Onto-Semiotic Complexity of the Definite Integral. Implications for Teaching and Learning Calculus

Autor/inn/en	Burgos, María; Bueno, Seydel; Godino, Juan D.; Pérez, Olga
Titel	Onto-Semiotic Complexity of the Definite Integral. Implications for Teaching and Learning Calculus
Quelle	In: REDIMAT - Journal of Research in Mathematics Education, 10 (2021) 1, S.4-40 (40 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2014-3621
Schlagwörter	Semiotics; Mathematics Instruction; Teaching Methods; Decision Making; Calculus; Mathematical Concepts; Intuition; Arithmetic; Guidelines; Learning Problems; Problem Solving; Epistemology; Schemata (Cognition) + Suchen Sie Ihr Suchwort? Semiotik; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Decision-making; Entscheidungsfindung; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Richtlinien; Lernproblem; Problemlösen; Erkenntnistheorie; Cognition; Schema; Kognition
Abstract	Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and instruction. The goal is to understand the diverse meanings of the concept of the definite integral and potentials semiotic conflicts based on the given data. We focus attention on a first intuitive meaning, which involves mainly arithmetic knowledge, and the definite integral formal meaning as Riemann's sums limit predominantly in the curricular guidelines. The recognition of the onto-semiotic complexity of mathematics objects is considered as a key factor in explaining the learning difficulties of concepts, procedures and its application for problem-solving, as well as to make grounded decisions on teaching. The methodology analysis of a mathematical text, which we exemplify in this work applying the tools of Onto-Semiotic Approach, provides a microscopic level of analysis that allows us to identify some semiotic-cognitive facts of didactic interest. This also allows for the identification of some epistemic strata, that is, institutional knowledge that should have been previously studied, which usually goes unnoticed in the teaching process. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01