From the standpoint of symbolic algebra as a language, we characterize teaching models as successions of mathematical texts that are exchanged between pupil and teacher. Said characterization involves notions such as that of text and of textual space, the differentiation of which corresponds to the difference between meaning and sense, given that once one understands that a text is the result of reading a textual space, teaching and learning in mathematics class may be interpreted as a repeated reading process – transformation of textual spaces into texts, which are in turn taken as textual spaces to be read, and so on and so forth. This theoretical treatment of teaching models is completed by use of the notions of mathematical sign system and of language strata, to be applied to the case of concrete modeling introduced in the previous chapter, as well as to the analysis of syntactic models in algebra and of the semantic – syntactic relationship in algebra, the discussion of which was also begun in the preceding chapter.
KeywordsProblem Situation Teaching Model Concrete Model Algebraic Semantic Semantic Field
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