NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

About seven years ago, the mathematics teachers at the author's secondary school came to the conclusion that they were not satisfied with their rather traditional geometry textbook. The author had already begun using a problem-based approach to teaching geometry in her classes, a transition for her and her students that inspired her to write about…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

"I CAN Learn"[R] is a computer software system that provides math instruction through a series of interactive lessons. These lessons are delivered with a one-to-one student-to-computer ratio. Students determine the pace of each lesson and must demonstrate mastery of the lesson before progressing to the next one. Teachers provide…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

Whereas origami is said to have pedagogical benefits in geometry education, research is inclusive about its effect on spatial ability and geometric knowledge among preservice teachers. The study investigated the effect of origami instruction on these aspects using pretest posttest quasi-experiment design. The experimental group consisted of 52…

The uptake of technology and specifically, GeoGebra software, in teaching mathematics has had mixed success in spite of its documented benefits. This study investigated teachers' perspective towards training and eventual use of GeoGebra as a tool to enhance learning of mathematics. In this article we share findings from a larger study that was…

Although research on the effectiveness of differentiated and enriched instruction in improving the achievement of diverse students is still emerging, some studies suggest that students in academically diverse classrooms benefited academically from differentiated learning experiences. The primary research question explored in this study was…

The 2005 National Assessment of Educational Progress (NAEP) High School Transcript Study (HSTS) found that high school graduates in 2005 earned more mathematics credits, took higher level mathematics courses, and obtained higher grades in mathematics courses than in 1990. The report also noted that these improvements in students' academic records…

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers' content knowledge for teaching. However, there is no course…

"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 was conducted with the aim of comparing the behaviors and attainments related to the plane geometry in the old and new 6th-8th grades mathematics curricula (MC) in terms of Van Hiele geometry understanding levels. With this purpose document analysis method was used. In the study, the levels of behaviors and attainments in the old and…

"Achieving Fluency" presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on…

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…