The advancement of online technologies in recent years has increased the number of teacher learning opportunities offered in virtual environments. The development of the online medium for educational purposes has raised challenges for organizing and conducting professional development for teachers, especially relative to the ways subject matter disciplinary knowledge may be facilitated in such a medium. Using a survey instrument, data were collected from a national sample of mathematics teacher educators related to the content of their pedagogical practices in online mathematics teacher education. Results highlighted eight dimensions associated with mathematics teacher educators’ decisions when designing and implementing online mathematics teacher professional development or academic courses. Knowledge required for mathematics teacher educators for each dimension of decisions is discussed.
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.