From engineering to didactic suitability in mathematics education
Abstract
Didactics of mathematics has a scientific component (descriptive, explanatory and predictive) and a technological component (prescriptive), which involves the design and experimentation of optimal educational interventions in each context and circumstances. Consequently, general educational research theories and methods are applied and developed, as well as specific and local instructional theories. In this paper we analyse three theories widely used in Didactics of Mathematics highlighting the features they incorporate related to the technological component of Didactics, that is, as theories of instructional design or didactic engineering. These are the Theory of Situations, the Anthropological Approach and Realistic Mathematics Education. Likewise, we describe the Theory of Didactic Suitability, as a component of the Onto-semiotic Approach, which addresses the axiological problem of identifying and structuring criteria for optimising mathematical instructional processes, by means of which the gap between didactic engineering and teaching practice can be bridged. Finally, the concordances and complementarities between the four mentioned theories are analysed. The clarification and comparison of the didactic suitability criteria of different theoretical frameworks and their articulation into a coherent system is a research programme that we only suggest in this article.
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