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Educational Algebra: A Theoretical and Empirical Approach by Eugenio Filloy

By Eugenio Filloy

This booklet takes a theoretical point of view at the learn of faculty algebra, during which either semiotics and heritage ensue. The Methodological layout allows the translation of particular phenomena and the inclusion of proof now not addressed in additional basic remedies. The ebook offers 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 task with mathematical language.

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

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6 We remark that Fibonacci’s Liber Abaci (L. E. Sigler, 2002) is one of the most famous of this collection of books. 3. CHAPTER 2 CURRICULUM DESIGN AND DEVELOPMENT FOR STUDENTS, TEACHERS, AND RESEARCHERS OVERVIEW We first suggest that it is necessary to make the conception of the nature of mathematics explicit, as it underlies curriculum organization and curriculum development, and show some of the risks that appear when this is not done. Section 2 explains what we understand by theoretical model through four basic characteristics, distinguishing it from other uses of the same term, and then introducing the methodological concept of the local theoretical model (LTM) and its four interrelated components.

This example points to the kind of semantic antecedents of the MSSs used by 12- to 14-year old students, which are the foundations upon which their algebraic language skills must be developed. It is there that open expressions, for instance, will denote new mathematical objects at a higher level of generality, involving more general concepts such as that of generalized number (a and b in a + b) and that of suspended operation (the addition in a + b). 5. ALGEBRA AS A LANGUAGE: APPROACHES FROM LINGUISTIC, SEMIOTIC, AND HISTORICAL PERSPECTIVES In this section, we review several works on mathematical language and language and mathematics that are especially relevant to the issues raised and analyzed in this book.

We content ourselves with calling on the reader’s intuitive concepts concerning terms such as semantics, syntax, semantic load, a more concrete or more abstract level of language, and of the reading level of a text. Even though one consequence of the interpretations obtained in the corresponding empirical studies — described later in the book— is precisely the fact that many of the mistakes that are usually made when using new expressions come from the anticipatory mechanisms of the individual who is decoding a situation that needs to be modeled in that mathematical sign system (MSS), where the semantic load — the custom of certain uses— produced by the individual’s prior experience plays a decisive part in possible conceptual errors or mistakes in the syntactic use of the new signs.

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