Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

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…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…

Mathematical objects are the outcomes of human discourse and come to life through the process of objectification. Primary and concrete discursive objects (d-objects) play an important role in this process, forming different realizations through the objectification process. In the present study, we analyze the written discourses about the…

This study investigates how three widely used calculus textbooks realise integrals as a potential to prompt mathematical competencies, adapting the rating scheme used in Boesen et al. ("The Journal of Mathematical Behavior," 33:72-87, 2014), Pettersen and Braeken ("International Journal of Science and Mathematics Education,"…

An interactive open-source calculus textbook is compared to a popular commercial textbook. Structured as a non-inferiority study, use of the open-source textbook does not harm student outcomes, and there is evidence that the open-source textbook is better than the commercial textbook in promoting post-course enjoyment of mathematics and confidence…

Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on…

Textbooks have been the subject of research within and across disciplines, but have not yet been widely studied from a disciplinary literacy perspective. Readerly agency is also understudied in disciplinary literacy. The present paper aims to illuminate both of these areas by examining facets of agency that readers demonstrated during think-aloud…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…

In this study, we investigated the literacy practices of undergraduate calculus students and non-mathematics STEM faculty members as they read excerpts from a calculus textbook. We found several differences in their practices that appeared to be tied to the didactical nature of the excerpts and the participants' identities and power relationships…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

We investigate how an inquiry-oriented, dynamic, open-source calculus textbook shaped one college instructor's planning. We rely on Dietiker et al.'s [(2018). Research commentary: Curricular noticing: A framework to describe teachers' interactions with curriculum materials. "Journal for Research in Mathematics Education," 49(5), 521-532.…

Infinite series are known to be challenging for Calculus II students, perhaps because they lack intellectual need for the content. In their analysis of Calculus textbooks found few instances of potential intellectual needs for infinite series. This study combines a textbook analysis with interviews of four professors and observations of their…

Textbooks are a standard component of undergraduate mathematics courses, but research shows that students often do not view textbooks as productive resources to support learning. This article seeks to understand the factors affecting how individuals engage in reading a calculus textbook excerpt and what they learn from reading. To better…