The main difficulty in studying molecular symmetry is the mental manipulation of molecules when searching for symmetry. Numerous methods of teaching molecular symmetry require students to identify symmetry elements of objects or molecules. As an alternative, we propose activity that identifies symmetry using elements outside the objects, together…

This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…

This paper concerns teaching Euclidean geometry at the university level. It is based on the authors' personal experience. It describes a sequence of learning activities that combine geometrical constructions with explorations, observations, and explanations of facts related to the geometry of triangle. Within this approach, a discussion of the…

Unlike studies on cooperative learning that have focused on the verbal communication aspect of learning, this study focuses on the non-verbal aspect--mindful movement, which is the use of body movement to aid academic learning. Our research examined the link between five learning activities occurring within a cooperative group of children using…

This paper discusses insights for using geometry sketching software to teach geometric concepts for kindergarten to grade 4. The authors created hands-on resources that incorporate technology in a user-friendly environment. When working with "Geometer's Sketchpad" with middle and high school students, the teacher educators noticed the…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

The Public Broadcasting Service (PBS) sought to build on the strengths of high quality professional development through an online venture funded under the U.S. Department of Education's Ready To Teach (RTT) program. PBS TeacherLine was designed to provide high-quality, facilitated online professional development for K-12 teachers nationwide.…