The Story of Definite Integrals: A Calculus Textbook Narrative Analysis

IF 1.3 Q3 EDUCATION, SCIENTIFIC DISCIPLINES
Amanda Huffman Hayes
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Abstract

There is a plethora of textbooks to choose from. While most textbooks contain the same content, teachers need to understand the textbook they have chosen to support their students’ learning, as textbooks can significantly impact student learning and teacher instruction. When searching for a way to understand the various textbooks, my research question became, How do calculus textbooks tell the story of definite integrals? My research is in response to the never-ending search for how teachers can select and use their resources. Also, this study contributes to understanding the relationships between stories and knowledge construction using Dietiker’s (2015) narrative framework to analyze the written calculus curriculum. I wrote the specific stories of introducing the definite integral as told by five calculus textbooks. Analyzing how the stories developed disclosed the similarities and differences among the texts in teaching definite integrals. The analysis also revealed a variety of avenues to introduce and teach definite integrals, including a focus on the area under the curve, Riemann sums, or the Fundamental Theorem of Calculus, and some implications to the context of physics related to these avenues. These insights provide teachers with a deeper understanding of textbook lessons and the variances that can potentially alter student learning.
定积分的故事:微积分教科书叙事分析
有太多的教科书可供选择。虽然大多数教科书都包含相同的内容,但教师需要了解他们选择的教科书来支持学生的学习,因为教科书可以显着影响学生的学习和教师的教学。在寻找理解各种教科书的方法时,我的研究问题变成了:微积分教科书是如何讲述定积分的故事的?我的研究是对教师如何选择和使用他们的资源的永无止境的探索的回应。此外,本研究有助于理解故事与知识建构之间的关系,使用Dietiker(2015)的叙事框架来分析书面微积分课程。我将五本微积分课本中介绍定积分的具体故事写了下来。通过分析故事的发展过程,揭示了定积分教学中各教材的异同。分析还揭示了引入和教授定积分的各种途径,包括对曲线下面积、黎曼和或微积分基本定理的关注,以及与这些途径相关的物理背景的一些含义。这些见解为教师提供了对教科书课程和可能改变学生学习的差异的更深入理解。
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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