The problem of angle trisection continues to fascinate people even though it has long been known that it can't be done with straightedge and compass alone. However, for practical purposes, a good iterative procedure can get you as close as you want. In this note, we present such a procedure. Using only straightedge and compass, our procedure…

The authors derive distance formulas in two-and-three-dimensional coordinate geometry utilizing the concept of similar triangles and the Pythagorean theorem. (MN)

The activities are designed to have students manipulate physical models of geometric figures, engage in spatial visualization and observe relationships between triangles and parallelograms and between triangles and rectangles. Worksheets designed for duplication are included in the materials and an answer key is provided. (MP)

Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to…

This paper reports a case study which involved 32 secondary school students participating in an online collaborative learning (OCL) activity known as Diary of Discovering Geometry. This activity aimed to explore the real contents in the learners' surrounding for discovering the spatial concepts and the applications of geometry. The purpose of the…

In this article we describe our experiences using picture books to provide young children (five- to six-year-olds) with a learning environment where they can explore and extend preliminary notions of mathematics-related concepts, without being taught these concepts explicitly. We gained these experiences in the PICO-ma project, which aimed to…

Adam, an 11th grader, was identified as gifted and accepted into a two week summer enrichment program. He signed up for "Geometry with Flash Programming." He had no prior programming experience but had a strong and healthy self-image as mathematics student. Although Adam had a positive attitude toward mathematics and saw himself as a successful…

This article reports on an investigation of how teachers of geometry perceived an episode of instruction presented to them as a case of engaging students in proving. Confirming what was hypothesized, participants found it remarkable that a teacher would allow a student to make an assumption while proving. But they perceived this episode in various…

Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…

Engaging students with real-world activities can be effective in supporting the learning of mathematics, "whenever possible, real-world situations will provide a context for both introducing and applying geometric topics" (NCTM 1989). Tool making is a way to bring real-world mathematics into the classroom and using the tool is a way of…

The authors investigated the effects of drama-based instruction on students' geometry achievement, geometric thinking level, attitudes toward mathematics and geometry, and retention of achievement, in comparison with traditional teaching. The sample involved 102 7th-grade students from a public school. Multivariate analyses of covariance revealed…

Whether they are third graders or teacher candidates, students can learn about perimeter and area while having fun manipulating two-dimensional figures into three-dimensional objects. In this article, the author describes a common mathematical activity for geometry students by creating nets for a cube. By making connections between nets in two…

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…