In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

In this article, the authors present an approach to developing open-ended problems through capturing contextualised mathematics in photographs. They draw upon their research with the Problem Posing Research Project, a collaborative venture between an Australian and a Canadian university to broaden pre-service teachers pedagogical practices in the…

In this article, the authors discuss how acknowledging and embracing that the sample space is one of many ways to partition the set of all possible outcomes impacts the teaching and learning of sample space and probability. After recounting an exchange surrounding two viable answers to a probability question, the authors detail how developments…

Traditional review sessions are intended to help students learn and prepare for upcoming exams. Most sessions are passive question and answer sessions that look backward at content deficits rather than advancing student learning. By incorporating active and cooperative learning approaches during a review session, students are able to recognize…

A method of solving the Schrodinger equation using a basis set expansion is described and used to calculate energy levels and wavefunctions of the hindered rotation of ethane and the ring puckering of cyclopentene. The calculations were performed using a computer algebra package and the calculations are straightforward enough for undergraduates to…

The purpose of this paper is to familiarize instructional designers and researchers with a useful design and research paradigm known as "Ask Systems." Ask Systems are interrogative interfaces to information and learning environments that model conversations with a skilled, reflective practitioner (Schon, The reflective practitioner, "1983") or…

Street intersections are a source of accidents--for both automobiles and pedestrians. This article presents an intersection challenge that allows students to explore some possible ways to change the traditional intersection. In this challenge, teachers open up the boundaries and allow students to redesign their world. The first step is to help…

It is well documented that when solving problems experts first search for underlying concepts while students tend to look for equations and previously worked examples. The overwhelming majority of end-of-chapter (EOC) problems in most introductory physics textbooks contain only material and examples discussed in a single chapter, rarely requiring…

This article develops the notion of resistance as articulated in the literature of critical pedagogy as being both culturally sponsored and cognitively manifested. To do so, the authors draw upon John Dewey's conception of tools for inquiry. Dewey provides a way to conceptualize student resistance not as a form of willful disputation, but instead…

This article focuses on life career perspectives within the field of counseling psychology. The first goal is to promote reflection and discussion of counseling psychologists' planning and decision making as it pertains to their career journey; the second goal is to promote additional discussion around implicit and explicit cultural perspectives…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the…

When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

In this article, I share the shape and findings of a participatory action research project with newcomer youths on the contours of status in society. This project was nested in a professional internship experience for newcomer youth, and this experience provided the context in which we explored how privilege and status are afforded in American…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…