Didactic proposal to overcome the difficulties in the learning of Area and Volume in Spanish Primary Education students

Abstract: This work presents a didactic proposal for the learning and measure of surface area and body volume. This proposal is framed in the Anthropological Theory of the Didactic (ATD), based on the recognized errors in the learning of these magnitudes and considering their connection with the typified learning difficulties or epistemological obstacles. The proposal was developed as a didactic sequence, including the tasks from didactic situations (as considered by Brousseau) and with a cross-curricular perspective in relation to the social-systemic structure (ATD), without restricting them in any didactic unit. The praxeology was structured in accordance with the approaches of the ATD, and the didactic methodology was based on the definition of the errors, which followed the phases of development of the usual models in the learning of Geometry.  These phases were defined under a generic framework influenced by the developed Van Hiele model for the learning of Geometry. The tasks that composed the didactic sequences were created “ad-hoc” or extracted from adequate sources throughout the Spanish curriculum of Primary Education. The proposal was designed to be applied in the 5th Primary Education grade. The collection of evidences on the students learning regarding the area and the volume after the implementation of the proposal constitutes the natural next step of this project.

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