In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…

The objective of this research is to consider the possible relationship between academic performance and university students' beliefs about Mathematics, particularly in the subject of Integral Calculus. The methodology employed is quantitative, descriptive and correlational, based on a non-experimental design. The instrument used for the…

The concept of integration appears in many different scientific fields, and students' understanding of and ability to use the definite integral in applications is important to success in their STEM (science, technology, engineering, and mathematics) classes. One of the first types of application problems that students encounter is finding the…

Background and Context: Computer Science has traditionally had poor student retention, especially among women. Prior work has found that student attitudes are a key factor to retention, especially with "weedout" courses such as Calculus. Objective: To determine how student attitudes towards CS 1 and Calculus change over active-learning…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

This study aims to prepare an educational program based on integrating Science, Technology, Engineering and Mathematics (STEM) to develop students' mathematical thinking skills. It also aims to provide proposals that could have a major role in rebuilding some of the general features on which mathematics curricula can be built according to the STEM…

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

The expectations gap -- the difference between the level at which high schools prepare students and the preparation colleges expect -- is believed to be accountable for hindering access to, and success in, higher education. It has been largely attributed to misalignment of priorities and lack of communication among policy makers and educators and…

In the current study, using self-determination theory as a theoretical framework, we used multiple real-time assessments to investigate the dichotomous relationship between autonomy need satisfaction and frustration, and how these constituents underpin student functioning among higher education students during a learning activity. In total, 124…

The goal of this study is to identify the multiple ways in which instructors take advantage of a feature designed into university textbooks that seeks to invite students to get acquainted with the content prior to attending the class in which such content will be discussed. We present an analysis of teacher instrumentation of this feature, which…

The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…

Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…

Spatial reasoning is required for many topics in undergraduate mathematics as well as other STEM fields. In calculus specifically, there are few interventions that assess students' spatial skills and provide remediation. Haptic technology is a novel approach to spatial skills remediation due to its unfamiliarity to students and its flexibility…

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be…

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…