From Mike Freeman
You quote Gerd Gigerenzer saying that children need to be taught uncertainty as well as the certainty of mathematics (12 December 2015, p 30). While developing my book The Doubtful Realities, I proposed a teacher able to answer arithmetic questions only with a question mark or a cross. To the question “what is 9 × 9?”, the answer 81 would get a “?”. The answers 18 and 80 would both get “x”; they are both wrong. But are they equally wrong?
When I put this question to people, I was surprised to find that their responses divided evenly across the three possible answers. To some it is a daft question: 18 and 80 are both wrong and that is an end to it. To others, 18 is the least wrong – perhaps the digits were inadvertently reversed or the person mistook a multiplication sign for an addition sign.
To another group 80 is better because it is closer to the right answer. It seems that only a third of people had a feel for approximation. I therefore disagree with Gigerenzer’s thinking that it isn’t difficult to teach uncertainty – it is very difficult to counter certainty with uncertainty.
One example is climate change deniers refusing to accept the idea of warming due to uncertainties about the specifics. The clash between science and religious certainty is another. Too often, to our shame, we try to use scientific certainty even when it isn’t there.
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Most of the time, science has only the answer 80 rather than 81 – but at least it generally knows how to get to closer answers.
Denbigh, UK
