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Learning to Teach as Assisted Performance
Running head: Learning to Teach as Assisted Performance
Learning to Teach as Assisted Performance
Denise S. Mewborn
David W. Stinson
University of Georgia
Please address all correspondence to the first author at
Department of Mathematics Education
105 Aderhold Hall
Athens, GA 30602-7124
Phone: 706-542-4548
Fax: 706-542-4551
e-mail:
Paper presented at the Research Presession of the Naitonal Council of Teachers of Matheamtics Annual Meeting, April 21, 2004, Philadelphia.
Submitted to Teachers College Record.
The research reported in this manuscript was funded by the Spencer Foundation. The views expressed in this paper are those of the authors and do not necessarily reflect official positions of the Spencer Foundation.
Abstract
Using ideas that can be traced to Dewey, Feiman-Nemser (2001) questioned the deeply-rooted assumption that teacher education, in general, and field experiences, in particular, are supposed to provide future teachers with an opportunity to practice the things that they will be expected to do as teachers. In contrast, she proposed that teacher education programs should provide an opportunity for future teachers to engage in “assisted performance” (p. 1016) that enables them to “learn with help what they are not ready to do on their own” (p. 1016). In this manuscript we provide evidence of how preservice elementary school teachers learned to teach mathematics via assisted performance.
Learning to Teach as Assisted Performance
Feiman-Nemser (2001) proposed that teaching should be viewed as a continuum with specific tasks to be accomplished in the preservice, induction, and continuing professional phases of a teacher’s career. She identified five tasks that are central to the preservice years:
- Examine beliefs critically in relation to vision of good teaching
- Develop subject matter knowledge for teaching
- Develop an understanding of learners, learning, and issues of diversity
- Develop a beginning repertoire
- Develop the tools and dispositions to study teaching. (p. 1050)
In discussing the first of these three tasks, Feiman-Nemser (2001) suggested that the images and beliefs about teaching and learning that preservice teachers bring to their teacher preparation programs act as filters for new learning. Therefore, they must critically analyze “their taken-for-granted, often deeply entrenched beliefs so that these beliefs can be developed and amended” (p. 1017). Feiman-Nemser also noted that this examination of beliefs should be coupled with the formation of new “visions of what is possible and desirable in teaching to inspire and guide their professional learning and practice” (p. 1017).
In order to develop an understanding of learners and learning, Feiman-Nemser recommended that preservice teachers need to learn what children are like at different ages, how they make sense of their worlds, how their thinking is shaped by language and culture. These types of understandings enable teachers to design age-appropriate, meaningful instructional activities, make and justify pedagogical decisions, and communicate with others.
Feiman-Nemser said that preservice teachers need to develop the tools to study teaching because “learning is an integral part of teaching and …serious conversations about teaching are a valuable resource in developing and improving their practice” (p. 1019). She proposed that teachers could develop the tools to study teaching by analyzing student work, comparing different curricular materials, interviewing students, studying other teachers, and observing their own instruction. Feiman-Nemser argued that when these activities are carried out in the company of other teachers they advance norms for professional discourse as teachers gain confidence in critically examining their own and their colleagues’ teaching. Feiman-Nemser also questioned the deeply-rooted assumption that teacher education, in general, and field experiences, in particular, are supposed to provide future teachers with an opportunity to practice the things that they will be expected to do as teachers. For example, is the purpose of a field experience to immerse future teachers in the daily life and routines of classrooms so that they become comfortable with such tasks as taking attendance, collecting morning seatwork, preparing bulletin boards, and conducting calendar time? In contrast, Feiman-Nemser proposed that teacher education programs should provide an opportunity for future teachers to engage in “assisted performance” (p. 1016) that enables them to “learn with help what they are not ready to do on their own” (p. 1016).
The prevailing apprenticeship model of teacher education often leaves preservice teachers with a feeling that the only way to learn to teach is to wait until they have their own classrooms and are able to devise their own methods of teaching. Lanier and Little (1986) caution that this “wait and see” approach makes it difficult for preservice teachers to see the range of possible decisions and actions available in teaching, resulting in a continuation of the teaching practices by which they were taught and a tendency to see these patterns of teaching as the only options. This restricted view of teaching makes it “less likely that they will escape from intellectual dependency and begin to take responsibility for decisions about curriculum and students” (p. 552).
Feiman-Nemser identified three characteristics of high quality teacher preparation programs that provide opportunities for future teachers to engage in the five tasks identified above via assisted performance. First, the program must have conceptual coherence by being built upon a “guiding vision of the kind of teacher the program is trying to prepare” (p. 1023). This vision includes a particular view of learning, the role of the teacher, and the goal of schooling. Second, the program includes purposeful, integrated field experiences that provide preservice teachers with opportunities to “test the theories, use the knowledge, see and try out the practices” (p. 1024) they have learned in their courses. Third, the program treats preservice teachers as learners, recognizing that they bring experiences and knowledge with them and that their learning is continuous and dynamic.
In this manuscript we provide a description of a mathematics methods course that was coherent, included purposeful, integrated field experiences, and was based on a view of teachers as learners. We substantiate this claim by showing how the preservice teachers addressed three of the central tasks identified by Feiman-Nemser: examine their beliefs, develop an understanding of learners, and develop the tools and dispositions to study teaching via assisted performance.
Methodology
Setting
The study took place in the context of the professional education program for elementary education majors (certification PreK-5) at the University of Georgia. Prior to entering the program, students completed a 60-hour liberal arts curriculum, including a mathematics content course designed specifically for elementary education majors. The professional education program was a 60-hour, four-semester program that included two mathematics methods courses (3 semester hours each). These courses were taken during the first two semesters of the program, along with methods courses in other content areas. The final two semesters consisted of additional methods and content courses and student teaching.
The first author was the mathematics methods instructor for all of the students in the study. The mathematics methods courses focused on eliciting, understanding, and crafting teaching practices based on children’s mathematical thinking. The goal of the instructor’s teaching was to help novice teachers craft practices that were consistent with current reform efforts but that were also respectful of their personal theories and the institutional constraints of their teaching situations. The instructor’s goals were to help teachers see unexpected student responses as teachable moments rather than as management problems (Floden & Buchmann, 1990), learn to encourage students to continue to seek understanding rather than concede defeat (Floden & Buchmann, 1990), challenge students’ mathematical misconceptions (Ball & McDiarmid, 1990), and focus on pursuit of meaning rather than pursuit of truth or fact (Grimmett, 1989). Experiences with children were coupled with an examination of appropriate research and theoretical literature (i.e., constructivism, children’s solutions to addition and subtraction word problems, children’s fraction knowledge). Novices had structured opportunities to use their experiences with children to make sense of the theory and vice versa. The intertwining of theory and practice also provided the novices with opportunities to examine their personal theories in light of actual teaching practice and research-based theories.
Participants
The data reported in this paper came from a larger five-year research project entitled Learning to Teach Elementary Mathematics. The goal of the project is to develop conceptual frameworks for understanding teaching and learning in elementary mathematics teacher education by studying how novice teachers craft their teaching practices across time as a result of their personal theories, teaching experience, and teacher education programs. Specifically, the goal of the larger study resonates with Feiman-Nemser’s (2001) call for teacher educators to view preservice teachers as learners because we seek to build a theory of how preservice teachers learn to teach mathematics.
The participants for the project were selected from two cohort groups who began the four-semester teacher education program in the fall of 2000 (Group A) and 2001 (Group B) and remained together as a cohort for the four semesters. Some data were collected on all students from each cohort, but the majority of data collection focused on two target subsets—six students from Group A and nine students from Group B. The target students were selected by purposeful sampling (Bogdan & Biklen, 1992) to represent a range of personal theories about mathematics. And to the extent possible, the target students were reflective of the diversity of students enrolled in each cohort (i.e., gender, race, age, etc.). In this manuscript we use data from a further subset of these participants—two participants from Group A and five participants from Group B–to illustrate the ways in which our program implemented an assisted performance model of teacher education.
Data Collection and Analysis
Data were collected and analyzed using the interpretive paradigm for teacher socialization (Zeichner & Gore, 1990). This interpretive approach involves an attempt to understand the nature of a social setting at the level of subjective experience. The purpose of this approach is to gain an understanding of the situation from the perspective of the participants and within their levels of consciousness and subjectivity. The goal is to “capture and share the understanding that participants in an educational encounter have of what they are teaching and learning” (Kilpatrick, 1988, p. 98). Eisenhart (1988) noted that the purpose of the research questions posed by researchers using the interpretive paradigm is to first describe what is “going on” and second to uncover the “intersubjective meanings” (p. 103) that undergird what is going on in order to make them reasonable.
To conduct interpretivist research, it is essential for the researchers to “be involved in the activity as an insider and able to reflect upon it as an outsider” (Eisenhart, 1988, p. 103). It is important for the researcher to be able to “take on the views of those being studied” (Eisenhart, 1988, p. 105) and also to be able to “step back from the immediate scenes of activity and to reflect on what is occurring from the perspective of someone who is aware of other systems and of theoretical perspectives”(Eisenhart, 1988, p. 105). Our research team attempted to accomplish these objectives in several ways. As mentioned previously the first author was the instructor for all mathematics methods courses taken by the participants, thus making her an insider. A graduate student who contributed to the data collection and analysis for this manuscript was a participant-observer in every class period. The second author joined the research team after the two mathematics methods courses were completed. He assisted with data collection during the remainder of the study and participated in data analysis. Thus, the researchers had varying degrees of involvement with the participants.
For research studies in the interpretivist tradition, Eisenhart (1988) advocated the use of ethnographic methods of data collection. Ethnographic methods have traditionally been used to study populations that are radically culturally different from the researcher, but these methods can be adapted for use in educational research. Ethnographic studies have often involved researchers literally living with a group of people over time to come to understand their lives. In the educational setting, the researcher “lives” with the participants within the community of the teacher education program. This study made use of all four methods of data collection attributed to ethnographic study: collection of artifacts, participant observation, ethnographic interviewing, and researcher introspection. Each of these methods provided a different perspective and allowed for triangulation of data.
Data collected for the larger project includes a mathematics beliefs survey (Integrating Mathematics and Pedagogy, 2004) and all written work produced by the students during both mathematics methods courses. In addition, the six students from Group A and the nine students from Group B were observed four times teaching a mathematics lesson and individually interviewed on four occasions. The observations occurred during field experiences in the second and third semesters of the program (one observation each) and during their student teaching experience (two observations). The four interviews were semi-structured and took place at the end of every semester of the teacher education program. Currently, the students from Group A and B are being observed monthly and interview bi-annually as they progress through their first 2 years of teaching. The data analysis for this manuscript was chiefly focused on the participants’ written work produced during their first elementary mathematics methods course and transcriptions of their first four interviews.
All data were transcribed and organized for coding purposes, and the research team defined an initial set of 25 codes. Data coding and sorting was done using a computerized qualitative data coding tool. Line-by-line coding of data took place chronologically for all 15 participants with different researchers coding data for different participants and then sharing summaries, called “data stories.” Finally, the data stories and original data for the subset of seven participants were coded across participants with respect to the research questions.
Findings
We identified three aspects of the mathematics course that provided preservice teachers with an opportunity to engage in assisted performance. We describe each one in turn and provide data from the participants to indicate the ways in which these aspects of the course helped them develop their thinking about mathematics teaching and learning. We being this section with a brief description of the participants’ initial views of mathematics teaching and learning.
Participants’ Initial Views about Teaching Elementary Mathematics
The seven participants whose data we use in this manuscript include Adam and Sara from Group A; and Emily, Erica, Erin, Katie, and Stacie from Group B. All were Caucasian with Adam being the only male in the group. (Adam was one of two males in the combined group of 60 students.) We deliberately showcase both their more traditional views and their more constructivist-leaning views so as to capture the complexity of their beliefs upon entering the program. In general, their views, whether traditional or constructivist, were not well developed as evidenced by statements not supported by evidence, examples, or elaboration.
The participants’ reflections on their own mathematical learning generally contained references to liking or disliking the subject, their motivation to learn mathematics, and their perceptions of the value of mathematics. Adam said what he most remembered from elementary school mathematics classes was just paper-and-pencil drills. From this experience he learned that math was simply rote memorization: “There was no purpose to the math, except to get a certain grade.” Sara, on the other hand, experienced a mathematics teacher who made mathematics “fun and entertaining, as well as educational. It was a class where we would learn in so many different ways.” Stacie remarked that she liked learning mathematics to be like a cookbook where she knew exactly what to do and how to do it in order to be successful. Similarly, Emily reported that “One quality I loved about some of my teachers was that they would not only tell me what I was doing wrong, but they would also tell me how to fix it. It is much easier to correct yourself when you are given advice or possible solutions.” Katie noted, “I don’t like math! It isn’t that I don’t like math in general—in fact, I enjoy certain ‘practical’ math applications. Frankly, I believe the reason that I don’t enjoy math is because I don’t see the point to a lot of it.” The composite portrait that these participants painted of their mathematics learning experience was one that seemed to be devoid of an emphasis on conceptual understanding or the application of mathematics to real-world problems. However, the participants did report several examples of caring teachers who made mathematics learning fun.