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Re: How teaching factors rather than multiplicand & multiplier confuses kids!
Posted:
Nov 13, 2012 8:29 AM
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On Nov 13, 2012, at 2:48 AM, Clyde Greeno @ MALEI <greeno@malei.org> wrote:
> Within that context, I often use the phrase, "common sense" to exploit *one* lay meaning for that phrase: "Anyone who knows [such and such] ought to be able to 'see' that [so and so]." In THAT meaning, "common sense" is about the natural processes of human *thinking* ... rather than referring to what they think about or what they already know. It also is about how all humans are heavily dependent on learning, through personal reasoning.
Semantics aside, you need to now provide us examples of reasoning. You provided many examples of "common sense", the commonly known version, otherwise known as concrete examples. Now all you need to do is show us how you move past that and into formal reasoning.
Btw, when we show a graph of two linear functions interesting, anyone knows that the two lines cross. This is the problem with "anyone who knows such and such..." We are on the same page regarding the meaning of common sense. However, this isn't an indication of actual reasoning. An indication of actual reasoning is, actual reasoning.
Bob Hansen
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