As part of an integrative learning experience at the end of a sophomore Calculus II course at the United States Military Academy, this project served as a multidisciplinary problem-solving exercise that explored the connections among mathematics, biology, and other fields of study. During a seven-lesson block of instruction, this module was…

A typical Calculus class tends not to be very interactive. Students view the class as passive. The students expect the instructor to provide the information with very little activity or effort on their part. Asking students questions and trying to get them to respond is often a challenge. Many students know the answer, but are scared to respond.…

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

Nowadays, many technological means are available to support teaching, such as the interactive whiteboard, class sets of laptop or netbook computers, and high speed internet access. For mathematics education there are advanced software packages for geometry, algebra, calculus, and statistics, which in many cases are available on line at no cost.…

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

The integration of technology into modern classrooms has enhanced learning opportunities for students. With increased access to educational content, students gain a better understanding of the concepts being taught. "Flipped Instruction: Breakthroughs in Research and Practice" is a comprehensive reference source for the latest scholarly…

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…

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…

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…