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Becoming a Reflective Mathematics Teacher: A Guide for Observations and Self-Assessment

Alice F. Artzt and Eleanor Armour-Thomas
Lawrence Erlbaum
Publication Date: 
Number of Pages: 
[Reviewed by
Rick Seaman
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Becoming a Reflective Mathematics Teacher: A Guide for Observations and Self-Assessment is the latest in the well-received Studies in Mathematics Thinking and Learning Series, edited by Alan Schoenfeld. The book is a culmination of over 20 years of research and teaching and is an important read for preservice mathematics teachers, their professors, and those presently teaching mathematics. This review will focus on preservice teachers but the application to their professors and mathematics teachers will become apparent.

The authors argue that great teachers can be made through, among other things, a "willingness and ability to be a reflective, self-critical thinker" (p.xvii). This implies that the "perfect" lesson might be seen as the limit of reflections on one's lessons. But there is more. The process of reflection and self-assessment must be approached in a manner that has the preservice mathematics teacher, with the aid of a model, gaining control over instructional practice. The authors "argue that over time, the habitual use of reflective and self-assessment processes about learning experiences leads to transformation in teaching" (p.7). Accordingly, they developed activities designed to help preservice teachers make connections between what they learn in their methods course(s) and what they observe in actual practice, to how they and others observe their own teaching. One becomes excited at the possibility of preservice teachers transferring what they learn in their preservice teachers' mathematics education courses to their internship and their subsequent teaching careers.

The authors state that the fundamental premise of this book is that teachers' instructional practices and their thoughts behind the lessons must be student-centered for students to learn mathematics with understanding. The book is divided into three parts. Part I provides the philosophical basis for the model. The model consists of two interrelated frameworks where teaching for student learning with understanding is fundamental. The Phase-Dimension Framework considers such basic components of a lesson as the tasks provided to students, the learning environment and the classroom discussion that includes both teachers and students. The Teacher Cognitions Framework takes into consideration the goals that teachers establish for their students, their beliefs and knowledge about teaching and learning mathematics, the content, their students, and the decisions that they make before, during and after teaching a lesson. The two frameworks together help to provide some insight into the relationship between teachers' thoughts behind every lesson and their teaching. The model is utilized in the authors' teacher education programs to help the preservice teachers make sense of their own teaching and that of others. Evidence that supports the model's validity is provided in the chapter on "Putting It All Together."

Part II, "How to Use the Model," contains chapters that deal with preservice teachers examining their own and other teacher's instructional practice, the corresponding thinking that goes into making teaching decisions, and using a portfolio to document how to engage in self-assessment and reflection. The chapter on "Using the Model to Examine the Instructional Practice and Cognitions of Other Teachers" contains 10 observations of lessons actually taught in high school. The model helps focus the preservice teacher on various aspects of teachers' instructional practices and has the preservice teachers making conjectures regarding the observed teachers' related thoughts. The observations are arranged so that there is a focus on content, the teacher, and finally on the students. The 10th observation gives the preservice teacher an opportunity to apply what they have learned from the nine previous observations.

I look forward to utilizing this model with my preservice teachers when they visit classrooms during their pre-internship semester. Hopefully, the preservice teachers will evolve in how they teach mathematics by reflecting on both how they were taught and what they have learned in their mathematics education classes.

Part III, "Evidence: The Model in Action," contains five case studies that look at issues that come up when preservice teachers reflect and assess the thoughts behind their lesson planning and instructional practices. The case studies clarify further how the model works to improve instruction in mathematics. One gets a glimpse of the complex but dynamic interplay within the model on the journey to beginning to understand one's teaching. It is of interest where the reader becomes aware of the inconsistencies between the preservice teachers' thinking as they prepare their lessons and when they evaluate and revise their lessons after teaching them. Forms needed to apply the model are located in the appendices and include structured observation activities "designed to help students relate the concepts they learn in their methods course to the instructional practice they observe in actual mathematics classrooms" (p. xix). The model provides the preservice teacher with an instrument for reflecting on one's teaching and striving to improve it. As the authors remind us, "great teachers are not born, they are made" (p.xvii)!

Rick Seaman ( is Assistant Professor of Mathematics Education at the University of Regina in Regina, SK, Canada.

The table of contents is not available.