This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. A four-day introductory workshop was given in Nepal to provide an overview of GeoGebra and its possible integration in the teaching/learning of secondary school mathematics there. Teachers' impressions and…

We study how different sections voted on the same set of classroom voting questions in differential calculus, finding that voting patterns can be used to identify some of the questions that have the most pedagogic value. We use statistics to identify three types of especially useful questions: 1. To identify good discussion questions, we look for…

Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students' strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students…

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

The goal of this study was to examine the pathways to being college ready in mathematics. Students who enter high school already having demonstrated mathematics proficiency on a standardized test in the 8th grade have already taken a significant step towards being college ready. The best scenario is to enter high school proficient in mathematics…

In a national context of high failure rates in freshman calculus courses, the purpose of this study was to understand who is struggling, and why. High failure rates are especially alarming given a local environment where students have access to a variety of academic, and personal, assistance. The sample consists of students at Colorado State…

A substantial percentage of college students who enrol in Calculus I intending to take more calculus decide at the end of the semester not to continue with calculus. This represents a huge loss in terms of the need for more students to pursue a major in one of the science, technology, engineering and mathematics (STEM) disciplines. In this report…

This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…

The developing pedagogical content knowledge of elementary-certified teachers was supported in a course on concepts in algebra and calculus. Engineering thermodynamics was used as a domain through which participants could model rate-of-change for a variety of functions. The design of the professional development course is examined, and teachers'…

In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

Conventional application of these two calculus staples is stretched here, somewhat recreationally, but also to raise solid questions about the role of limit interchange in analysis--without, however, delving any deeper than first-year Calculus.

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. We determine Fay's optimal path minimizing segment length, and thus maximizing the number of times they meet…

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…