The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

While serving in the U.S. Congress, Abraham Lincoln, a self-taught learner, mastered Euclid's Elements (Basler 1953). Most students today do not study mathematics for recreation. Unlike Lincoln, they need a little help in learning how to write a geometry proof. Today's technology--specifically, The Geometer's Sketchpad[R] (GSP)--can help make…

The authors examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11…

The main goal of the Learning and Teaching Geometry (LTG) project is to build professional development (PD) materials that provide opportunities for teachers to engage in learning about geometric similarity through the use of video cases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom…

In this paper, we study how prospective teachers guide students' reasoning in GeoGebra-supported inquiry tasks. Twenty prospective mathematics teachers wrote about how they would react as a teacher in hypothetical situations where high school students present their GeoGebra-supported solutions to the teacher. Before writing their reactions, the…

The purpose of this qualitative case study involving six secondary school teachers was to obtain insight into how geometry is taught in selected Nigerian and South African high schools. It also aimed, by making use of the van Hiele model of geometry instruction, to elucidate what possible learning opportunities observed instructional methods could…

Unlike studies on cooperative learning that have focused on the verbal communication aspect of learning, this study focuses on the non-verbal aspect--mindful movement, which is the use of body movement to aid academic learning. Our research examined the link between five learning activities occurring within a cooperative group of children using…

Measurement is an integral component of the PK-12 mathematics curriculum. At various grade levels, much attention is given to the areas of geometric shapes. However, there is research evidence that measurement is problematic for US students. In this paper, the merits and demerits of two possible sequences (conventional and alternative) in teaching…

Circle Geometry, a senior mathematics topic, is often regarded as time-consuming and associated relational concepts difficult for students to grasp. Units of work that introduce students to circle geometry theorems are frequently described as a string of tedious constructions. This article explores teacher-designed dynamic geometry software…

This mixed methods study examined preservice secondary mathematics teachers' perceptions of a blogging activity used as a supportive teaching-learning tool in a college Euclidean Geometry course. The effect of a 12-week blogging activity that was a standard component of a college Euclidean Geometry course offered for preservice secondary…

Teachers are using technological innovations--including interactive whiteboards--in pre-K-grade 3 classrooms across the country. An IWB is a wall-mounted, touch-sensitive flat screen. When connected to a computer (or another electronic device) and a projector, it displays enlarged instructional content (such as a math word problem, pictures or…

In this paper, I report on preservice teachers' reflections and perceptions on their problem-solving process in a technological context. The purpose of the study was to investigate how preservice teachers experience working individually in a dynamic geometry environment and how these experiences affect their own mathematical activity when…

This study explored the predictive relationships of teacher efficacy, teacher knowledge, and teacher practices with student achievement. More specifically, secondary mathematics teachers' efficacy beliefs, geometry knowledge for teaching, and the cognitive complexity of the teachers' classroom practices were examined for 72 teachers in both urban…

A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The…

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…