Abstract

1. Professional Development Supporting Teachers in Developing Technology Pedagogical Content Knowledge (TPCK) Maggie Niess, Kwangho Lee, Gogot Suharwoto, Pejmon Sadri Department of Science and Mathematics Education Oregon State University Abstract Research is needed to identify and clarify ways to prepare inservice teachers in developing technology pedagogical content knowledge (TPCK) - the intersection of knowledge of mathematics with knowledge of technology (spreadsheets) and with teaching and learning – if they are to integrate technology in their classrooms. This professional development program guided teachers in learning about spreadsheets through the development of mathematical concepts, planning for teaching mathematics with spreadsheets, practicing teaching mathematics with spreadsheets. In their actual teaching situations, the teachers identified the specific activities that guided their planning and teaching mathematics with spreadsheets as well as factors that affected their efforts in teaching mathematics with spreadsheets. Teachers’ knowledge of mathematics contributed their ability to identify good problems for integrating spreadsheets. • Theoretical Perspective • Framework for the design of the professional development • Extending Grossman’s four central components of PCK (Grossman, 1989, 1990) to incorporate technology (Niess, 2005) • Experienced teachers need: • an overarching conception of teaching mathematics with technology; • knowledge of instructional strategies and representations for teaching mathematics with technologies; • knowledge of students’ understandings, thinking, and learning in mathematics with technology; • knowledge of curriculum and curricular materials that integrate technology. Results All of the teachers demonstrated a strong PCK but their TPCK was at best described as primitiveprior to the summer program. The idea of scaffolding mathematics lessons with spreadsheets was new for these teachers. This model was pivotal in shifting their thinking about integrating spreadsheets with learning mathematics in that they were able to begin to discuss and plan for scaffolding in their scope and sequence assignment for teaching in the coming year. By the end of the summer session, the teachers were able to describe and discuss scaffolding that integrates technology in mathematics lessons. They realized the advantages of using spreadsheets for solving complicated mathematics problems, motivating students, and providing opportunities for students to extend problems to other hypothetical situations. Their plans for teaching mathematics with spreadsheets were sketchy and seemed more like novice planning. The multiple teaching opportunities during the summer program supported the teachers in improving their teaching with spreadsheets. Observations of their teaching during the school year described a tentative TPCK. They had difficulty accepting student ideas while working and exploring spreadsheets with students; they preferred to give answers rather than guide student thinking. Their preparation of materials for teaching with spreadsheets was limited because of a concern of over-planning and limiting student creativity with a scripted lesson. They indicated, “If I guide them, they won’t make a mistake that I am not able to troubleshoot.” Objectives Inservice teachers need programs that help them to explore the intersection of knowledge of mathematics with knowledge of technology and knowledge of teaching and learning that help them develop a technology pedagogical content knowledge (TPCK). The key to TPCK is the integration of multiple domains of knowledge in a way that supports teachers in teaching their students the subject matter with technology (Margerum-Leys & Marx, 2004; Niess, 2005; Pierson, 2001). Introduction Spreadsheets offer a technology readily available among classroom technologies to support students in learning mathematics. Mathematics teachers have not been prepared to integrate spreadsheet technology as a tool for teaching and learning mathematics. Mathematics teachers need opportunities to develop their own knowledge and skills of using spreadsheets as tools for exploring and learning mathematics. Mathematics teachers need support in redesigning the mathematics curriculum to include spreadsheets as tools for exploring mathematics. Mathematics teachers need support in using spreadsheet tools to expand avenues for learning mathematics available at the disposal of their students. Mathematics teachers need a preparation that they have not experienced as they learned mathematics and as they learned to teach mathematics. Methodology The program guides inservice teachers in scaffolding lessons to incorporate learning about spreadsheets while learning mathematics. Supported by an NSF collaboration of mathematics educators and computer scientists utilized a four-week summer preparation of grade 7-14 mathematics teachers. The first week introduced spreadsheets, examined the role of spreadsheets in mathematics teaching with examples of scaffolding student learning with spreadsheets, collecting resources for lessons, designing dynamic and dependable spreadsheets, and planning lessons that integrate spreadsheets with mathematics instruction. The second week provided the teachers opportunities to practice teaching their lessons, followed by an exploration of advantages and improvement of the lessons in integrating learning about spreadsheets. The third week provided teachers an opportunity to practice teaching their lessons. The fourth week the teachers finalized their designs and plans for integrating spreadsheets into their upcoming mathematics classroom instruction. The third research question was completed during the following academic year Researchers observed three instructions respectively with the intent of supporting teachers where these teachers relied on their own TPCK in teaching students mathematics with spreadsheets. Research Questions 1. How does the professional development program affect the development of teachers’ TPCK? 2. What are the effects of the professional development program on the development of teachers’ plans to incorporate guided learning of mathematics with spreadsheets? 3. What is the impact of the professional development program on teachers’ implementation of their plans, guiding student learning of mathematics with spreadsheets? Significance of the Study This study emphasized the integration of learning mathematics and learning about spreadsheets. The integration of learning spreadsheet skills with mathematics demonstrated in this study specifically embraces the integration of the knowledge in TPCK. The summer program emphasized the notion of scaffolding, by using that same strategy to develop the teachers’ spreadsheet knowledge while they considered integrating spreadsheets with learning mathematics. In essence this study identified a process for developing the TPCK of inservice teachers, where they expanded their TPCK by planning, teaching and assessing students’ development of mathematical ideas using spreadsheets. Data Sources Pre- and post-questionnaires, daily journal prompts -- describe the individual teacher’s developing TPCK throughout the summer program. Scope and sequence plan for integrating spreadsheet instruction in mathematics classes provided a preliminary view of the teachers’ TPCK. Observations and interviews of teachers prior to and after teaching mathematics with spreadsheets. All assignments (resource cards, lesson plans) were collected and analyzed. An observation check list and protocol was adapted and developed from (1) Shulman’s (1987) checklist of observable behaviors of PCK and (2) the Reformed Teaching Observation Protocol (RTOP). The interview protocol was adapted from the Horizon teacher interview protocol.