In both baseball and mathematics education, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, it is not always the best strategy. Sometimes an analysis of errors provides much deeper insights into mathematical ideas and, rather than something to eschew, certain types of errors…

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…

A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical…

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

This exploratory study tests the assertion that instructional strategies that match field-dependence status of students are most effective. The study conducted with 12 graduate students registered in a graduate level online course. An online version of the Psychological Differentiation Inventory was used to measure the field-dependence status of…

Recently, e-learning in Taiwan's higher education faces new challenges as the Ministry of Education begins to loosen its control over degree-awarding programs. Studies on stakeholder perceptions toward important e-learning issues become critical at this juncture for policy makers to make viable investment decisions toward e-learning programs.…

In this paper, we examine the potential use of animation for supporting the teaching of some of the mathematical concepts that underlie computer games development activities, such as vector and matrix algebra. An experiment was conducted with a group of UK undergraduate computing students to compare the perceived usefulness of animated and static…

As schools are increasingly encouraging students to use the Internet and web-based technology at home and in the classroom, concerns among some parents have increased. Today's parents have learned about computers as adults and did not receive guided participation as children either from their parents or from their teachers. The essence of this…

As the use of web-based homework delivery and checking systems expands, we have greater need to evaluate how students engage with these systems and how changes in the systems influence student behavior. Reported here is the assessment of WeBWorK, an open-source web-based homework program used largely in postsecondary math and science courses, with…

The use of computerized adaptive testing (CAT) has expanded rapidly over recent years mainly due to the advances in communication and information technology. Availability of advanced mobile technologies provides several benefits to e-learning by creating an additional channel of access with mobile devices such as PDAs and mobile phones. This paper…

The effects of accompanying lectures with computer-mediated PowerPoint presentations or PowerPoint generated overheads on students' self-efficacy, attitudes, course performance, and class-related behaviors were examined. Two Introduction to Developmental Psychology sections were initially taught with lectures accompanied by either overheads or…

The design and empirical validation of a computer-based learning environment for acquiring long division skills, called the long division machine (LDM), are described. The construction of the LDM is primarily based on the didactic method of progressive schematisation. It offers the student a game-like environment for solving division problems by…

This paper argues for understanding ICT from the standpoint of philosophical world views. We present a framework, based on Pepper's root-metaphors (Formism, Contextualism, Mechanism, Organicism, and Animism/Mysticism) and we illustrate the use of the framework by looking at a common example of ICT: e-mail. It is argued that such a framework is…

The current paper details results from the Girls and ICT survey phase of a three year study investigating factors associated with low participation rates by females in education pathways leading to professional level information and communications technology (ICT) professions. The study is funded through the Australian Research Council's (ARC)…