Teacher Education in the 21st Century: A Mash-Up of Teaching Resources

• In Event: Proportionality Dynabook: Because “To Know Is Not Enough” in Mathematics Teacher Professional Development

Abstract

Teacher candidates must have expertise that extends beyond their content. They are expected to differentiate instruction, for example for children with disabilities and English Language Learners. In addition, they are expected to integrate technology in useful and educative ways. Mishra and Kohler (2006) describe these expectations of Technological, Pedagogical, and Content Knowledge (TPACK) as the complex interplay of content knowledge, pedagogical knowledge, and knowledge of technology. The questions we explore in this paper are: (1) Which aspects of each of the TPACK areas and their intersections may be accessible for the candidates even before they have any teaching experiences on which to reflect?, and (2) How might the combination of digital resources and innovative practices be designed to support this TPACK learning?
Our hypothesis is that TPACK cannot be taught directly; prospective teachers need to be involved in varied experiences where their instructors model differentiation strategies, assessment strategies, and the use of technology in effective ways. Moreover, their instructors must highlight and explicate the decisions that underlie these pedagogical moves (Brown & Nickerson, 2011). This modeling, then, requires teacher educators to become bricoleurs (Hatton, 1988) who create lessons from a diverse range of sources and bring them together to create new learning experiences. More colloquially, the results might be called “mash-up” lessons that bring together research-based ideas of pedagogy, experientially-real problems that cue multiple pathways for solutions, interactive applets that enable exploration, and technology-based sharing tools to facilitate the collection and review of multiple student approaches. To be supportive of this practice, Dynabook must serve as a conduit – a medium - through which teacher educators can draw on a variety of resources and integrate them into lessons in ways that add more value than textbooks or online videos and resources alone. In particular, Dynabook must itself cue and scaffold teacher candidates’ experience (at least “in miniature”) of bricollage.
This paper presents a case study of how one Dynabook-mediated mash-up lesson evolved over the course of four class periods in an undergraduate course for pre-service middle school teachers. This lesson focused on using a balance metaphor to provide visual and experiential opportunities to explore ratio and proportional relationships. Our analysis of what content, pedagogy, and technology teacher candidates actually learned will be used to shed light on the first question, above.
In responding to the second question, we describe the interplay between the various elements of the mash-up including the purposeful choice and ordering of mathematical tasks, the design and revision of the applets and assignments, and the instructor’s modeling of the integration of several communication technologies including an interactive white board and the Dynabook-based shared whiteboard space.
Finally, we discuss the evolution of symbolizations that arose as the prospective service teachers relied less on the interactive tools and more on inventing their own symbols to reify their activities (Sfard, 2009), illustrating the complex interplay among TPACK aspects.

Authors

• Janet S. Bowers, San Diego State University

• Susan D. Nickerson, San Diego State University