A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Expertise and expert performance has long been a rich area of research. Experts differ from novices in several ways including the depth of their knowledge base, the ability to detect and recognize salient features of problems, more skilled and accurate performance, and strong self-monitoring skills. Advances in neuroscience methods such as…

The goal of this study was to understand errors that student make when simplifying exponential expressions. College students enrolled in four college mathematics courses were asked to simplify and compare such expressions. Quantitative analysis identified three persistent errors: interpreting negative bases, negative exponents, and parentheses.…

Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

This article reports on a qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. DeBellis and Goldin's (2006) framework for affect as a representational system was used as a lens through which to understand the ways in which…

This article describes a modification of the popular TV game show, "Survivor," as conducted in an undergraduate first semester mathematics precalculus course. The objective of this game is a group-based competitive drill and practice activity to help students prepare and review for the fundamental concepts exam. The results of this activity…

This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs.…

This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal…

Attention to integrate technology in teaching and learning has provided a major transformation in the landscape of education. Therefore, many innovations in teaching and learning have been technology-driven. The study attempted to examine what is engineering students' perception regarding the use of Information and Communication Technologies (ICT)…

Projects highlighting Science, Technology, Engineering, and Mathematics (STEM) education in high schools have promoted student interest in engineering-related fields and enhanced student understanding of mathematics and science concepts. The Science and Technology Enhancement Program (Project STEP), funded by a NSF GK-12 grant at the University of…

Technology-rich student-centered classrooms such as SCALE-UP and TEAL are designed to actively engage students. We examine what happens when the design of the classroom (conventional or teacher-centered versus student-centered classroom spaces) is consistent or inconsistent with the teacher's epistemic beliefs about learning and teaching…

This paper provides a detailed analysis of the mathematical communication involving a pair of high school calculus students who are English language learners. The paper focuses on the word-use, gestures and dragging actions in the student-pair communication about calculus concepts when paper-based static and then touchscreen dynamic diagrams.…

The Aboriginal "How are we Doing?" report provides information about Aboriginal students (including adults) performance in Public school. Readers should notice that there are changes to historical and trend data. Once a student has self-identified as being of Aboriginal ancestry, the student is included in all report outcomes for…

The purpose of this article is to describe the development of elementary school teachers' mathematical knowledge for teaching as they participated in a Modeling Instruction environment that placed heavy emphasis on improving their subject-matter knowledge as a basis for affecting the development of their pedagogical content knowledge. We…