessarily a trivial exercise.
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