A Qualitative Approach to Assessing Technological Pedagogical Content Knowledge

Because technological pedagogical content knowledge is becoming an increasingly important construct in the field of teacher education, there is a need for assessment mechanisms that capture teachers’ development of this portion of the knowledge base for teaching. The paper describes a proposal drawing on qualitative data produced during lesson study cycles to assess teachers’ development of technological pedagogical content knowledge. The specific qualitative data sources include teachers’ written lesson plans, university faculty members’ reviews of lessons, transcripts and videos of implemented lessons, and recordings and transcripts of debriefing sessions about implemented lessons. Using these data sources, inferences about teachers’ technological pedagogical content knowledge are drawn and validated. An example of the implementation of this lesson study technological pedagogical content knowledge (LS-TPACK) assessment model is provided. The example includes inferences drawn about high school teachers’ technological pedagogical content knowledge in the context of two lesson study cycles that involved teaching systems of equations with graphing calculators. Reflections on the strengths and weaknesses of the LS-TPACK model are included from a qualitative perspective, as well as from a psychometric perspective. Contemporary Issues in Technology and Teacher Education, 9(4) 393 Technological tools have changed the landscape of mathematics teaching. In geometry, teachers can launch investigations by having students efficiently manipulate, measure, and analyze dynamic diagrams (Jackiw, 2001). The study of algebra can be facilitated by the graphing calculator’s ability to produce multiple representations of functions to be compared and contrasted with one another (Fey, 1989). The process of statistical investigation can be supported by software with the ability to import data quickly from the Internet for analysis (Finzer, 2002). Various other technologies, like online discussion boards (Groth, 2008), spreadsheets (Alagic & Palenz, 2006), and even robots (Reece et al., 2005), have been discussed in terms of their potential to support students’ mathematical learning. The rapid expansion of available technological tools has prompted scholarly discourse about how Shulman’s (1987) construct of pedagogical content knowledge might be built upon to help describe the sort of knowledge teachers need for teaching with technology. Recently, the phrase “technological pedagogical content knowledge” (or technology, pedagogy, and content knowledge; TPACK) has been used to describe “an understanding that emerges from an interaction of content, pedagogy, and technology knowledge” (Koehler & Mishra, 2008, p. 17). Such a conceptualization emphasizes that TPACK is more than just the sum of its parts. It implies that teachers must engage with content, pedagogy, and technology in tandem to develop knowledge of how technology can help students learn specific mathematics concepts. The emergence of the TPACK construct presents a dilemma: How can teachers’ acquisition of TPACK be assessed? Answering this question is necessary for determining the extent to which different teacher education programs and experiences foster the development of TPACK. Without viable assessment mechanisms, comparing approaches and making decisions about actions to take in teacher education is difficult. Pragmatic issues like program accreditation and grant evaluation also highlight the need for TPACK assessment. Accreditation agencies (e.g., National Council of Teachers of Mathematics & National Council for Accreditation of Teacher Education, 2005) have begun to ask for data about prospective teachers’ abilities to utilize technology in mathematics instruction, and agencies that provide funds to purchase classroom technology often want assessment data on how teachers are using the technology purchased. Hence, the development of TPACK assessment mechanisms is vital for helping build the infrastructure for current and future teacher education efforts. Two Contrasting Paradigms for the Assessment of Teachers’