A Calculus Student's Understanding of Graphical Approach to the Derivative through Quantitative Reasoning

Autor/in	Ozaltun-Celik, Aytug
Titel	A Calculus Student's Understanding of Graphical Approach to the Derivative through Quantitative Reasoning
Quelle	In: LUMAT: International Journal on Math, Science and Technology Education, 9 (2021) 1, S.892-916 (25 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2323-7112
Schlagwörter	Calculus; Mathematical Concepts; Logical Thinking; Graphs; Cognitive Processes; Students + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Grafische Darstellung; Cognitive process; Kognitiver Prozess; Student; Schüler; Schülerin; Studentin
Abstract	The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers' focuses to students' dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student's mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student's understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate. (As Provided).
Anmerkungen	LUMA Centre Finland. University of Helsinki. A.I. Virtasen aukio 1, 00014 University of Helsinki, Finland. Tel: +358-50-348-0567; e-mail: editor@lumat.fi; Web site: https://journals.helsinki.fi/lumat
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01