In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

This paper addresses a central issue in secondary school geometry, namely the role of proof. In an integrated mathematics and science curriculum, the role of proof as a process of conjecturing, explaining, and justifying within a small-group setting is analyzed. Particular attention is given to the students' use of empirical evidence and algebraic…

This study investigated whether the van Hiele model accurately describes the geometric thinking of gifted students in the 6th through 8th grades prior to a formal course in geometry and made comparisons with what has been found with other populations. The results from 120 students who completed a 25-item multiple choice paper-and-pencil test,…

In this unit of the Seeing and Thinking Mathematically series, students use geometry to analyze buildings from around the world, design and build their own house models, create plans for their designs, and build from each other's plans. Students start out the unit building with cubes and later move to other geometric shapes. As they learn to…

This yearbook focuses on the role of technology in school mathematics. Chapters are replete with classroom-tested ideas for using technology to teach new mathematical ideas and to teach familiar mathematical ideas better. Chapters included: (1) "Using the Graphing Calculator in the Classroom: Helping Students Solve the "Unsolvable" (Eric Milou,…

The Colorado Model Content Standards for Mathematics were designed to serve as a guide for school districts as they define standards that will enable every Colorado student to develop the mathematical literacy needed for citizenship and employment in the 21st century. A new vision is provided of the content students should study in order to…

Finding the number of cubes in rectangular solids provides a cognitive framework for understanding the measurement of volume. This study reveals whether the activities provided in the context of equal investing and equal sharing that emphasize both numerical and spatial aspects of cube configurations cause any improvement in student strategies…

This volume attempts to bring together a collection of reports on the Geometric Supposer, a series of computer software environments which can be a tool for exploring particulars and generalizations in geometry. The book contains the following chapters: (1) "A Personal View of the Supposer: Reflections on Particularities and Generalities in…

In the attempt to improve the quality of geometry instruction in schools, researchers and teachers alike have given considerable attention to the van Hiele theory of geometry learning and development, which proposes a series of cognitive levels through which every geometry student passes. This paper reports a study to determine the extent to which…

The papers in this report represent the imagination, analysis, and experiences of many people involved in recent curricular studies in secondary school mathematics. It differs from reports that seek broad agreement on conservative, traditional curricula, representing instead the point of view of those working with emerging electronic technology…

Activities in which students make models of a variety of geometric solids are described. (SD)

This study investigated the ability of middle school children to perform Euclidean transformations mentally. The results indicated that the tasks were more difficult than Piagetian theory would indicate. (SD)

Many fundamental geometric figures can not be constructed on the familiar square geoboard (e.g., equilateral triangle, regular hexagon). Activities which can be used with an isometric geoboard for study of these figures are catalogued. (SD)

A system for categorizing components of geometry class discussions is described. The unit of observation is the teacher question; responses are coded at four cognitive levels. The system is easier to use than many in the literature; use of it can help teachers develop questioning techniques. (SD)

The development of abstract mathematical thinking is an essential part of mathematics and the geometry is regarded as a suitable domain to serve this purpose. As different technologies such as computers and graphing calculators are widely being used, curriculum developers on geometry should take these technologies into consideration. Several…