I was a little surprised at the length of the comment thread in the post about the logic puzzle involving the monk Gaito going up and down a hill. On the one hand, I thought that there were some excellent explanations of why there had to be at least one instant where the monk was at the same location at the same time. These involved visualizing the situation in slightly different ways, such as instead of having one monk go up and down on two different days, having two monks going up and down on the same day or using graphs or films and so on.
But clearly these arguments were not persuasive enough for some and I have been trying to think why this might be so. In my teaching experience, it is often the case that what seems obvious to you as a teacher is by no means so to the student. It is no use repeating the same explanation more slowly or (worse) more loudly or (much worse) exasperatedly. There is clearly some opposing argument that the student finds persuasive that makes them reject your argument and yet they may not be able to identify and articulate what it is. Instead they feel that there must be some flaw in your reasoning that they cannot put their finger on. It is more fruitful as a teacher to try and figure out what their argument might be, rather than reiterating your own.
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