Symbols and Meanings in School Mathematics by David Pimm PDF

By David Pimm

ISBN-10: 0203296117

ISBN-13: 9780203296110

ISBN-10: 0203428617

ISBN-13: 9780203428610

ISBN-10: 0415113857

ISBN-13: 9780415113854

Symbols and Meanings in class Mathematics explores some of the makes use of and elements of symbols in class arithmetic and in addition examines the proposal of mathematical which means. it really is all in favour of the facility of language which allows us to do arithmetic, giving us the facility to call and rename, to rework names and to take advantage of names and outlines to conjure, converse and regulate our pictures. it really is within the interaction among language, picture and item that arithmetic is created and will be communicated to others. The publication additionally addresses a suite of questions of specific relevance to the decade of the 20th century, which come up because of the proliferation of machines providing mathematical functioning.

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An alternative view holds that mathematics is human and hence only inside our minds. We therefore need to place it onto the world, rather than finding it there. Curiously, Euclid, besides being a Greek geometer, also developed a theory of vision, according to which light rays emanated from the eye, striking the object, and that was how we were able to see them. Seeing involves projection. Paralleling this highly mathematical view of vision, it is in this same active sense that we see mathematics in the world, namely that we project mathematical forms onto it.

Caleb Gattegno’s (1974) intensive and inventive work with young children forming number complements on their hands draws extensively on precisely this dynamic control over folding fingers up and down. But what are the fingers doing in this case? Are they acting as substitutes of some sort. For what? Whatever else, forming complements is something that children can do. They can work with their fingers, and at the same time encounter multiplicity and equivalence (the myriad ways of showing four or seven, for instance), the reciprocal nature of stressing and ignoring (turning fingers up into fingers down and conversely produces the complement), the condensation of number naming as well as its uniformity (choose a unit for the fingers).

How does a touch triangle differ from a sight one? Lastly, having to use words alone may focus attention on the need and usefulness of having words for certain characteristics of a shape, allowing a teacher to seed the discussion with them, without the words themselves necessarily being the main focus of the class. A secondary-level lesson on angles involved each pupil using a pair of straws joined with a pipe-cleaner to represent angles. This improvised physical apparatus afforded tangibility, movement, and continuous change.

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Symbols and Meanings in School Mathematics by David Pimm

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