Some of the meaning of a word comes from its sound when pronounced -- and some of the meaning in a number comes from its visible "shape."
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Replying to @MathPrinceps @WriterobinRS
I've stressed that numbers are like words, and the metaphor continues: mathematics is like language, its masterpieces like great narratives.
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Replying to @MathPrinceps @WriterobinRS
Unfortunately, mathematics education aims to teach the written language of mathematics before its students have learned the spoken language.
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Replying to @MathPrinceps @WriterobinRS
Learning a new abstract system of symbolic representation in order to write the words of a language you do not speak is naturally very hard.
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Replying to @MathPrinceps @WriterobinRS
We wait until children have extensive experience of spoken language before we try to teach them to read and write. By then, they're eager.
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Replying to @MathPrinceps @WriterobinRS
To a child of five or six, reading and writing are like magical superpowers. The desire to wield them independently of adults is tremendous.
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Replying to @MathPrinceps @WriterobinRS
The desire to master an abstract symbolic system of representation must spring from a vivid, personal appreciation of its power and utility.
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Replying to @MathPrinceps @WriterobinRS
Such an appreciation can only come from extensive experience with the phenomena it was meant to make amenable to analysis and preservation.
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Replying to @MathPrinceps @WriterobinRS
But very few students of mathematics have an extensive experience of mathematical phenomena before we begin to teach technique & notations.
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Replying to @MathPrinceps @WriterobinRS
Ms Swicord, if you are as yet unacquainted with Paul Lockhart's MATHEMATICIAN'S LAMENT, I certainly recommend it: http://bit.ly/1iaLh2Q
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Among the things we must do, it seems to me, is to make more of the elegant fascination of numbers and their language immediately visible.
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Replying to @MathPrinceps @WriterobinRS
And then expose our students to these striking, immediately perceptible mathematical stimuli. Once they're fascinated, then we teach them.
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Replying to @MathPrinceps @WriterobinRS
This is a profoundly important point: all successful pedagogy is seduction. Only a smitten student can give to the art all that it requires.
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