We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

Common student errors and misconceptions can be addressed through the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small-group discussion, each student votes on the correct answer, using a clicker or a phone. If a large number of students have…

This study aims to develop student metacognition strategies based on behavioural learning in improving the mathematical abilities of students of mathematics education. There are two components developed in this study, namely: (1) Development of strategies to foster student metacognition based on behavioural learning, and (2) Development of…

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative…

This study examines the perceptions of first-year, mathematics graduate teaching assistants (GTAs) participating in a six-week summer course designed to deepen their knowledge of collegiate mathematics teaching practices before being assigned to instruct undergraduate students in the subsequent fall semester. Through hybrid deductive-inductive…

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions…

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…

The development of modeling skills in mathematics is essential for individuals to understand, describe, control, and predict phenomena around them. This article describes the results of an investigation to find out how an activity -- based on a Models and Modeling Perspective -- stimulates the mathematics modeling skills of undergraduate students…

The goal of this research is to make a theoretical reflection about connections that contributes to the development of the model for mathematical connections originally proposed by Businskas, and extended with the contributions of other researchers. This model is used in the most relevant investigations in this field. As a consequence of the…

The Mathematics Department at Cornell University has recently secured a grant from the University to implement systemic change in how we teach courses that reach students at critical transition points in their mathematical development. In this article, we report on the changes made to our large multi-section first-semester calculus course in order…

The aim of this research was to study and investigate first year university calculus students' misconceptions about how to use the definition of limit to find the first derivative of functions and then remediate these misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female and male) were selected based on…

This descriptive-comparative study investigated the impact of different instructional models on a university level Precalculus course on students' achievement. Participant data (N = 14,993) was collected from Fall 2008 to Spring 2019 and categorized into four different instructional models: traditional, modular, emporium v.1, and emporium v.2.…

This paper reports on data obtained during semi-structured interviews with students who had recently experienced a guided inquiry approach to learning ordinary differential equations (ODEs) in a service-taught module. Previous research identified the strengths and weaknesses of similar cohorts of students. The results from that research informed…

A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…