A heuristic description is given of the rediscovery with "Sketchpad" of a less-well-known, but beautiful, generalization of the nine-point circle to a nine-point conic, as well as an associated generalization of the Euler line. The author's initial analytic geometry proofs, which made use of the symbolic algebra facility of the TI-92 calculator,…

The Internet is increasingly being used as a medium for educational software in the form of miniature applications (e.g., applets) to explore concepts in a domain. One such effort in mathematics education, the Educational Software Components of Tomorrow (ESCOT) project, created 42 miniature applications each consisting of a context, a set of…

This article discusses 5 approaches that secondary researchers might use to obtain robust estimates in structural equation modeling analyses when using data that come from large survey programs. These survey programs usually collect data using complex sampling designs and estimates obtained from conventional analyses that ignore the dependencies…

Students of General Physics often complain that the course is too abstract and remote from daily life. As teachers, we emphasize that the abstract concepts of physics are indispensable for understanding our daily experiences, and we try to give the impression that quantitative descriptions can be achieved by adopting concrete mathematical…

In this conceptual article, the authors describe an alternative course structure that joins learning key marketing concepts to creative problem solving. The authors describe an approach using a convergent-divergent-convergent (CDC) process: key concepts are first derived from case material to be organized in a marketing matrix, which is then used…

This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

This lesson helps participants examine their own attitudes and feelings about being faced with an unplanned pregnancy and understand the difficult choices involved when women need to make a decision about unplanned pregnancy. The lesson uses brainstorming, discussion, an examination of "case studies," and role-playing to help participants develop…

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of…

A number of research agendas including teaching games for understanding, invasion games tactics, cooperative learning, seeking solutions to ill-defined problems, and examining learner's use of domain specific knowledge share thoughtful decision making as a common denominator. For the most part, each of these research strands have been investigated…

This article describes an integrated problem solving and program development environment, illustrating the application of the system with a detailed case study of a small-scale programming problem. The system, which is based on an explicit cognitive model, is intended to guide the novice programmer through the stages of problem solving and program…

It is likely difficult for academics to think of a college or university that does not have some program of general education (GE). Over the past century, GE's model of liberal learning has become so entrenched in U.S. universities that it is widely seen as the core of the national undergraduate curriculum. In a series of distributed courses that…

In this paper, we describe an innovative approach to promoting effective classroom-based groupwork and the development of children's speaking and listening at Key Stage 1. This approach, known as Thinking Together, was initially developed for use with Key Stage 2 children. The work reported here explains how this approach has now been applied to…

In this article, the authors explain how curriculum-based measurement (CBM) differs from other forms of classroom-based assessment. The development of CBM is traced from computation to concepts and applications to real-life problem solving, with examples of the assessments and illustrations of research to document technical features and utility…

The principal mode of environmental education is to integrate environmental education into science classes. Biology is a life science. To study biology it is necessary to talk about the living environment and the relationship between biological organisms and their environment. Studying biology not only enables students to learn a great deal of…