Currently, there is very little research that connects what is learned in educational methods courses to teacher practice (Cochran-Smith & Zeichner, 2005). Looking specifically at math methods this remains true.  In fact, most of the studies in a recent meta-analysis of research investigating aspects of math methods showed that most studies did not examine what was taught in math methods, and few followed pre-service teachers into their student teaching classrooms to look at practices (Clift & Brady, 2005).

Although we do not have a research base for effective practices in a math methods course, for the past 25 years research have been working to conceptualize the knowledge required for teaching (Ball & Bass, 2002; Grossman, 1990; Hill, Schilling, Ball, 2004; Shulman, 1986). Trying to get closer to the practice of teaching, Ball & Bass (2002) approach the question of what teachers need to know by looking at what teachers do in the classroom, instead of what they know, calling this a “practice-based theory of mathematical knowledge for teaching” (p. 5).  Ball and Forzani (2009) reassert this need to make teacher practice the center of teacher education. They summarize this potential teacher education curriculum as “a practice-focused curriculum for learning teacher [that] would include significant attention not just to the knowledge demands of teaching but the actual tasks and activities involved in the work” (p. 503).  

Taking this approach, this research looked at the practices of math pre-service teachers because if the goal is to move the knowledge for teaching closer to the practice of teaching, then we must figure out how to do that for pre-service teachers.  If the knowledge for teaching should be closer to practice than the learning of teaching needs to move closer to practice.

There have been many calls for greater research into the connection between what is taught to pre-service teachers and how those teachings emerge in teacher practice (Cochran-Smith & Zeichner, 2005; Grossman, 2008). Understanding this connection and strengthening it is vital to the increased effectiveness of not just teacher education programs but of teachers and the increased learning of students.  This study aimed to gain a better understanding of the connection between what is taught in a university-based methods course and how those teachings emerged in the practices of pre-service teachers by following six pre-service teachers through a year-long methods course and into their student teaching classrooms. Focusing on secondary math in a large urban school district, this study sought to answer the questions - How do the strategies taught in a math methods class emerge in pre-service teachers’ student teaching practice? Which strategies do student teachers in secondary math use and why?  What supports the emergence of these practices in a pre-service teacher’s student teaching instruction and what impedes it? 

Methods and Data Sources

Multiple methods were used to understand pre-service teacher learning and practice.  Primarily a qualitative study, the principal data sources for this study are observations of a year-long course in mathematical methods and 42 observations of six Algebra I pre-service teachers (7 observations/teacher X 6 teachers).  Each of the observations, which involved taking notes and audio recording, was followed by a brief interview asking about the decision-making process while planning and implementing the lesson and the reasons behind those decisions. In addition, to better understand prevalence of practices and strategies emerging in pre-service teachers’ classroom logs of teacher practice were used for two weeks.  These multiple methods of data collection worked to create a broad picture of pre-service teacher practice and its links to the math methods class. 

Results

The results of the study show trying non-traditional practices and strategies is difficult for pre-service teachers even if they full-heartedly believe in the ideas behind the reform-oriented practices taught in math methods.  Multiple reasons were given for not trying these practices including not having seen it work in urban schools, having mentor teachers who teach traditionally, and being unsure how the method will work with his/her students. However, having pre-service teachers try reform-oriented practices (taught in math methods) with a teacher educator observing and discussing the lesson afterward gave students the encouragement, support and feedback that helped them to try non-traditional practices.  Pre-service teachers who were reluctant or nervous to try reform-orientated strategies that encouraged mathematical discussion and equitable participation, experienced teaching something using non-traditional strategies and often had increased student engagement and discourse.  When the results were not as successful, the discussion that followed led to reflection and most often a desire on the part of the pre-service teacher to try the strategy again. 

However, picking the right practice for pre-service teachers to try was important – it must be versatile for many types of contexts including different kinds of lessons and students and manageable to try, which generally meant not a lot of preparation was required. Practices that pre-service teachers tried included strategies to encourage student mathematical discourse and equitable participation such as variations on Think, Pair, Share, interactive notebooks, quick write, and sharing multiple strategies.  It was valuable for pre-service teachers to see that their students could be successful in carrying out a discussion about math and that they themselves had the pedagogical skill to be successful at a practice that created mathematical discourse and a high level of participation in the classroom.

Scholarly Significance of the Study and Connection to AERA Conference

The connection between university coursework in math methods and teacher practice is not well researched (Clift & Brady, 2005). The study presented here addresses some of these gaps in the research by observing in a math methods course for a year and then following six teachers into their student teaching classrooms to see how the ideas and practices taught in math methods emerge in teacher practice.  Through close collaboration with the math methods teacher, the study also investigated how trying practices can be encouraged and supported by professors and field supervisors. These findings have great implications for strengthening the connection between methods classes and student teaching practices and by getting back to the core of what practices make a difference in math instruction. By using what was learned through this research in our own teacher education program, we have already put the research knowledge to work to improve education through a greater connection between university methods courses and pre-service teacher practice.