The purpose of this study was to enhance pre-service secondary mathematics teachers' skills of using the Geometer's Sketchpad (GSP) through Lesson Study. Twenty-four Lesson Study groups each comprising four or five pre-service secondary mathematics teachers who attended a mathematics teaching methods course in a local public university were set up…

Students' lack of understanding about the relationships between geometry in two and three dimensions led the author to a surprising source of inspiration--the ancient philosopher and geometer Plato. From a theoretical perspective, the author's approach embodies the four instructional strategies that Eggen and Kauchak (2001) suggest for engaging…

"From Another Perspective" is a year-long course for teachers of mathematics that is designed to enhance teachers' awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal &…

We present a guided-inquiry experiment using Spartan Student Version, ready to be adapted and implemented into a general chemistry laboratory course. The experiment provides students an experience with Spartan Molecular Modeling software while discovering the relationships between the structure and properties of molecules. Topics discussed within…

Given the importance of algebra, middle school mathematics teachers have a responsibility to help students transition from understanding arithmetic to understanding the algebra that will be necessary for success in high school. One method of transition involves introducing algebraic concepts in concrete ways using meaningful contexts. The series…

The Sami are an indigenous people of the Arctic, and through a resolution of the United Nations, Norway is bound to take care of the Sami culture and language. Since 1987 the Sami have had their own curriculum, but they have no mathematics syllabus. In this paper we summarize the legal acts that take care of the Sami culture within the Norwegian…

The Department of Mathematics and Statistics at Utah State University offers two courses for preservice secondary school mathematics teachers that complement each other in working toward a vision for school mathematics in which "all students have access to high-quality, engaging mathematics instruction." Through these courses, students…

Each year on a one-year full-time programme at the University of Hong Kong, the author devotes a couple of tutorial sessions in the mathematics major modules to "interesting or challenging questions raised by pupils". The main purpose of the sessions is for students to think about how they would react to such questions and often to…

The question explored here is whether having a 90[degrees] angle is the most fruitful analogue in spherical geometry to right triangles in Euclidean geometry. A strong case is made for the property of a triangle with one angle equal to the sum of the other two.

We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple…

Improving student achievement in mathematics in secondary schools remains a priority for public education in our country. With continued federal and state mandates to improve overall student achievement in mathematics, as well as to close the achievement gap, many school districts have sought programs, such as Advancement Via Individual…

Although there are increasing numbers of professional development (PD) materials intended to foster teachers' mathematical knowledge for teaching within the topics of number and algebra, little attention has been given to geometry. In this article we describe the Learning and Teaching Geometry project's approach to the development of PD materials…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

It is widely accepted that learning becomes more enduring and deeper if geometric concepts are presented in various orientations and dimensions in textbooks. The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and the textbooks in terms of sizes and orientations. For this…

This article presents a web-based tool designed to compute certified equations and graphs of geometric loci specified using standard Dynamic Geometry Systems (DGS). Complementing the graphing abilities of the considered DGS, the equations of the loci produced by the application are remotely computed using symbolic algebraic techniques from the…