In the early stages of working with dynamical geometry environments, students make many more mistakes than if they thought out and implemented the same constructions on paper. Most Czech teachers have very little experience of doing geometry using computers. A methodology which could help them to teach students to avoid mistakes dependent on the…

Although the nature of the research varies, as do concepts of angle, research in general supports the supposition that angle is a complex idea, best understood from a variety of perspectives. In fact, the concept of angle tends to be threefold, consisting of: (1) the traditional, static notion of two rays meeting at a common vertex; (2) the idea…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

Twenty third-year students from two rural teachers' colleges in Jamaica carried out a coordinated set of individual investigations into children's learning of geometrical concepts during their assignment to schools as intern teachers. All the studies, which covered classes from grade 2 to grade 10, included some initial testing of children's…

A teacher tells how she uses the game of chess to introduce students to formal geometry by drawing analogies between rules of chess and deductive systems. (JP)

This textbook presents the foundation for a second high-school year mathematics course. It aims to teach "how to study" as well as the "content" of a second unit of secondary mathematics through the nature and form of the material, explicit exhibits, formulated tests of both sound and unsound reasoning, through study-helps,…

Reported are the results of a study to determine if there is a difference in learning as measured by an achievement test between high school students who study plane analytic geometric topics via a vector approach and those who study the same topics via a traditional approach. Secondary objectives concerned the transfer to further topics in solid…

A sequence of ellipses and a sequence of hyperbolas, both graphically approaching some parabola, are expressed algebraically and then shown to approach the parabola. (MN)

An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)

The author examines certain areas of confusion which arise in the teaching of linear equations for lines. (SD)

Several approaches to the teaching of matrices are discussed. (SD)