This study explores the effects of a computer algebra system on students' mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students' capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was…

The purpose of this mixed-methods study was to explore how undergraduate students in an applied calculus course used the written curriculum (i.e., textbook, online homework system, and previous exams). The study design included three phases: (a) an online survey, (b) individual observations, and (c) student interviews. Students' survey responses…

Many factors play a role in a students' learning experience, but students' course interaction behaviors are particularly important toward fostering success. Instructors build learning tools (such as videos, online quizzes, etc.) that provide students with the opportunity to extend their learning outside the classroom. These tools require students…

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

The research relates to undergraduate students' understanding of mathematical concepts that relate to the conceptualisation of the continuous such as the notion of limit. The cognitive difficulties that accompany the learning of these concepts at the different stages of the mathematics education are well reported in the literature. I analyse the…

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we…

Supporting student success in entry-level mathematics courses at the undergraduate level has and continues to be a challenge. Recently we have seen an increased reliance on technological supports including software to supplement more traditional in-class instruction. In this paper, we explore the effects on student performance of the use of a…

In this paper we demonstrate how video game mechanics can be used to help improve student engagement with online mathematics homework. Specifically, we integrate two common video game systems, levels and achievements, with the online homework program "WeBWorK." We describe the key features of the implementation of these systems and…

Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…

A group of six math instructors used tablet PCs to teach their individual sections of a high enrollment gateway Pre-Calculus course in a diverse urban four-year college. Student performance in the experimental sections were compared to those in 31 other sections in terms of student retention, pass rates, and score on the department-wide…

This article describes a quantitative and qualitative assessment from a study done on the possible effectiveness of including an online homework component in first-semester calculus. Two instructors, each teaching two sections of Calculus I, agreed to treat one of their sections as an experimental group and the other as a control group. Students…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

We describe an ambient awareness tool, named "Lantern", designed for supporting the learning process in recitation sections, (i.e., when students work in small teams on the exercise sets with the help of tutors). Each team is provided with an interactive lamp that displays their work status: the exercise they are working on, if they have…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…