By Eugenio Filloy
This booklet takes a theoretical point of view at the examine of college algebra, during which either semiotics and background ensue. The Methodological layout permits the translation of particular phenomena and the inclusion of facts now not addressed in additional normal remedies. The booklet 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 job with mathematical language.
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Extra info for Educational algebra : a theoretical and empirical approach
This component is bound up with institutionalized social contracts, so that it is necessary to take into account not only the traditional, customary ways in which the messages of an MSS are emitted in the educational system, but also —and this seems more important— the presence of the entire historical evolution of such sign systems. Notation is the first aspect that appears, but it is not the only one of all the particular ways in which nowadays, after a historical evolution, we tend to use MSSs and their applications to problems in present-day science, technology, and social information processes.
In the first case they are the phenomena that are organized in mathematics taken in its state at the present moment and assuming its present use. In the didactical case they are the phenomena present in the world of the students and the phenomena that are proposed in the teaching sequences. In the genetic case, the phenomena are considered with respect to the learners’ cognitive development. In the historical case, special attention is paid to the phenomena for the organization of which the concept in question was created, and how it has extended to other phenomena.
Such practices occur in the current educational systems and they are the direct cause of the poor progress of students and of the rejection of mathematics by the general population. As a result of proceeding partially, placing some aspects above others, a false dilemma appears, in which the relational aspects of mathematical thinking work to the disadvantage of its instrumental use and viceversa. Similarly, the adoption of a particular bias makes the dilemma between understanding and mere mechanization more acute, in relation not only to mathematical operations but to mathematical thinking in general.
Educational algebra : a theoretical and empirical approach by Eugenio Filloy