Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

This qualitative study examined the link between content knowledge and classroom practice from the perceptions of two university lecturers. The study was contextualized at a higher education institution in South Africa where the two university lecturers were lecturing to a second year undergraduate teacher trainee class (n = 78). The research was…

This study was conducted to discover and examine school-level characteristics that can affect change in high school graduates from being college-eligible to college-ready. Using the National Educational Longitudinal Study (NELS:88), the article describes and interprets the results. Findings indicate school personnel (principals, teachers,…

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

By understanding what motivates students to learn mathematics, instructors can adapt their teaching strategies to help students achieve a level of engagement conducive to learning mathematics. There is a substantial body of research on motivations and academic achievement at the elementary and high school levels, but less is known at the college…

Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the…

This article presents Stephen Humphry's response to the commentaries for his article "The Role of the Unit in Physics and Psychometrics." The commentaries covered a range of important considerations and implications. Given that the author fully agrees with the majority of the content, attention will be confined mainly to points that call…

Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study…

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…

Many authors have discussed the question "why" we should use the history of mathematics to mathematics education. For example, Fauvel ("For Learn Math," 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing "how" to introduce history into mathematics lessons is a…

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students'…

On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…

Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an…