On a typical day in a university precalculus classroom, as students arrive, they settle into their small groups and begin sharing their ideas and questions from the homework assigned the previous night. It can be quite challenging to create a learning environment in which students engage in mathematical thinking outside class and are prepared to…

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

In an undergraduate Calculus III class, we explore the effect of "flipping" the instructional delivery of content on both student performance and student perceptions. Two instructors collaborated to determine daily lecture notes, assigned the same homework problems, and gave identical exams; however, compared to a more traditional…

This article reports on the design, development, and validation of a new instrument, the Technology-Enabled Active Learning Inventory (TEAL), to measure students' perceptions of active learning in a technology-enabled learning context. By laying the theoretical foundation, a conceptual framework for technology-enabled active learning was…

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

The purpose of this study was to investigate how a set of physical and digital instructional activities can serve as an example space to help further develop a concept image that is aligned with the formal concept definition for the limit of a sequence. In addition, the unique affordances and constraints allowed by using either a physical or…

Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

Activities for Students appears five times each year in Mathematics Teacher, promoting student-centered activities that teachers can adapt for use in their own classroom. In the course of the activities presented here, students will "look for and make use of structure" by observing algebraic patterns in the power rule and "use…

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually…

Mathematical skills have been recognised as a core competence for engineering and science students. However, learning mathematics has been recognised as a difficult and challenging task for most students, in particular, calculus for first-year students in university. Consequently, the development of effective learning strategies and environments…

This study aimed at investigating the effectiveness of using flipped classrooms in teaching the Math2 course for the preparatory year's students at the University of Tabuk, Saudi Arabia. The Math2 course was organized via an (ADDE) design model, with recorded videos of the topics included in the study; it was implemented by a Moodle platform and…

This study examines graphing calculator affordances in learning mathematics among college precalculus students. The study draws from the Cognitive Load Theory (CLT) and the "Intelligent Technology" theoretical framework proposed by Salomon, Perkins, and Globerson (1991). From these perspectives the effects "with" the graphing…

"WeBWorK" CLASS combines the best features of online homework and digital whiteboards to create a system that provides instructors with information on students' problem-solving processes, as well as their final answer. The system's utilization of tools that can sort students based on correct and incorrect homework and quiz answers and…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…