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

Aytug Ozaltun-Celik
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引用次数: 1

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.
一个微积分学生通过定量推理对导数的图形化方法的理解
导数的概念被用于许多领域,包括应用问题和不同学科的数学建模。教授导数最重要的方法之一是帮助学生将概念形象化。同时,也需要将研究者和教师的关注点转移到学生在学习衍生品时的动态心理活动上,从而进行有效的教学过程。有了这种必要性,我把重点放在了与导数的图形方法相关的定量推理的角度上。本研究旨在揭示微积分学生的心理行为与图形方法的导数。数据收集自一年级的微积分学生从事的任务需要图形解释的导数。结果表明,学生对斜率的理解影响了她对切线的推断,因为比值的数量是学习瞬时变化率的先验知识。此外,由于该学生有与函数概念相关的对应概念,她在解释导数的全局视图时存在困难。这一结果表明,要全面了解导数,需要对函数和速率有深刻的理解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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