In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

This article aims to examine the impact of an online learning environment enriched with computer activities on geometry achievement and geometric habits of mind (GHoM). The study includes reflections from an online application of a one-term computer-aided mathematics teaching course in which the participants were preservice teachers (PTs) enrolled…

The objective of this paper is to present two preservice secondary mathematics teachers' beliefs about teaching Geometric Transformations (GTs) using Geometer?s Sketchpad (GSP). The study comprised of series of five task-based interviews with each of two participants, who were senior undergraduate preservice teachers, at a medium-sized public…

This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge…

Background: This article reports contributions of an assessment tool called Portfolio of Evidence (PE) in learning college geometry. Material and methods: Two classes of second-year students from one Ethiopian teacher education college, assigned into Treatment and Comparison classes, were participated. The assessment tools used in the Treatment…

It has been common to use video records of instruction in teacher professional development, but participants have rarely been encouraged to evaluate teachers and students' actions in those records, allegedly because evaluation deters from the development of a professional discourse. In this study, we inspected teachers' online discussions of…

When properly implemented, the vision of "Beyond Crossroads" will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to "Beyond Crossroads," students will be expected…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…