Didactic Engineering in the Study of the Sense of Variation of Functions: Preliminary Analysis

Autor/inn/en	Cabañas-Ramírez, Noé Oswaldo; Locia-Espinoza, Edgardo; Morales-Carballo, Armando
Titel	Didactic Engineering in the Study of the Sense of Variation of Functions: Preliminary Analysis
Quelle	In: International Electronic Journal of Mathematics Education, 15 (2020) 2, (14 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1306-3030
Schlagwörter	Mathematical Concepts; Foreign Countries; Secondary School Mathematics; Calculus; Difficulty Level; Learning Processes; Textbook Content; Undergraduate Students; Definitions; Mathematics Instruction; Mexico + Suchen Sie Ihr Suchwort? Ausland; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Schwierigkeitsgrad; Learning process; Lernprozess; Lehrbuchtext; Begriffsbestimmung; Mathematics lessons; Mathematikunterricht; Mexiko
Abstract	This paper shows the results of the epistemological and didactical analysis of the sense of variation of functions. Specifically, on the conceptions of growth and decay in a function that underlie the demonstrations of the theorem that links the sign of "f" with the sense of variation of "f". The epistemological approach covered the years 1795 to 1912. It was identified that the conceptions of Fourier, Lagrange and Cauchy about growth and decay differ from the conception in the formal current definition; however, the posed procedures and definitions provide elements that foster reconstruction processes of the definitions and properties of increasing and decreasing functions. It is important to highlight that the current definition of growth and decay has a solid foundation on the definition made by Osgood in 1912. The didactical analysis identified that the current text books inherit some of the limitations and inconsistencies of the definitions found on the epistemological approach. The conflicting issues enhance the starting point for the development of a didactic engineering for the treatment of the sense of variation of a function at a preuniversity level. (As Provided).
Anmerkungen	International Electronic Journal of Mathematics Education. Suite 124, Challenge House 616 Mitcham Road, CR0 3AA, Croydon, London, UK. Tel: +44-208-936-7681; e-mail: iejme@iejme.com; Web site: https://www.iejme.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01