Discusses a conjecture of a ninth-grade student that extended a geometry theorem about trisecting sides of a triangle. Presents a proof and extensions. (MKR)

Describes how a 3-inch by 5-inch card can be used to develop properties of similar triangles and prove the Pythagorean theorem. (MKR)

Presents interesting investigations and activities for inscribed and escribed circles of right-angled triangles. (ASK)

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…

Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

This book is loaded with hands-on measurement and geometry activities that will get students rolling up their sleeves, excited to use their math skills. The author has created these activities to supplement a teacher's existing math curriculum. They are flexibly designed for use as either introductory, reinforcement, or assessment activities. This…

In this article, the author uses a range of simple materials to facilitate students' understandings of measurement concepts. The six activities presented are essentially about looking at different configurations of a given volume. (Contains 6 figures.)