Dawn of science

Descartes discovered the link between algebra and geometry, which forms the cornerstone of applied geometry today.     

Integrating synchronous and asynchronous internet distributed education for maximum effectiveness

Distributed education delivered via the Internet is a growing practice, with most institutions offering at least course websites and many expanding to full course offerings and even online degree progams. There are two schools of thought with regard to delivery mode: the larger group has focused on asynchronous delivery, accessible at any time via webpages and interactive tutorials and quizzes, while a smaller group advocates synchronous delivery where students are online and interact during class time. This paper summarizes the advantages and disadvantages of the two delivery modes and describes our successful and growing experience of more than a decade using an open source synchronous delivery tool blended with a variety of asynchronous capabilities and classroom instruction. We conclude that a synergistic combination of the two modes with in-person instruction, designed to provide maximum flexibility to the student within the constraints of the subject, offers the best support for student learning. www:     

The brachistochrone

The brachistochrone problem posed by Bernoulli and its solution highlights one of the most famous experiments in physics which illustrates the variational principle. This pedagogical study is designed to ignite a classroom discussion on the variational problem. We overview the Euler–Lagrange formalism of the variational principle and obtain the solution to the brachistochrone problem. We demonstrate the success of the variational method using brachistochrone models which were fabricated specially for this purpose.     

The role of university-based induction in beginning elementary teacher enactment of effective mathematics teaching

The purpose of this paper is to describe the school-based contextual constraints perceived by beginning elementary teachers as they attempted to enact their visions of effective mathematics teaching and the components of a mathematics-specific, university-based induction program designed to support elementary teachers in their teaching of mathematics. A significant number of beginning teachers in the program indicated that curriculum pacing guides and grade level teachers often discouraged their enactment of effective mathematics teaching. We describe the components of the induction program in general and then discuss the specific ways that program mentors, who were elementary teachers with expertise in mathematics teaching, supported beginning teachers in navigating the constraints identified. Data suggest that supporting teachers’ pedagogical agency to navigate local school contexts should be an additional consideration in teacher preparation and induction programs.     

Learning Strategies Training

A learning strategies program emphasizing primary (text-oriented), and support (affective) strategies was evaluated. Participants were given training in one of two sequences: primary-support or support-primary. A no-treatment group served as a control. In general, the results revealed that strategy training significantly improved performance on both text-processing and self-report measures. The primary-support group typically scored higher than the support-primary group on the text-processing measures. Conversely, the support-primary group reported more positive responses on the self-report measures. Long-term follow-up results are also presented.