Understanding in Mathematics - download pdf or read online

By Anna Sierpinska

ISBN-10: 0750703342

ISBN-13: 9780750703345

The idea that of knowing in arithmetic with reference to arithmetic schooling is taken into account during this quantity. the most challenge for arithmetic academics being how you can facilitate their scholars' knowing of the maths being taught. In combining components of maths, philosophy, good judgment, linguistics and the psychology of maths schooling from her personal and eu study, Dr Sierpinska considers the contributions of the social and cultural contexts to knowing. the end result is an perception into either arithmetic and knowing.

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Anna Sierpinska's Understanding in Mathematics PDF

The idea that of knowing in arithmetic in regards to arithmetic schooling is taken into account during this quantity. the most challenge for arithmetic academics being the way to facilitate their scholars' figuring out of the math being taught. In combining components of maths, philosophy, common sense, linguistics and the psychology of maths schooling from her personal and ecu study, Dr Sierpinska considers the contributions of the social and cultural contexts to realizing.

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The skeptical historicist goes further than that. He argues— to return to our previous analogy—that a natural speaker of English has to understand a Greek text in English rather than in Greek. He converts the plausible idea that the mastery of unfamiliar meanings is arduous and uncertain into the idea that we always have to impose our own alien conventions and associations. But this is simply not true. If we do not construe a text in what we rightly or wrongly assume to be its own terms then we do not construe it at all.

And this, Wittgenstein remarks, would not be an answer to a question, but a grammatical statement. ’ is a sensible question—the word ‘length’ would be used in it according to its grammar. Wittgenstein was against looking at language as a calculus proceeding according to strict rules (The Blue Book, p. 25). It is only in mathematics, he would say, that the meaning of terms can be given by a set of defining criteria. In the practice of ordinary life and language we recognize things and give them 17 Understanding in Mathematics names on the basis of ‘symptoms’ rather than definitions.

But lesser men, raising the same question and finding no answer, would very likely commit suicide or join the Church. ’ the effects are less serious, amounting only to the writing of books). (Austin, ibidem, p. ’ were of this less serious kind. I wrote the pages below. What Has Meaning? There are a few ‘grammatical’ questions that one can ask about any predicate like ‘has meaning’. The first is ‘what is it that has meaning’? To this, the most natural answer seems to be ‘the sign’. If anything has meaning, it is a sign.

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Understanding in Mathematics by Anna Sierpinska


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