A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

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 an...

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Autor principal:	Aytug Ozaltun-Celik
Formato:	article
Lenguaje:	EN FI SV
Publicado:	LUMA Centre Finland 2021
Materias:	calculus student derivative graphical approach quantitative reasoning Education (General) L7-991 Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/5151cf1b9f364eed85a62be85fd6cb4a
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id	oai:doaj.org-article:5151cf1b9f364eed85a62be85fd6cb4a
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spelling	oai:doaj.org-article:5151cf1b9f364eed85a62be85fd6cb4a2021-12-03T13:09:38ZA calculus student’s understanding of graphical approach to the derivative through quantitative reasoning10.31129/LUMAT.9.1.16632323-7112https://doaj.org/article/5151cf1b9f364eed85a62be85fd6cb4a2021-12-01T00:00:00Zhttps://journals.helsinki.fi/lumat/article/view/1663https://doaj.org/toc/2323-7112 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. Aytug Ozaltun-CelikLUMA Centre Finlandarticlecalculus studentderivativegraphical approachquantitative reasoningEducation (General)L7-991Science (General)Q1-390ENFISVLUMAT, Vol 9, Iss 1 (2021)
institution	DOAJ
collection	DOAJ
language	EN FI SV
topic	calculus student derivative graphical approach quantitative reasoning Education (General) L7-991 Science (General) Q1-390
spellingShingle	calculus student derivative graphical approach quantitative reasoning Education (General) L7-991 Science (General) Q1-390 Aytug Ozaltun-Celik A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
description	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.
format	article
author	Aytug Ozaltun-Celik
author_facet	Aytug Ozaltun-Celik
author_sort	Aytug Ozaltun-Celik
title	A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
title_short	A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
title_full	A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
title_fullStr	A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
title_full_unstemmed	A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
title_sort	calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
publisher	LUMA Centre Finland
publishDate	2021
url	https://doaj.org/article/5151cf1b9f364eed85a62be85fd6cb4a
work_keys_str_mv	AT aytugozaltuncelik acalculusstudentsunderstandingofgraphicalapproachtothederivativethroughquantitativereasoning AT aytugozaltuncelik calculusstudentsunderstandingofgraphicalapproachtothederivativethroughquantitativereasoning
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A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

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