It has been projected that by 2020 one out of three children will be from a culturally and linguistically diverse (CLD) background. Rapid changes in school demographics and student needs are already presenting new challenges to school-based service-delivery methods and there have been calls for increased professional development efforts to better…

This article examines a case study framework designed to aid in the preparation of emerging community college leaders. The framework is multidimensional and fluid in nature, taking into account the multiplicity of factors affecting leadership in community colleges. The steps in the framework consist of (a) assuming the role of the leader; (b)…

This article presents a discussion of research and theoretical perspectives on creativity and instructional design, offering a conceptual model of the connection between these two constructs that was originally proposed in the dissertation work of the first author (Clinton, Creativity and design: A study of the learning experience of instructional…

We recently proposed the Creative Reasoning Test (CRT), a test for reasoning in ill-defined problem spaces. The test asks children who first performed the Standard Progressive Matrices test (SPM) to next generate an SPM-style test item themselves. The item is scored based on different aspects of its complexity. Here we introduce a method to…

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

Just as students need plenty of time to practice skills such as solving fraction problems, they also need time to practice the skills of discourse to become better communicators and stronger mathematicians. Embedded within discourse strategies are specific ways to maximize communication. When repeatedly practiced, students learn to listen to one…

Within composition studies, transfer and rhetorical genre studies have found an especially productive partnership for exploring together whether and in what ways students transfer writing-related knowledge from one context to another. This article continues this synthesis by turning to Anne Freadman's notion of uptake to suggest a more robust…

This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.

This article describes a grading approach that encourages students to employ particular problem-solving skills. Some strengths of this method, called "process-based grading," are that it is easy to implement, requires minimal time to grade, and can be used in conjunction with either an online homework delivery system or paper-based homework.

In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and…

Designing an optimal Norman window is a standard calculus exercise. How much more difficult (or interesting) is its generalization to deploying multiple semicircles along the head (or along head and sill, or head and jambs)? What if we use shapes beside semi-circles? As the number of copies of the shape increases and the optimal Norman windows…

Current theories argue that human decision making is largely based on quick, automatic, and intuitive processes that are occasionally supplemented by slow controlled deliberation. Researchers, therefore, predominantly studied the heuristics of the automatic system in everyday decision making. Our study examines the role of slow deliberation for…

The problem of charge motion governed by image force attraction near a plane metal surface is considered and solved self-consistently. The temporal dispersion of metal dielectric permittivity makes the image forces dynamic and, hence, finite, contrary to the results of the conventional approach. Therefore, the maximal attainable velocity turns out…

Literacy in STEM is critical to individual and national success in the twenty-first century, the century of science. Gifted students are in a position to make especially profound contributions to solving the world's major challenges and creating new economic opportunity. But modern American culture and the way STEM education is approached and…

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…