Educational Algebra: A Theoretical and Empirical Approach by Eugenio Filloy

By Eugenio Filloy

This publication takes a theoretical standpoint at the examine of college algebra, during which either semiotics and heritage take place. The Methodological layout makes it possible for the translation of particular phenomena and the inclusion of facts no longer addressed in additional normal remedies. The e-book supplies precedence to "meaning in use" over "formal meaning". those ways and others of comparable nature bring about a spotlight on competence instead of a user’s job with mathematical language.

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Educational Algebra: A Theoretical and Empirical Approach (Mathematics Education Library)

This e-book takes a theoretical standpoint at the learn of college algebra, within which either semiotics and heritage take place. The Methodological layout permits the translation of particular phenomena and the inclusion of facts now not addressed in additional normal remedies. The ebook provides precedence to "meaning in use" over "formal meaning".

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Extra info for Educational Algebra: A Theoretical and Empirical Approach (Mathematics Education Library)

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Raymond Duval, on the other hand, in his book Sémiosis et Pensée Humaine. Registres sémiotiques et apprentissages intellectuels (Duval, 1995), tackles the subject of learning in mathematics from a semiotic perspective, based on the relationship between semiosis (apprehension or production of a semiotic representation) and noesis (cognitive acts such as conceptual apprehension, understanding of inferences or discrimination of differences). Duval emphasizes the role of this relationship in the cognitive functioning of thinking and in its implications for the learning of mathematics and the native language.

Consequently, this viewpoint not only includes the central role of formal grammar, but also recognizes that it should be incorporated in a broader framework that combines formal and functional explanations. In other words, that in order to interpret the complete meaning of some mathematical messages during normal teaching/learning processes, alongside the strictly formal meaning of the mathematical text in question we also have to admit some other meanings of certain other (logical) messages that are not explicitly communicated either by the sender or by the receiver.

To begin, we point out four characteristics. The first characteristic is the fact that a theoretical model consists of a set of assumptions about some concept or system. First, it is necessary to distinguish theoretical models from diagrams, illustrations, or physical models, which, although sometimes useful to represent the model, must not be identified with the model itself. Second, it is true that at times, albeit not always, what is called a model is also termed a theory. This interchangeability of names is possible because, in such cases, the terms “model” and “theory” refer to the same set of assumptions, although the same things are not suggested about this set when we call it a model as when we call it a theory.

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