By Eugenio Filloy
This ebook takes a theoretical point of view at the learn of college algebra, during which either semiotics and historical past ensue. The Methodological layout permits the translation of particular phenomena and the inclusion of proof no longer addressed in additional common remedies. The publication provides precedence to "meaning in use" over "formal meaning". those techniques and others of comparable nature result in 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
To the foregoing we could add many other examples of how, with a global approach, using the results of some general theory of certain branches of knowledge, the analyses of the phenomena that belong to mathematics education, performed thus, reduce the field of investigation very substantially, preventing a clear understanding of the specific phenomenon that one is trying to observe. For example, consider what we would achieve if we wished to use only a general linguistic theory to construct a useful semiotics for mathematics education.
This implies a comparison in which one observes properties and principles that are similar in certain aspects, which fits in with the previous observation that theoretical models have the aim of providing a useful representation of a system. To provide such a representation, it is often helpful to establish an analogy between the system in question and some known system that is governed by rules or principles that are understood, and one supposes that some of those rules, or others like them, also govern the system that one is trying to describe with the model.
In both cases, we see that the letters and operation symbols still suggest to the student meanings associated with those signs in primary school. In other words, expressions that include letters or that are formulae or that are simple equations, even when the equals sign —necessary in these two cases— is absent. It is the student who completes the expression in order to be able to read it within contexts that are familiar to him or her. 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.