Download Understanding in Mathematics by Anna Sierpinska PDF

By Anna Sierpinska

The concept that of figuring out in arithmetic with reference to arithmetic schooling is taken into account during this quantity. the most challenge for arithmetic academics being tips to facilitate their scholars' knowing of the math being taught. In combining parts of maths, philosophy, common sense, linguistics and the psychology of maths schooling from her personal and ecu learn, Dr Sierpinska considers the contributions of the social and cultural contexts to figuring out. the end result is an perception into either arithmetic and realizing.

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He would speak of the ‘grammar of an expression’ as of the rules that govern the use of it. Some sentences are grammatical, some are not: in learning to distinguish this, we learn the meanings of words in a language. ’ 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.

Instead of seeming beautiful, profound or brilliant, the work seemed misguided, trivial, and false, and its meaning was no longer one that the author wished to convey. However, these examples do not show that the meaning of the work has changed, but precisely the opposite. If the work’s meaning had changed (instead of the author himself and his attitudes) then the author would not have needed to repudiate his meaning and could have spared himself the discomfort of a public recantation. No doubt the significance of the work to the author had changed a great deal, but its meaning had not changed at all.

If understanding a sentence is knowing the conditions of its truth, do we also have to know whether these conditions are fulfilled? There has been a suggestion to extend the Frege-style approach to meaning in such a way that understanding be distinct from cognition (Danto, 1969). Suppose truth is considered as but one class of ‘positive semantic values’, and sentences but one class of ‘semantic vehicles’, while the ‘descriptive meaning’ of a semantic vehicle is a rule that specifies the conditions under which this semantic vehicle bears a positive semantic value.

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