The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

We provide several constructions, both algebraic and geometric, for determining the ratio of the radii of two circles in an Apollonius-like packing problem. This problem was inspired by the art deco design in the transom window above the Shadek Fackenthal Library door on the Franklin & Marshall College campus.

The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…

While many school psychologists agree that part of the satisfaction in their profession lies in the challenges, dealing with these challenges daily can be exhausting. With NASP's 2010 "Model of Comprehensive and Integrated School Psychological Services" (also known as the NASP Practice Model), school psychologists are challenged to take time to…

One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

This article presents a few methods for generating Sudoku puzzles. These methods are developed based on the concepts of matrix, permutation, and modular functions, and therefore can be used to form application examples or student projects when teaching various mathematics courses. Mathematical properties of these methods are studied, connections…

This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

The conceptual foundation for Direct Behavior Rating as a behavior assessment method is reviewed. A contemporary definition of Direct Behavior Rating is framed as combining strengths of systematic direct observation and behavior rating scales, which may result in a usable and defensible assessment tool for educators engaged in formative purposes.…

Intervention integrity or adherence describes qualities of carrying out an intervention plan and in research is fundamentally linked to experimental validity questions addressed by measurement of independent and dependent variables. Integrity has been well described in conceptual writing but has been a continuing thorny subject in research and…

Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key "stumbling blocks" for students as they attempt to make this transition? How do differences in faculty expectations for students…

It is widely held that, by teaching individuals how to reason through and analyse everyday problems, the teaching of critical thinking develops the deliberative capacities essential to the healthy functioning of democracy. Implicit in this view is the assumption that a certain commensurability exists between the problems presented in such…

Integrated dance has featured in several publications from the mid-1990's onwards, particularly from the standpoints of equity of access, and contesting perceptions of dominant conventional notions of what dance is and who can dance including issues of embodiment and representation. Other publications and manuals focus primarily on how to teach…

Real world mathematical modeling activities can develop needed and valuable 21st century skills. The knowledge and skills to become adept at mathematical modeling need to develop over time and students in the elementary grades should have experiences with mathematical modeling. For this to occur elementary teachers need to have positive…

A university's seminar model suggests the design of a collaborative structure that promotes team sharing and problem solving. The mentoring that occurs in the seminar comes mainly from the student teachers sharing their experiences with each other and working together to make sense of their classrooms in the context of the theories they have…