Describes a long term teaching experiment carried out with students from grades 9 and 10. Aims at clarifying the role of the Cabri environment in teaching-learning processes. Analysis of protocols shows the possible evolution of a justification into a proof but at the same time indicates that this evolution is not expected to be simple and…

This article describes the integration of transformational geometry, mathematics, history, art, and cultural studies in a middle-grades mathematics classroom. Its intent is to illustrate how providing students with real-world experiences allows them to see and model mathematics as an integrated whole and make both thoughtful connections between…

The effect of intervening use of molecular visualization software was tested on 73 first-year general chemistry students. Pretests and posttests included both traditional multiple-choice questions and model-building activities. Overall students improved after working with the software, although students performed less well on the model-building…

An interdisciplinary course centered on mathematical ideas (involving infinity and geometry) is described. The course was developed by the authors, both mathematicians, as a vehicle for engaging students in learning about mathematical ideas that are rarely found in the general undergraduate curriculum. The course was offered to honors students…

Teachers tend to design worksheets to assist their students to develop their spatial skills. Many secondary schools students may not have sufficient concrete experiences to tackle abstract reasoning in geometrical concepts competently. In addition, students who are non-visual and spatial learners may have difficulties in learning geometrical…

This article presents teaching ideas designed to support the belief that students at all levels (preservice teachers, majors, secondary and elementary students) need exposure to non-routine problems that illustrate the effective use of technology in their resolution. Such use provides students with rapid and accurate data collection, leading them…

Mathematics teacher education programs are designed with an intention, explicit or implicit, to produce graduates who are competent in both pedagogic knowledge and discipline knowledge. This paper explores students' experiences in coming to learn mathematics and mathematics education. Using an example from a quiz question, supplemented with…

This paper reports the results of a doctoral research pilot study that paired a researcher with an experienced classroom teacher for a 12-week time span with the goal of effectively integrating the use of Geometer's Sketchpad (GSP) into the classroom teacher's practice. Using a teacher development experiment, the researcher created an…

"Differentiating Instruction With Menus Grades 3-5" offers teachers everything they need to create a student-centered learning environment based on choice. Addressing the four main subject areas (language arts, math, science, and social studies) and the major concepts taught within these areas, these books provide a number of different types of…

Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student's progress. To identify fallacies in students' preconceived ideas, "Uncovering Student Thinking in Mathematics" offers educators a powerful diagnostic technique in the form of field-tested assessment…

There has been concern over the validity of the Algebra Diagnostic Test (ADT) used to determine the actual level of student preparation for the first quarter of calculus as taught at the University of California, Santa Barbara. It has been hypothesized that performance-based questions, along with the more traditional multiple choice questions,…

The objective of this study was to investigate the effects of Logo Mathematics Tutorial Two (LMT2) for teaching polygons to minority students. The polygons were chosen to develop a sound foundation for further knowledge and exploration in geometry. The subjects (N=23) were middle and high school students that were trained using LMT2. The subjects…

This book examines the Navajo system of spatial knowledge and describes a culture-based curriculum for the development of an intuitive geometry based on the child's experience of the physical world. Aspects of the Navajo cosmology relevant to spatial knowledge are discussed: the structure of the world; the dynamic nature of the universe;…

This conference proceedings volume for PME-NA-XIX contains a total of 87 reports: one plenary session report; 39 research reports; 20 short oral reports; 25 poster session reports; and two discussion group reports. Only the plenary and research reports are full reports; the others are generally one-page abstracts. The full reports include: (1)…

In 1988-89 the Connecticut Vocational-Technical School System initiated a program for the ongoing review and upgrading of all trade and academic curricula used in the system's 17 schools to insure that each curriculum is consistent with current standards. Every 3 years the Curriculum Steering Committee for the trade or academic subject conducts a…