Historians of mathematics considered the nineteenth century to be the Golden Age of mathematics. During this time period many areas of mathematics, such as algebra and geometry, were being placed on rigorous foundations. Another area of mathematics which experienced fundamental change was analysis. The drive for rigor in calculus began in 1797…

A pair of masses or opposite-sign charges released from rest will move directly toward each other under the action of the inverse-distance-squared force of attraction between them. An exact expression for the separation distance as a function of time can only be found by numerically inverting the solution of a differential equation. A simpler,…

Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area…

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.

A classroom response system (CRS) involves the use of remote devices allowing all students in a class to respond to questions displayed on a projection screen. A CRS instantly collects, tallies, and shows students' answers to a question on a classroom projection screen--a similar system used in the TV show "Who wants to be a millionaire"…

Physicians and other health professionals are an important part of the national scientific and technical workforce, and it is important to understand the factors that attract (or fail to attract) young adults into these fields. Using data from the 20-year record of the Longitudinal Study of American Youth (LSAY) and working within a social…

This article describes a quantitative and qualitative assessment from a study done on the possible effectiveness of including an online homework component in first-semester calculus. Two instructors, each teaching two sections of Calculus I, agreed to treat one of their sections as an experimental group and the other as a control group. Students…

Research on student learning in higher education suggests that threshold concepts within various disciplines have the capacity to transform students' understanding. The present study explores students' understanding in relation to particular threshold concepts in mathematics--integral and limit--and tries to clarify in what sense developing an…

This article illustrates the power of Bloom's revised taxonomy for teaching, learning, and assessing in aligning our curriculum expectations and our assessment tools in multivariable calculus. The particular assessment tool considered involves a common matching problem to evaluate students' abilities to think about functions from graphical and…

One of the most important applications of the definite integral in a modern calculus course is the mean value of a function. Thus, if a function "f" is defined on an interval ["a", "b"], then the mean, or average value, of "f" is given by [image omitted]. In this note, we will investigate the meaning of other statistics associated with a function…

We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…

After students have constructed a conceptual understanding of a mathematical idea, applying mathematical symbolism to represent and define the idea concisely becomes an easier task. In fact, Moore (1994) found that students "often needed to develop their concept images through examples, diagrams, graphs, and other means before they could…

We report on efforts to design the "Collaborative Workshop Physics" (CWP) instructional strategy to deliver the first interactive engagement (IE) physics course at Khalifa University of Science, Technology and Research (KU), United Arab Emirates (UAE). To our knowledge, this work reports the first calculus-based, introductory mechanics…

Peer assessment typically requires students to judge peers' work against assessment criteria. We tested an alternative approach in which students judged pairs of scripts against one another in the absence of assessment criteria. First year mathematics undergraduates (N?=?194) sat a written test on conceptual understanding of multivariable…

This paper describes an action-research experience carried out with second year students at the School of Engineering of the National University of Entre Ríos, Argentina. Vector calculus students played an active role in their own learning process. They were required to present weekly reports, in both oral and written forms, on the topics studied,…