Learning to teach preservice mathematics teachers: The role of a doctoral course

Over the past two decades while the challenges of learning to teach mathematics have been widely documented (see Ball, 1990; Borko et al, 1992), the challenges of learning to teach future teachers have received much less attention. Challenges of teacher education have been explored broadly (e.g., Katz & Raths, 1992) and several dilemmas endemic to teacher education have been identified, such as assessment and coherence. Learning to teach future teachers has also been explored from the perspective of individual teacher educators as they reflect on and study their own practice. Nicol (1997), for example, examined the struggles she experienced as a beginning teacher educator. She reports being troubled by some of the contradictions she found between the practice she advocated and her own teaching. In one example, she writes that while she expected preservice teachers to “listen” to students’ ideas and use these in their teaching, she found herself neglecting to do so when teaching teacher education students.

In light of such challenges, Nicol along with others (e.g., Heaton 1994) raise questions about the lack of attention to learning to teach prospective teachers in graduate schools of education. Yet, as a recent study of doctoral students' experiences reports, 83 percent of doctoral students surveyed stated that, “enjoyment of teaching made them interested in being a professor” (Golde & Dore, 2001, p. 21). The respondents also indicated that support for such work - organized and sustained training and induction into teaching- varies greatly across institutions and within and across departments. Furthermore, as Golde and Dore note, it is not preparation for teaching that comprises a significant portion of graduate student work. Rather, preparation to conduct research tends to receive the greatest attention in courses, guided practica, and faculty-student interactions. Yet, it is a widespread practice for graduate students to teach undergraduate preservice courses in their departments as part of their graduate assistantships.

In response to the above concerns, two years ago our Department of Teacher Education launched a programmatic effort to socialize and mentor graduate students into their roles as future teacher educators. Doctoral students, who are or will be teaching preservice teachers for the first time, are required to take a “practicum in teaching” doctoral course. This course is designed to support graduate students’ learning to teach future school teachers to teach mathematics. The purpose of this study is to investigate the role such a course plays in helping doctoral students learn to teach and to inquire into their teaching of future teachers of mathematics.

Theoretical Perspectives
The design of the course and the study draw on the perspective of learning to teach as a complex life-long process (e.g., Feiman-Nemser, 1983). Similarly, we consider the process of learning to teach prospective teachers a life-long endeavor that cannot be addressed solely through course work or teaching experience. It is also consistent with constructivist views of learning as prospective teachers and teacher educators come to teacher education with past experiences, knowledge, and beliefs, which influence how each will experience the teacher education program as learner and as teacher. The study also takes the perspective that teachers’ practices (planning, instructing, and reflecting) are shaped by their knowledge and beliefs (Borko & Putnam, 1996; Calderhead, 1996) and therefore these must be the object of inquiry and sites of learning. With these in mind, the course aimed to provide students with the following experiences:
• examine perspectives on what teachers need to know and be able to do to teach mathematics in elementary and secondary schools;
• experiment with a variety of pedagogical approaches and resources in mathematics teacher education;
• become familiar with the variety of contexts for teaching and learning in the TE program;
• Consider questions, approaches, and methods of research in mathematics teacher education; and
• Design and conduct research in the context of their teaching.

Data Sources and Analysis
Data collected focus on class activities and participants in the “practicum in teaching” course. Instructors for the course are both junior faculty who teach in the teacher preparation program at this Institution. The course meets throughout the Fall and Spring semesters and it is scheduled as a 2-hour seminar and a lab activity every other week. The data consist of class agendas, written assignments, audiotapes of selected class discussions, students’ feedback and interviews regarding their experiences, and classroom observations of the participants’ teaching.

Participants include first and second year doctoral students with varying degrees of K-12 teaching experience, with different nationalities, and with different teaching assistantships (secondary or elementary). Data of eight course participants collected over two years are used to construct individual cases that are later used to uncover patterns and develop themes across cases (Yin, 1989). The case studies document the prior experiences, knowledge, and beliefs these novice teacher educators brought to the course, as well as how those factors interacted with their learning from course activities and from their own teaching experiences. Here we present preliminary insights and provide an overview of questions we are continuing to explore.

A theme that have emerged is that of identity, which has led us to explore how it does or does not play a role in the ways in which participants engage with course activities. One identity-related theme is students’ reluctance to call themselves “ teacher educators.” One participant, for instance, wrote “Sometimes when I really think about where I am and why, I am surprised. My most bizarre vision of what I might become when I finally grew up never included math teacher educator.” Another stated: “While I have always wanted to be a teacher educator, I was as surprised as anyone to discover that what I wanted to focus on was math.” And another confessed: “I found myself interested in teaching teachers because I needed a job in graduate school.” Following up on these statements, we examine at what point, if ever, participants begin to identify themselves as teacher educators. In addition, we investigate how identified themes might inform the design of experiences that would support these novice teacher educators’ development.

Another question we examine is the value participants attribute to the “practical” and “research” oriented aspects of the course, and the ways these activities influence their thinking and teaching practices. Throughout the course, students have opportunities to analyze course syllabi, create and discuss records of teacher educators’ practice (lesson plans, cases, class videos, observations of others’ teaching), and analyze preservice teachers’ work. They also have opportunities to engage in more research-oriented activities, such as reading and analyzing research papers with a focus on mathematics teacher education, designing and conducting a research project within their teaching context, and sharing their work with a broader audience through presentations and proposals to research groups and conferences. Understanding our participants’ perceptions of their experiences with these two kinds of activities at different points in time (e.g., during course and a year later) can shed light on their development processes.

Educational Contribution
This study contributes to the scarce literature on the preparation and development of beginning mathematics teacher educators. It provides another perspective to the largely “self-study” approach to the process of learning to teach future teachers of mathematics. It examines this process in the context of a graduate course aimed at supporting the development of future teacher educators. This study serves to open the conversation on (a) what is involved in learning to teach prospective teachers of mathematics and (b) the kinds of formal and programmatic experiences that might help prepare future mathematics teacher educators to learn to teach K-12 preservice mathematics teachers.

References

Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.
Borko, H., & Putnam, R. T. (1996). Learning to Teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 673-708). New York: Macmillan Library Reference USA: Simon & Schuster Macmillan.
Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D., & Agard, P. C. (1992). Learning to teach hard Mathematics: Do novices and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222.
Calderhead, J. (1996). Teachers: Beliefs and Knowledge. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 709-725). New York: Macmillan Library Reference USA: Simon & Schuster Macmillan.
Feiman-Nemser, S. (1983). Learning to teach. In L. S. Shulman & G. Sykes (Eds.), Handbook of teaching and policy (pp. 150-170). NY: Longman.
Heaton, R. M. (1994). Creating and studying a practice of teaching elementary mathematics for understanding. Unpublished doctoral dissertation, Michigan State University, East Lansing, MI.
Golde, C. & Dore, T. (2001). At cross purposes: What the experiences of today's doctoral students reveal about doctoral education. U.S. Wisconsin. Accession No: ED450628
Katz, L. G. & Raths, J. (1992). Six dilemmas in teacher education. Journal of Teacher Education, 43(5), 376-385.
Nicol, C. (1997). Learning to teach prospective teachers to teach mathematics. Unpublished Doctoral Dissertation. University of British Columbia, Vancouver, B.C.
Yin, R. K. (1989). Case study research: Design and methods. Newburry Park, CA: Sage Publications