This paper describes a possible dragging experiment in a dynamic geometry environment (DGE) that explores a necessary and sufficient condition for cyclic quadrilateral. The dragging modalities identified by Arzarello, Olivero, Paola, and Robutti (2002) and the functions of variation realized in DGE discussed by Leung (2003) will be used as tools…

In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 students commented on various problems and the likelihood that their teachers would use those problems to engage students in proving. We use their responses to…

This article discusses how a teacher can prepare the terrain for students to understand what it means to define a figure. Drawing on writings from mathematicians and mathematics educators on the role of definitions in mathematics, the authors argue that students develop a greater appreciation for the conciseness of a mathematical definition if…

The purpose of the present study was to present examples of the utilization of social processes such as teacher questioning and collective argumentation coupled with an appropriate use of a manipulative material to stimulate students' thinking in teaching geometry. We first present theoretical issues concerning the use of manipulatives, teacher…

Technological tools have the potential to offer students the possibility to represent information and relationships embedded in problems and concepts in ways that involve numerical, algebraic, geometric, and visual approaches. In this paper, the authors present and discuss an example in which an initial representation of a mathematical object…

If we look into the past we will discover that the teachers of thermodynamics were always trying to interpret an important part of their science by using geometry. The relation between geometry and thermodynamics is of great interest and importance in teaching thermodynamics. This article examines the way undergraduate students of thermodynamics…

This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…

Readers will find several papers that address high-level issues in the use of technology in education, for example architecture and design frameworks for building online education materials or tools. Several other chapters report novel approaches to intelligent tutors or adaptive systems in educational settings. A number of chapters consider many…

Purpose: The purpose of this scientific monograph is to show new and creative approaches to different school subjects in primary and secondary level. Methodology: Interdisciplinary and international comparative approaches were used. Now according to the 7th Framework Program, the preferred form of Science Education (www.scientix.eu) is preferred…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

The What Works Clearinghouse (WWC) looked at elementary school math curricula designed to promote math knowledge and skills among elementary school students (average ages 5 to 10 years). Curricula included in this review are replicable, materials-based instructional programs that cover one or more of the following content areas: numbers,…

The "Connected Mathematics Project" ("CMP)" is a problem-centered mathematics curriculum designed for all students in grades 6-8. Each grade level of the curriculum is a full-year program and covers numbers, algebra, geometry/measurement, probability, and statistics. The program seeks to make connections within mathematics,…

This book contains activities and projects designed to be congruent with three underlying philosophies: the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards; Howard Gardner's multiple intelligences; and manipulatives, activities, and projects. The introduction contains information about educational reforms; multiple…