How to teach linguistic and mathematical notation? A three-pronged approach: epistemic, interdisciplinary and sociocultural
Sílvia Llach Carles y Ángel Alsina Pastells
In this paper we argue that the external systems of linguistic and mathematical representation teaching should be carried out using an epistemic, interdisciplinary ans sociocultural approach enabling the semiotic and instrumental functions of these languages to be combined. Within this framework, we analyze a number of aspects that ought to be considered in the classroom: the learning path, informal practices, and formal practices. The analysis of these factors suggests that the best way forward is (i) to start from the cognitive possibilities of the students and their zone of proximal development to design activities that are flexible and consistent with the learning of the two systems, (ii) to continue informal practices in order to integrate everyday experience and school work and, finally, (iii) to implement classroom practices that, in the case of direct, formal instruction, focus on the relationship between signs and concepts that are represented by them establishing abstract categories and their possible relationships BBS and, in the case of indirect instruction, are lÂ¡S| based on related fields whose impact on learning external systems of representation has been demonstrated, and finally, are based in contextual situations that are meaningful and motivating.
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