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Romashka comments on Open Thread, January 4-10, 2016 - Less Wrong Discussion
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Teaching subtraction:
'See, you had five apples, and you ate three. How many apples do you have?' 'Five.' 'No, look here, you only have two left. Okay, you had six apples, and ate four, how many apples do you have now?' 'Five.' 'No, dear, look here... Okay...' Sigh. 'Mom?' 'Yes, dear?' 'And if I have many apples, and I eat many, how many do I have left?..'
Piagets problem: The child tries to guess what the teacher/parent/questioner wants.
I never teach math. At least not in the school way of offering problems and asking questions about them. For example I 'tought' subtraction the following way:
(in the kitchen)
Me: "Please give me six potatoes." Him: "1, 2, 3" Me (putting them in the pot): "How many do we still need?" Him: "4, 5, 6" (thinking) "3 more."
A specific situation avoids guessing the password.