This article "opens up" the study of the relationship between quadrilaterals and circles to two sets of quadrilaterals--those that can be drawn either inside (cyclic) or outside (tangential) a circle (or both). Of course, "all" triangles are both cyclic and tangential. Or, to use the traditional Euclidean language for triangles, a unique…

This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

This paper reports on a 3-year, NSF-funded research and development project called ACED: Adaptive Content with Evidence-based Diagnosis. The purpose of the project was to design, develop, and evaluate an assessment for learning (AfL) system for diverse students, using Algebra I content related to geometric sequences (i.e., successive numbers…

This paper examines students' self-motivation in mathematics learning between girls and boys using secondary analysis of the Third International Mathematics and Science Study (TIMSS) conducted in 2003 by the International Association for the Evaluation of Educational Achievement (IEA) involving eighth graders. Components of self-motivation include…

In this narrative of teacher educator action research, the idea for and the context of the lesson emerged as a result of conversations between Shelly, a mathematics teacher educator, and Lisa, a quilter, about real-life mathematical problems related to Lisa's work as she created the templates for a reproduction quilt. The lesson was used with…

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology. This paper reports on the development of a software environment called "3DMath", a dynamic three-dimensional geometry microworld aimed at enabling learners…

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,…

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…

One of the four cornerstones of the National Council of Teachers of Mathematics (NCTM) "Curriculum and Evaluation Standards for School Mathematics" asserts that connecting mathematics to other subjects in the curriculum and to the everyday world is an important goal of school mathematics. This yearbook is designed to help classroom…

This volume contains the full text of 2 plenary papers and 26 research reports. In addition, brief, usually one-page, reports are provided for 6 discussion groups, 10 technology focus groups, 7 symposiums, 7 oral presentations, and 17 position sessions. The two full plenary reports are: (1) "Problems of Reification: Representations and…

In this study, the effects of a form of cooperative group instruction (Student Teams Achievement Divisions) on student motivation and achievement in a high school geometry class were examined. Ninety (mostly 10th-grade) students were randomly assigned to either a control group receiving traditional instruction or one of two treatment groups…

An effective way to teach the concept of image is to give students a model of human vision which incorporates a simple mechanism of depth perception. In this study two almost identical versions of a curriculum in geometrical optics were created. One used a mechanistic, interpretive eye model, and in the other the eye was modeled as a passive,…

This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

This paper is based on efforts to bring change to school mathematics by trying to develop mathematics classroom communities in predominantly minority classrooms. In these communities, students work towards doing mathematics by working on open-ended, investigative situations; sharing ideas and strategies; and jointly negotiating meanings. Students…

This book reinforces the outstanding work done by the National Council of Teachers of Mathematics (NCTM) in developing curriculum standards for students in kindergarten through fourth grade by discussing the 13 strands of mathematics and their implications for teachers and parents who work with students. It also provides some suggested resources…