A systems approach provides insight for expanding teachers’ pedagogical reasoning for integrating multiple technologies in inquiry, communication, and collaboration. An online learning trajectory supports the integration of a systems pedagogical approach for guiding teachers in developing their technological pedagogical thinking and reasoning so they in turn are able to implement a systems pedagogical approach with their own students. Specific instructional strategies guide teachers in refining their mental models for integrating multiple technologies in teaching mathematics through their increasingly complex technological pedagogical understanding as they learn about the technologies and teaching with those technologies. This study focuses on the impact that a system of multiple technologies as pedagogical tools has on teachers’ technological pedagogical reasoning as they integrate multiple technologies in their classrooms. A systems pedagogical understanding is at the core of teachers’ enhancement of their technological pedagogical reasoning, and supports the transformation of their knowledge called technological pedagogical content knowledge.

Inservice teachers need ways to gain an integrated knowledge of content, pedagogy, and technologies that reflects new ways of teaching and learning in the 21st century. This interpretive study examined inservice K -8 teachers' growth in their pedagogical content knowledge (PCK) toward technology, pedagogy, and content knowledge (TPACK) in an online graduate course designed for integrating dynamic spreadsheets as teaching and learning tools in mathematics and science. With the lens of four TPACK components (Niess, 2005), the analysis describes teachers' development from recognizing to accepting, adapting, and exploring TPACK levels. Implications and recommendations for the design of future professional development courses and continuing research are identified to support inservice teachers' knowledge growth for teaching with technologies. (Keywords: Teacher knowledge, spreadsheets, inservice teachers, elementary and middle school, online, professional development)

Teaching and learning in a technology rich digital context challenge established thinking about student engagement in their learning. This chapter presents a reconstructed conception of learner engagement for online environments consisting of: engagement with community; engagement with technology; engagement with mathematics content; and an amalgam of all three. This descriptive, cross-case study combines current literature with the authors' past research to develop characterizations of these components of online learner engagement. This reconstructed model of learner engagement is the focus of the study, providing: 1) a vocabulary for developing a narrative describing how teachers as students think and learn with technology in an online environment and 2) a framework for mathematics teacher education professional development. Results indicate that this model supports teacher educators in both describing and evaluating how teachers as learners engage in a unit of instruction, and framing the course design and instructional strategy choices that support learner engagement.

Traditional classrooms are fast becoming a minority in the education field. As technologies continue to develop as a pervasive aspect of modern society, educators must be trained to meet the demands and opportunities afforded by this technologyrich landscape. The Handbook of Research on Teacher Education in the Digital Age focuses on the needs of teachers as they redesign their curricula and lessons to incorporate new technological tools. This book includes theoretical frameworks, empirical research, and best practices. Readers: This book serves as a guide for researchers, educators, and faculty and professional developers of distance learning tools.

The purpose of this chapter is to describe the impact engaging collaborative software has on technological pedagogical content knowledge (TPACK) development through collaboration and reflection. Situating teaching and learning in an online teacher education environment creates challenges for developing learning communities supporting reflection and collaboration. This cross case analysis reveals the impact of Google Docs to facilitate reflection and collaboration in an online integrated mathematics, science, and technology education graduate program has on developing in-service teachers' TPACK. Using a social metacognitive constructivist lens to focus the course design, this study collected student learning products, including essays, Blackboard forum transcripts, and Google Docs editing histories to understand how participants' TPACK thinking matured through their collaboration and reflections. Results suggest Google Docs provided a rich online environment where participants were able to engage in and reflect on a community that developed both individual and shared knowledge.