"Integrating Cultural Awareness and Innovative Practices for Mathematics Teacher Professional Development: A Video-Based Project Focused on Student Mistakes"
Assistant Professor Rossella Santagata, presented with Wendy Bray (University of Central Florida) at the Jean Piaget Society in Berkeley, California, on June 2
Poster title : "Integrating Cultural Awareness and Innovative Practices for Mathematics Teacher Professional Development: A Video-Based Project Focused on Student Mistakes"
Abstract
Project Description and Central Question
Many authors have described the unchanging persistence of U.S. teaching across centuries (Cuban, 1994; Tyack & Tobin, 1994). Others have discussed how professional development has traditionally had little impact on teachers' practice (Cohen & Hill, 2000; Porter et al., 2000; Wilson, 2003). One reason for this is teachers' tendency to adapt new strategies into what they are most familiar with, often missing key elements that made those new strategies effective for student learning (Stigler & Hiebert, 1999). Another reason is that teachers seldom have opportunities to observe alternative strategies as they are implemented in real classrooms (Gallimore & Santagata, 2005). Yet another reason is that researchers rarely engage with teachers in conversations that facilitate the contextualization and reconstruction of their scholarly knowledge into workable classroom strategies (Ruthven, 2002). This project investigates a video-enhanced researcher-teacher collaboration model that encourages joint reflections on culturally ingrained teaching strategies and promotes "collaboration in the borderlands between research and practice" (Silver, 2003, p. 183). The aspect of teaching targeted here is the fundamental problem of handling students' mistakes.
Teachers in high-achieving countries are reported to use a constructivist approach and to regard mistakes as having a positive function. Students in Japanese mathematics lessons, for example, are called to the front of the classroom to share their own problem solutions. Teachers require that not only correct but also wrong solutions be shared. These are sources of useful discussions (Stevenson & Stigler, 1992). Despite widespread agreement within the U.S. education community on the important role of mistakes in learning (Ball, 1991; Borasi, 1994; Kazemi, 1998; Lampert, 1992), U.S. mathematics teachers' instructional decisions involving mistakes have been documented as quite different from those observed in Japanese classrooms (Schleppenbach et al., 2007; Stevenson & Stigler, 1992). Eighth-grade U.S. mathematics teachers videotaped as part of TIMSS (Stigler & Hiebert, 1999), for example, avoided the discussion of students' errors, to mitigate their responses using such expressions as "You are close," and "You are almost right," and to ask the same question to the next student until they received the correct answer. Trying to protect their students from failure, U.S. teachers lowered the cognitive demands of problems, turning them into risk-free sets of procedures (Santagata, 2004, 2005). This project addresses the following research question: Does a video-enhanced professional development (PD) model that encourages researcher-teacher joint reflections on culturally ingrained teaching practices, as well as exposure to innovative practices, facilitate teachers' integration of research-based mistake-oriented strategies into their daily lessons?
PD Structure and Research Methods
In the last decade, many video-based PD programs have been developed to effectively support teacher learning (Wang & Hartley, 2003). This project's PD model draws from existing approaches, such as teacher video clubs (van Es & Sherin, 2008) and Japanese lesson study groups (Lewis et al., 2006). It adds to these approaches an explicit effort to (1) make teachers aware of cultural practices and beliefs and (2) combine researcher and teacher knowledge to design strategies that work in specific contexts. A group of 4 elementary school teachers were recruited. The researcher metwith the group for a total of 22 hours, two days at the beginning of the project and once a month in 90-minute after-school sessions during the school year. In addition, the researcher visited each teacher's classroom once a month to assist in the integration of new strategies. After reviewing relevant literature and common U.S. mistake-handling strategies in mathematics teaching, teachers observed video examples of constructivist approaches to mistake-handling strategies in math lessons. Teachers also began to formulate specific instructional methods they wanted to incorporate in their daily practices. Teachers were then videotaped while they attempted these strategies in their classrooms. The classroom videos were viewed in subsequent group meetings and teachers discussed what worked, what they found challenging, and how the strategies could be improved. They then tried these modified strategies and repeated this cycle several times.
Measures
Classroom observations and meetings: Teachers were observed in the classroom at the beginning of the project to capture baseline pracices. Subsequent classroom observations were videotaped throughout the project to document changes in practices as teachers attempted to integrate new strategies into daily lessons. All meetings were also videotaped. All videos were transcribed.
Artifacts and researcher's journal: Artifacts including lesson plans, instructional materials, meeting agendas and correspondence were collected. The researcher recorded reflections and impressions related to meetings and classroom observations.
Teachers' interviews: Each teacher was interviewed at the end of the project to investigate their perceptions of the collaborative process and changes in their beliefs.
Data Analyses
Videotapes of teachers' lessons were coded to capture teachers' approach to student mistakes over time. A four -dimension coding system (Bray, in press) was used: (1) Design and implementation of mathematical tasks that allow for errors to surface, (2) Intentional focus on flawed solutions, (3) Promotion of conceptual understanding through discussion of errors, and (4) Mobilization of a community of learners to address errors. Summary tables were created to summarize and describe themes and nature of discussions during PD meetings. Interviews were analyzed thematically.
Findings
Data analyses reveal four different learning paths for participating teachers. These highlight both promising aspects and challenges of the PD model. To summarize, significant changes in practices were observed for two teachers who were most engaged with the ideas discussed by the research and had opportunities to collaborate outside of the PD meetings. These teachers used the video-supported analyses of teaching as opportunities to learn about new practices, question their routines, try out new strategies, and refine them over time by attending to important details of mistake-oriented instructional practices. Challenges included maintaining interest and focus for teachers who were committed to other groups at their schools; addressing beliefs that counter the idea of mathematics as focusing on problem solving; moving beyond teaching that focuses only superficially on student errors while not providing effective connections to conceptual ideas.
