YESS-4Laurindareadablel_b

YESS-4Laurindareadablel_b - Observing systems how do we see...

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Observing systems – how do we see what we see? Laurinda Brown University of Bristol Graduate School of Education
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I KNOW YOU BELIEVE YOU UNDERSTAND WHAT YOU THINK I SAID, BUT I AM NOT SURE, YOU REALISE, THAT WHAT YOU HEARD , IS NOT WHAT I MEANT
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What takes your attention? - There were some counterexamples to that. Remind me what that is. ~ One that does not fit the conjecture. - OK, Ben has done something very mathematical. He’s gone back and looked again and changed it [the conjecture]. ~ [Later in the same lesson.] All two digit numbers will add up to 99. [David’s conjecture is written on the board.] ~ I’ve got another counterexample to Ben’s. - This is how mathematicians work; are there counterexamples? Are two conjectures actually linked and so on.
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Bigger questions, questions with more than one answer, questions without an answer are harder to cope with in silence. Once asked they do not evaporate and leave the mind to its serener musings. Once asked they gain dimension and texture, trip you on the stairs, wake you at night-time. (Jeanette Winterson, Written on the body , Vintage, 1993)
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What is learning? How do we do it? So, what should I do as a teacher? (particularly teaching mathematics – another thing that keeps me awake nights and as a mathematics teacher educator)
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conscious thought is the tip of an enormous iceberg. It is the rule of thumb among cognitive scientists that unconscious thought is 95 per cent of all thought and that may be a serious underestimate. Moreover, the 95 per cent below the surface of conscious awareness shapes and structures all conscious thought (Lakoff and Johnson, 1999:13)
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Every living being categorizes. Even the amoeba categorizes the things it encounters into food or non-food, what it moves toward or moves away from . .. We have evolved to categorize, if we hadn’t, we would not have survived. Categorization is, for the most part, not a product of conscious reasoning. We categorize as we do because we have the brains and bodies we have and because we interact with the world in the way we do (Lakoff and Johnson, 1999:18).
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Minds make motions, and they must make them fast - before the predator catches you, before your prey gets away from you. Minds are not disembodied logical reasoning devices (Clark, 1997, p. 1).
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This note was uploaded on 11/11/2011 for the course MATH 220 taught by Professor Kearn during the Fall '11 term at BYU.

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YESS-4Laurindareadablel_b - Observing systems how do we see...

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