The present paper explores the relationship between attitudes towards mathematics (ATM) and achievement in college calculus in active learning (AL) and lecture-based (LB) classrooms. Previous work on this relationship has mainly been limited to LB instruction, neglecting the impact of innovative approaches such as AL. Less attention has been paid…

The growing adoption of active learning pedagogical methods has shown significant positive effects in higher education as they promote students' engagement and meeting of learning outcomes. Similarly, problem-based learning and media-based learning allow instructors to model educational experiences that prepare students with knowledge and skills…

The area under the curve is a fundamental concept for students to build their understanding of the Definite Integral. This research reveals how students comprehend the area under the curve in given contextual problems and how the Hypothetical Learning Trajectory (HLT) can help students find the concept. This research follows the development…

We investigated the effects of a major revision of the differential and integral calculus curriculum, the primary goal of which was to improve STEM retention. The revamped curriculum has greater emphasis on the power of computing to help visualize patterns and gain insights to better prepare students for STEM majors, and less emphasis on…

Standards-based grading is an alternative grading system that gives students multiple opportunities to demonstrate proficiency in course standards or objectives. It has the potential to provide flexibility and reduce student anxiety, which are particularly important during difficult times such as the COVID-19 pandemic. In this study, students in a…

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

Contributing to research on undergraduate students' thinking about problem solving tasks, the present study reports on students' reasoning about two initial-value problems i.e. first-order linear ordinary differential equations with initial conditions. A qualitative analysis of task-based interviews and work written by 34 students revealed that…

Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women)…

The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for…

The curricular unit Calculus I -- Extraordinary Semester (UCCISE) -- was explicitly created to respond to students' difficulties in the curriculum unit Calculus I (UCCI). Only students who fail the UCCI are allowed to attend UCCISE. Considering the enrolled students' familiarity with mathematical software, the potential of group work to stimulate…

This study investigates the impact of GeoGebra, a dynamic, accessible, and easy-to-use mathematics software, on student confidence and perceptions of its helpfulness in the context of Calculus III courses. A quasi-experimental design was employed to compare four sections of Calculus III, with two sections integrating GeoGebra for in-class…

Despite growing theoretical and empirical evidence that writing has the potential to be an effective tool for student learning in undergraduate mathematics, writing-to-learn integration in mathematics is rare. Major deterrents include perceived lack of alignment between writing and learning goals, deficit views of students' writing abilities, and…

A significant portion of mathematics education research has focused on factors that impact student pursuit of science, technology, engineering and mathematics (STEM). Low rates of STEM student enrollment combined with high drop-out rates have consistently drawn attention from educators, administrators and policy-makers at all levels. Many studies…

The National Science Foundation identified a shortage of STEM professionals in the United States. There is a dire need to promote STEM education to secure high-paying and skilled jobs for the country's residents and the overall healthy economy. This shortage is partly due to students' low retention and persistence to graduate in STEM fields. Due…