The purpose of this study was to investigate a function machine in the form of a Vending Machine applet as a means to motivate preservice teachers to examine their own understanding of the function concept. The applet was designed to purposefully problematize common misconceptions associated with the algebraic nature of typical function machines. Findings indicate that the preservice teachers for which the applet provoked a dilemma elaborated on or transformed their understandings related to the definition of function.
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.