Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

The Boltzmann distribution lies at the heart of essentially all of statistical thermodynamics. In most textbooks, this distribution is introduced either "ad hoc" or it is mathematically derived by constrained entropy optimization using the method of Lagrange multipliers. Unfortunately, when students enroll in a statistical thermodynamics…

Early exposure to data science skills, such as relational databases, is essential for students in statistics as well as many other disciplines in an increasingly data driven society. The goal of the presented pedagogy is to introduce undergraduate students to fundamental database concepts and to illuminate the connection between these database…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Historically, what people can learn is co-determined by the "representational infrastructure" for knowledge building. When Latin was the required medium of knowledge building, few could engage in scholarly activities; without the change to the vernacular, nearly universal access to higher education would not be possible. The highly…

An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

We report the qualitative and quantitative results of incorporating interdisciplinary application projects and increasing the use of teaching with technology into Calculus I, II and III at the University of Colorado Denver. Minimal changes were made to the curriculum and minimal time was required of instructors to make the changes. Instructors…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

The constraints of a computer algebra system (CAS) generally induce limitations on its usage. Via the pedagogical features implemented in such a system, "motivating constraints" can appear, encouraging advanced theoretical learning, providing a broader mathematical knowledge and more profound mathematical understanding. We discuss this issue,…

Two related sequences of definite integrals are considered. By mixing hand-work, computer algebra system assistance and websurfing, fine connections can be studied between integrals and a couple of interesting sequences of integers. (Contains 4 tables.)

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

An online homework system created for use by beginning calculus students is described. This system was designed with the specific goal of supporting student engagement outside of class by replicating the attempt-feedback-reattempt sequence of events which often occurs in a teacher's presence. Evidence is presented which indicates that this goal…