The goal of the present study was to report an instrument designed to determine students' mathematical performances and preference for visual or analytic thinking for the calculus derivative and antiderivative tasks as well as examine the relationships among students' cognitive style, cognitive ability, and mathematical performance in calculus.…

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…

This article takes another look at the sliding ladder problem that students meet in the study of related rates in calculus. Physically realistic situations with both constrained and understrained ladders are explored.

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

This study tested whether the Stereotype Threat effect is mediated by achievement goals, in particular performance-avoidance goals. Threat level was altered before a difficult math test to observe how the endorsement by females of various achievement goal dimensions was affected. 222 people (96 females) in a pre-calculus class at a Mid-Western…

This paper reports on the results of an observational parallel study conducted simultaneously at 2 universities--one each in New Zealand and Germany. It deals with university engineering students' difficulties in the formulation step of solving a typical application problem from a first-year calculus course. Two groups of students (54 in New…

As a college mathematics teacher for six years, the author has learned his share of pedagogical techniques through research, practice, and reflection. He adopts new theories into classroom practice, differentiates instruction when necessary, and remains open to the diversity his students bring with respect to academic readiness, cultural norms,…

This study investigates how the beliefs and values of physics faculty influence their choice of physics problems for their students in an introductory physics course. The study identifies the goals these instructors have for their students, the problem features they believe facilitate those goals, and how those features correspond to problems they…

A multi-stage pre/post testing scheme is developed to gauge course effectiveness using gain and loss components of normalized change. The components, unlike normalized change itself, can be used to distinguish courses that promote acquisition as well as retention of information from courses that promote acquisition at the expense of retention or…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

In this study we examine the introduction of on-line homework to a Calculus II course as a replacement for ungraded pencil-and-paper homework assignments. We consider how this had an impact on students' performance in the course, on student behavior in completing the assigned work, and on student attitudes toward it. We find that students working…

The choice of pedagogy in statistics should take advantage of the quantitative capabilities and scientific background of the students. In this article, we propose a model for a statistics course that assumes student competency in calculus and a broadening knowledge in biology. We illustrate our methods and practices through examples from the…

This study examines 59 students' perceptions of using Facebook as an extension of the traditional classroom instruction, the value of Facebook as an educational tool, and the effects of blended learning in the class. A survey tool was used to assess students' perceptions pre and post implementation of Facebook page after nine weeks of integration.…

This paper presents a study of instructors' and students' perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I modeled these perceptions using a theoretical framework that combines elements of the Anthropological Theory of the Didactic, developed…

The GeoGebra software is attracting a lot of interest in the mathematical community, consequently there is a wide range of experience and resources to help use this application. This article briefly outlines how GeoGebra will be of great value in statistical education. The release of GeoGebra is an excellent example of the power of free software…