We have used "GeoGebra," a dynamic geometry software environment, to explore how Year 4 students understand definitions of angles. Seven students defined angle and then completed several activities adapted for the dynamic environment. Afterward, students again shared their definitions of angles. We found that even a short investigation…

Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

This paper examines the role of scaffolding in the process of abstraction. An activity-theoretic approach to abstraction in context is taken. This examination is carried out with reference to verbal protocols of two 17 year-old students working together on a task connected to sketching the graph of |f|x|)|. Examination of the data suggests that…

The thinking-out-loud procedure provides teachers with an excellent mechanism for collecting information about students' thought processes and affective states during problem solving. Mathematics teachers can implement this process by modeling it during whole-class problem-solving sessions, proceeding slowly and encouragingly, working with small…

In this paper I will explore three contrasting teaching and learning environments, including one in which students engage in a "dance of agency". I will move from a consideration of classroom practices to a contention that our work as researchers of mathematics education should pay more attention to teaching practices. Further, that understanding…

Differences among students can yield rich benefits as well as pose difficult problems during collaborative learning. Students can draw on diverse individual experiences to exchange information, to understand different expressions of shared commonalities, and to construct new possibilities jointly. However, they also face the potential pitfalls of…

This study compared interaction with a computer vs. observation as learning situations for low and high ability student's learning of spatial visualization and geometric transformations. Thirty-two fifth grade boys took the Differential Aptitude Test, Space Relations Subset (DAT), and then participated in the experiment. Pre-test and post-test…