This case study investigates prospective middle school mathematics teachers' use of the Angle tool in GeoGebra, focusing on reflex angles in a geometric construction task. They constructed a parallelogram with individual heights for any two consecutive sides. We analyzed their screencasts to identify the ways in which they used reflex angles in…

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

This study aimed to document pre-service elementary teachers' (PSTs'), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs' knowledge of content in which they were being asked to prove influenced their ability to…

The purpose of this research is to examine preservice elementary school teachers' geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as…

Opportunities for teacher candidates to investigate and enact the work of teaching in settings of reduced complexity--what are called "approximations of practice"--offer a promising path toward preparing more ambitious and equitable mathematics teachers. However, these approaches face the risk of not preparing individuals to continue…

While teaching a methods class for preservice secondary school mathematics teachers, Christopher E. Smith found that although all students could draw a reasonably close approximation of a circle, not all could provide an entirely accurate definition of a circle. A discussion with students led him to think about ways of reintroducing students to…

This exploratory research project investigated graduate students' satisfaction levels with online learning associated with human (professor/instructor and instructional associate) and design factors (course structure and technical aspects) using a survey study. A total of 81 graduate students (master's students who majored in math and science…

Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

The purpose of this study was to enhance pre-service secondary mathematics teachers' skills of using the Geometer's Sketchpad (GSP) through Lesson Study. Twenty-four Lesson Study groups each comprising four or five pre-service secondary mathematics teachers who attended a mathematics teaching methods course in a local public university were set up…

"From Another Perspective" is a year-long course for teachers of mathematics that is designed to enhance teachers' awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal &…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

This paper describes the genesis and purpose of our geometry methods course, focusing on a geometry-teaching technology we created using NVIDIA[R] Chameleon demonstration. This article presents examples from a sequence of lessons centered about a 3D computer graphics demonstration of the chameleon and its geometry. In addition, we present data…

Presents a miniresearch project from a college geometry class for preservice mathematics teachers involving Venn diagrams for five sets. (Author/MKR)

In this paper, I examine some issues within the new frontier of integrating technology into teacher education and professional development. I present an approach to teach a secondary mathematics methods course integrating technology. Specifically, this study focuses on how the integration of multimedia and online discussion into a mathematics…