This is the third part of a study of plane transformations described in a complex setting. After the study of homotheties, translations, rotations and reflections, we proceed now to the study of plane similarities, either direct or inverse. Their group theoretical properties are described, and their action on classical geometrical objects is…

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…

This paper tabulates the correlation of Virginia's mathematics performance expectations with Virginia's 2009 mathematics standards of learning.

We investigate the impact of integrating dynamic geometry environments with haptic devices, which allow users to not only see and manipulate geometric figures on a screen but also feel, through force-feedback, the result of interacting with such objects. The feedback loop can be assigned to varying attributes of objects, for example, the changing…

A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…

Dynamic geometry software (DGS), such as Geometer's Sketchpad[TM], Cabri Geometry[TM], and GeoGebra[TM] has become a widely used classroom technology. The broad availability of DGS has given students the opportunity to engage in many aspects of reasoning and proof, including exploration, conjecture development, and proof, in its many roles. By…

Storytelling can provide unique teachable moments. Mathematics content found in a good story can be seamlessly woven throughout a lesson. The technical vocabulary used in some stories occurs in a natural way, outside a textbook setting. A great story can also motivate students to actively engage in meaningful mathematics. With a wide range of…

Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but also because it has a language of its own and…

The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

Assessment is a tool used in the classroom as a way to deepen students' learning and to allow the educator to make informed decisions regarding instruction. In this article, the authors focus on the role of assessment, both in terms of teachers and students, while developing students' understanding of geometry. In particular, the authors are…

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…

Trends in International Mathematics and Science Study raised the concern that the United States (US) mathematics teachers place less emphasis on topics and teach a variety of content strands (Goldsmith, Mark & Kantrov, 2000; Kerachsky, 2008). The overall pattern in the US mathematics classrooms today is that primary and upper elementary…