Gloriana González

Students' Conceptions of Congruency through the Use of Dynamic Geometry Software.

This paper describes students’ interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK¢ model of conceptions, suggests that incorporating technology in mathematics classrooms enabled a measure-preserving conception of congruency with which students’ could shift focus from shapes to properties. Students also interacted with dynamic diagrams in a novel way, which we call the functional mode of interaction with diagrams, relating outputs and inputs that result when dragging a figure. Students’ participation in classroom interactions through discourse and through actions on diagrams provided evidence of learning using tools within dynamic geometry software.

''Doing Proofs'' in geometry classrooms

Proof in advanced mathematics classes: semantic and syntactic reasoning in the representation system of proof

Facilitating Teacher Learning When Using Different Representations of Practice

Providing opportunities for learning through professional development requires the examination of facilitation of sessions with teachers. This study investigates facilitation of professional development to promote teacher learning when using animations and videos in a study group with five teachers. We ask: What practices (and moves within those practices) do the facilitators enact during high-quality conversations and specific to the professional development activities? We found that moves for sustaining an inquiry stance were more frequently performed than other moves, suggesting that the facilitator’s practices increase teachers’ learning opportunities when studying representations of teaching. In addition, the study suggests that there are no significant differences when facilitating discussions of animations and videos. The teacher learning goals seem to be more important than the type of representations of teaching used for the enactment of facilitation moves. Our findings are relevant for designing and implementing professional development that supports teacher learning through inquiry and collaboration.

Moving Toward Approximations of Practice in Teacher Professional Development: Learning to Summarize a Problem-Based Lesson

This chapter describes a set of activities in a professional development intervention with in-service geometry teachers that engaged them in role-playing a lesson summary. The activities included discussion of animations of classroom instruction with examples of how to lead a summary of a problem-based lesson. The animations were representations of teaching that supported the development of shared knowledge about how to summarize a lesson. In addition, the teachers decomposed the practice of summarizing prior to their engagement in a role-play of a summary. This role-play constituted an approximation of practice that enabled the teachers to envision how a summary would unfold in real time and required the teacher leading the summary to make tactical decisions. Observations of a teacher leading a summary in his classroom provided evidence of teacher learning. Overall, the professional development included a sequence of activities that validated teachers’ knowledge and provided them with the capabilities for engaging in an authentic approximation of practice in a safe environment.