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Technological pedagogical and content knowledge (TPACK) presents a dynamic framework for describing teachers' knowledge required for designing, implementing, and evaluating curriculum and instruction with technology. TPACK strategic thinking includes knowing when, where, and how to use domain-specific knowledge and strategies for guiding students' learning with appropriate information and communication technologies. Multiple visual and verbal descriptions reflect evolving recognitions of teacher educators and educational researchers as they have struggled to respond to the challenges in describing and developing teachers' TPACK. This extensive reflection maps the historical acceptance of pedagogical content knowledge (PCK) with the emerging views of and challenges with TPACK. A review of empirical progress in the investigation of TPACK serves to illuminate potential insights, values, and challenges for directing future educational implementations designed to identify a teacher's learning trajectory in the development of a more robust and mature TPACK for supporting them in teaching with current and emerging technologies.New and emerging digital technologies are more accessible for incorporation in educational programs with increased access and societal uses in day-to-day actions. Teachers are confronted with challenges and questions of how and when to incorporate such technologies for teaching and learning various subject matter topics. Rather than focusing on the features, affordances, and constraints 299

We describe a new curriculum for the final two years of a B.S. program in Physics. Case studies in the junior year provide concrete examples or Paradigms as pillars to support systematic Capstone lectures in the senior year. In each of nine three-week Paradigms, the junior progresses from a descriptive lower-division understanding to an advanced analysis of a topic defined by phenomenon rather than discipline. Students generally view the new format with favor. They are better at visualization and make important connections among physics disciplines. Independent assessment is ongoing.

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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.