As technology becomes more prevalent in the mathematics classroom, teachers will need to be able to effectively evaluate technological tools to use with students. In this study, the authors examined secondary mathematics teachers’ evaluation of online dynamic geometry tools. The analysis focused on the teachers’ noticing of technology; specifically, what features within the tools mathematics teachers attended to, how they interpreted these features, and in what ways they responded. Findings indicated that secondary mathematics teachers attended mostly to mathematical features of the tools and considered the tools’ ability to focus on student engagement and student thinking to be very important, as well as the ease of implementation of the tool. The secondary mathematics teachers tended to begin their evaluation by determining how the tools work and attending to its appearance and then moved toward examining the mathematical features and how they related to student thinking.
Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers’ abilities to construct sketches that focus users’ attention on the desired variant or invariant relationships. The study described in this paper looked at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. The authors identified common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. They then discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended.
A student, Stuart, related perimeter to pixels and the professor, Beth, moved back and forth between reserved believing and reserved doubting and doubting teacher actions (Elbow, 1986; Harkness & Noblitt, 2017) while assessing the merit of his conjecture in the moment. Video allowed the researchers to rewatch the episode multiple times after the moment and to attempt to believe (Elbow, 1986; 2006), or find merit or strength, in Stuart’s conjecture and then explore the mathematics that he suggested. Within this paper the researchers “restory” (Creswell, 2012) chronologically what transpired in the moment in the classroom, their later conversations, and their after-the-moment mathematical explorations of Stuart’s conjecture. Video can, perhaps, allow teacher educators to help preservice teachers and classroom teachers notice and reflect on missed opportunities for believing. Video also has the potential to empower teachers to explore the mathematics suggested by students after the moment and then use what they learn in future lessons.
This study examines whether preservice teachers’ experiences with video analyses during teacher preparation have long-lasting effects on their practices once they enter the profession. Specifically, the authors examined whether teachers who had opportunities to analyze student thinking and learning during teacher preparation continued to do so when they reflected on their teaching effectiveness as full-time teachers. A group of elementary school teachers who attended a video-enhanced mathematics methods course were compared to a control group at the end of their first year of full-time teaching. Teachers were asked to assess two lessons they had just taught by describing lesson learning goals and providing a rating of lesson effectiveness and a rationale for their evaluation. Teachers who attended the video-enhanced course during teacher preparation outperformed their counterparts in both the quality of evidence they drew upon and their attention to individual or subgroups of learners. Study limitations and future directions are discussed.