Open AccessA calculus student’s understanding of graphical approach to the derivative through quantitative reasoning
Author(s) -
Aytug Ozaltun-Celik
Publication year - 2021
Publication title -
lumat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.169
H-Index - 3
ISSN - 2323-7112
DOI - 10.31129/lumat.9.1.1663
Subject(s) - tangent , calculus (dental) , function (biology) , perspective (graphical) , computer science , interpretation (philosophy) , derivative (finance) , process (computing) , mathematics education , mathematics , artificial intelligence , geometry , programming language , medicine , dentistry , evolutionary biology , financial economics , economics , biology
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.