The definition of creativity among professional mathematicians and the definition of mathematical creativity in the classroom context are significantly different. The purpose of this study was to investigate the relationship between students' mathematical creativity (i.e., cognitive flexibility) and figure apprehension when solving geometric…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

There is a consensus that certain cognitive abilities and mathematics performance are related. This link also extends to geometry. Surprisingly, however, little research has examined specific aspects of cognition that may contribute to successful performance in geometry, particularly at the secondary level. In this study, we explored in what ways,…

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

Discusses the development of visual thinking in students. Also presents a strategy that incorporates visualization exercises within the framework of traditional mathematics. The technique appears successful for students studying geometry, fractions, and problem solving. Visualization abilities increase understanding and therefore give students…

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…