In traditional introductory physics classes, there is often limited opportunity for students to contribute their own ideas, interests, and experiences as they engage with the subject matter. This situation is exacerbated in university lecture-format classes, where students may not feel comfortable speaking during class. In the last few years,…

A number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centered…

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a…

Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…

The main objective of this paper is to apply the onto-semiotic approach to analyze the mathematical concept of different coordinate systems, as well as some situations and university students' actions related to these coordinate systems. The identification of objects that emerge from the mathematical activity and a first intent to describe an…

Historically, biology has not been a heavily quantitative science, but this is changing rapidly (Ewing 2002; Gross 2000; Hastings and palmer 2003; Jungck 2005; Steen 2005). Quantitative approaches now constitute a key tool for modern biologists, yet undergraduate biology courses remain largely qualitative and descriptive. Although biology majors…

Multimodal feedback could promote college students' conceptual, procedural and heuristic knowledge learning. This study used an experimental design to investigate the interaction effects of instructor's narrated feedback (with procedural feedback delivered visually and heuristic feedback auditorily) and gender on their post-test performance of a…

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…