Riv. Mat. Univ. Parma, Vol. 14, No. 2, 2023

Esteban Pablo-Díaz [a], Avenilde Romo-Vázquez [b] and Mario Sánchez Aguilar [c]

A Redesign of a mathematical modelling teaching proposal based on the Hazen-Williams model for engineering education

Pages: 299-315
Received: 10 April 2022
Accepted in revised form: 18 September 2023
Mathematics Subject Classification: 97M10, 97C70.
Keywords: Mathematical models, higher education, engineering education.
Authors address:
[a],[c]: Instituto Politécnico Nacional, CICATA Unidad Legaria, Mexico City, Mexico
[b]: Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, CINVESTAV, Mexico City, Mexico

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Abstract: This article reports ongoing research about training for engineers framed in the Anthropological Theory of the Didactic (ATD). Specifically, we show the redesigning of a mathematical modelling teaching proposal based on a civil engineering situation following two aims: 1) bringing an authentic mathematical modelling activity from the engineering workplace to engineering education and 2) framing it as closely as possible into an inquiry-based approach. For this purpose, we use the didactic engineering methodology. Firstly, we deepen the analysis of the mathematical modelling activity of a civil engineer’s workplace, which is based on the Hazen-Williams model to design pipelines and on different notions of hydraulics, topography and mathematics. Then, we perform a more specific didactic transposition over this workplace mathematical modelling activity to convert it into knowledge to be taught. Based on this and the characteristics of an engineering training Mexican university, we redesigned a mathematical modelling teaching proposal, generating a 'didactic milieu', a set of resources, to allow the engineer's students to perform, under an inquiry approach, the central modelling task: to determine the Diameter of the pipe and ensure a water flow rate of 50 lt/sec. According to our a priori analysis, the didactic milieu proposed motivates students to analyse the Hazen-Williams model qualitatively, relate knowledge of various kinds, investigate, work autonomously, and use practical and theoretical knowledge.

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