Learning to Teach as Assisted
Performance
DENISE S. MEWBORN
University of Georgia
DAVID W. STINSON
Georgia State University
Background: Although preservice teachers bring well-established views of teaching to their teacher
education programs, Tabachnick and Zeichner (1984) claimed that it is possible to amend preservice teachers’ views. They portrayed the learning of teachers as a negotiated and interactive
process rather than as one that is predetermined by teachers’ prior experiences. Feiman-Nemser
(2001) suggested that having preservice teachers examine their beliefs in light of images of good
teaching should be one of the central tasks of preservice teacher education.
Purpose: The study reported in this manuscript was conducted in an effort to document and
examine the interplay between novice teachers’ personal theories, their mathematics education
coursework, and their field experiences.
Research Design: Using all four methods of data collection attributed to ethnographic research
(Eisenhart, 1988)—artifact collection, participant observation, ethnographic interviewing, and
researcher introspection—this interpretivist study (Zeichner & Gore, 1990) attempted to document and examine the learning of seven preservice elementary teachers as reflected in their mathematics methods coursework and subsequent field experiences.
Findings: This manuscript describes three tasks from the mathematics methods course—critiquing an essay written by a teacher as she reflected on her teaching practice; working one-onone with a child in mathematics for an extended period of time; and observing an experienced
teacher teach an elementary mathematics lesson—that provided preservice elementary school
teachers with opportunities to learn and grow as teachers by making their beliefs explicit and then
reflecting on their beliefs and linking these beliefs to the practice of teaching mathematics. The
tasks described engaged the preservice teachers in examining beliefs critically in relation to visions
of good teaching, developing an understanding of learners and learning, and developing the
tools and dispositions to study teaching.
Teachers College Record Volume 109, Number 6, June 2007, pp. 1457–1487
Copyright © by Teachers College, Columbia University
0161-4681
1458 Teachers College Record
Conclusions: While an analysis of the data showed evidence that the preservice teachers became
aware of their beliefs, reflected on their beliefs, and began to change their beliefs, the purpose of
this manuscript is not to claim that the teachers changed for the good and that this change was
enduring. Rather, the goal is to illuminate the tasks, provide the preservice teachers’ responses
and reactions to the tasks, and to argue that these tasks constitute a form of learning to teach
mathematics through assisted performance.
Elementary mathematics teachers’ practices are shaped largely by their
personal theories—“a person’s set of beliefs, values understandings,
assumptions—the ways of thinking about the teaching profession” (Tann,
1993, p. 55). These personal theories, including ideas about what it
means to teach mathematics and what the roles of teachers and students
should be, are well developed by the time novice teachers enter their professional education programs and profoundly affect what they learn from
their education (Nickson, 1992; Staton & Hunt, 1992).1 Mathematics
education researchers have conducted numerous studies that document
future teachers’ beliefs and their propensity to reflect on these beliefs.
These studies have generally found that preservice teachers’ beliefs are
not conducive to teaching for understanding, that their beliefs change
very little during a teacher education program, and that preservice teachers are not prone to reflect on their beliefs (e.g., Borko, Eisenhart,
Brown, Underhill, Jones, & Agard, 1992; Cooney, Shealy, & Arvold,
1998). It is widely accepted that mathematics education courses that are
predicated on reform-oriented documents such as the National Council
of Teachers of Mathematics’ (NCTM) standards for curriculum, teaching, and assessment (NCTM, 1989, 1991, 1995, 2000) are often in conflict
with novice teachers’ personal theories.
Field experiences, another central component of teacher education
programs, often serve to perpetuate apprenticeship and trial-and-error
views of teaching (Cruickshank, 1990; Lanier & Little, 1986) to the exclusion of using thought, scholarship, or information gained in a teacher
education program to solve classroom problems (Britzman, 1986; Lanier
& Little, 1986). Field experiences tend to reinforce preservice teachers’
conservative, present-oriented, and authoritarian approaches to teaching
(Britzman, 1986; Cruickshank, 1990).
Although preservice teachers bring well-established views of teaching
to their teacher education programs, Tabachnick and Zeichner (1984)
claimed that it is possible to amend preservice teachers’ views. They portrayed the learning of teachers as a negotiated and interactive process
rather than as one that is predetermined by teachers’ prior experiences.
Feiman-Nemser (2001) suggested that having preservice teachers exam-
Learning to Teach as Assisted Performance 1459
ine their beliefs in light of images of good teaching should be one of the
central tasks of preservice teacher education. Limited research, however,
has been conducted that sheds light on the process by which preservice
teachers learn to teach mathematics and the dialectic relationship
between their personal theories and their experiences in a teacher education program. Thus, the study reported in this manuscript was conducted in an effort to document and examine the interplay between
novice teachers’ personal theories, their mathematics education coursework, and their field experiences, with particular attention to activities in
the teacher education coursework and field experiences that were especially conducive to helping the novices examine their personal theories
and implications for their teaching practices.
THEORETICAL PERSPECTIVE
Although much of the prior literature on teachers’ beliefs (both preservice and inservice) has looked at changes in beliefs (Brown & Borko,
1992; Fennema & Nelson, 1997; Schifter & Fosnot, 1993; Simon &
Schifter, 1991), we have deliberately chosen not to focus on change.
Rather, we focus on learning. The notion of changing beliefs seems to
imply that there is a value-laden continuum in which it is clear that movement in one direction is positive. Acknowledging that both learning to
teach and teaching are complex, multi-faceted, and contextual processes,
we agree with Lerman (2001) that it is more useful to talk about teacher
learning rather than change. Similarly, Feiman-Nemser (2001) argued
that it is imperative that teacher educators attend to preservice teachers
as learners. She suggested that exemplary programs should engage in
“monitoring students’ personal responses to new ideas and experiences,
and … offering an appropriate mixture of support and challenge in
response to students’ changing knowledge, skills, and beliefs” (p. 1025).
Although the field of mathematics education has well-developed frameworks for talking about student learning in general and in particular content domains (Carpenter, Fennema, & Romberg, 1992; Carpenter &
Moser, 1984; Fuson, 1992; Wood, Cobb, Yackel, & Dillon, 1993), we lack
a similarly robust set of frameworks for talking about teacher learning.
This study is an attempt to contribute to the development of such a
framework.
We also choose not to focus on “mismatches” between preservice teachers’ espoused beliefs and their evolving teaching practices, despite the
popularity of this approach in the literature (e.g., Cooney, 1985;
Thompson, 1984; Wilcox, Lanier, Schram, & Lappan, 1992). Again, we
agree with Lerman (2001) that examining these mismatches is not par-
1460 Teachers College Record
ticularly fertile ground for understanding teacher learning because
beliefs are often elicited from teachers in decontextualized or “laboratory-like” settings. Thus, it is perhaps not surprising that these beliefs do
not always manifest themselves in the context of the classroom.
In contrast to these two previous approaches to examining beliefs, our
approach is to document the interplay between preservice teachers’ personal theories and their mathematics education coursework and field
experiences in order to describe their learning. Thus, we did not deliberately attempt to ferret out their beliefs via instruments or interviews.
Rather, we sought to capture instances where they spontaneously articulated their beliefs and linked them to the practice of teaching mathematics. Therefore, we approached this study from an interpretivist stance
(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.
RELATED LITERATURE/ANALYTICAL FRAMEWORK
The prevailing model of teacher education is one of apprenticeship in
which teacher education, in general, and field experiences, in particular,
provide future teachers with an opportunity to practice the things that
they will be expected to do as teachers (cf. Zeichner, 1983, for a detailed
explication of the apprenticeship model of teacher education). This
model is predicated on the assumption that good teaching is a form of
cultural knowledge that is best developed through trial and error by the
novice in the company of an experienced practitioner.
Critics note that the apprenticeship approach 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) cautioned 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. Similarly,
Learning to Teach as Assisted Performance 1461
Zeichner (1983) noted that “the problem of teacher education is defined
within an educational and social context that is largely accepted as given”
(p. 5) and therefore offers no avenue for changing or improving teaching. This restricted view of learning to teach also makes it “less likely that
[preservice teachers] will escape from intellectual dependency and begin
to take responsibility for decisions about curriculum and students”
(Lanier & Little, 1986, p. 552).
Many authors trace this notion of an apprenticeship to Dewey
(1904/1965). A close reading of Dewey, however, reveals that his description of an apprenticeship in teaching was considerably more robust and
complex than the way the term is commonly used in the literature today.
Dewey advocated both an incremental approach to a novice assuming
responsibility for teaching and a laboratory approach to field experiences. Echoing Dewey, Feiman-Nemser (2001) recently 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).
Because the term “apprenticeship” has become corrupted and overused,
we choose to use Feiman-Nemser’s notion of “assisted performance” to
interrogate the learning experiences of preservice teachers.
In the same manuscript in which she proposed a return to Dewey’s
ideas of teacher learning via the assisted performance model, FeimanNemser (2001) also laid out a continuum of teacher learning and specified tasks to be accomplished in the preservice, induction, and continuing professional development phases of a teacher’s career. She identified
five tasks that are central to the preservice years:
1. Examine beliefs critically in relation to visions of good teaching.
2. Develop subject matter knowledge for teaching.
3. Develop an understanding of learners, learning, and issues of
diversity.
4. Develop a beginning repertoire.
5. Develop the tools and dispositions to study teaching (p. 1050).
In our analysis of preservice teacher learning, we focus on tasks 1, 3,
and 5, and thus we elaborate on them here. 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
1462 Teachers College Record
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 (2001) recommended that preservice teachers need to
learn what children are like at different ages, how they make sense of
their worlds, and 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 (2001) 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. FeimanNemser suggested 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.
In this manuscript, we describe three tasks from a mathematics methods course that provided preservice elementary school teachers with
opportunities to learn and grow as teachers by making their beliefs
explicit and then reflecting on their beliefs and linking these beliefs to
the practice of teaching mathematics. As we describe each task and provide evidence of the preservice teachers’ learning, we also detail the ways
that the tasks engaged the preservice teachers in three of FeimanNemser’s (2001) tasks: examine beliefs critically in relation to visions of
good teaching; develop an understanding of learners and learning; and
develop the tools and dispositions to study teaching. While the data do
show evidence that the preservice teachers became aware of their beliefs,
reflected on their beliefs, and began to change their beliefs, our purpose
is not to claim that the teachers changed for the good and that this
change was enduring. Rather, our goal is to illuminate the tasks, provide
the preservice teachers’ responses and reactions to the tasks, and to
argue that these tasks constitute a form of assisted performance.
METHODOLOGY
This manuscript comes from one piece of a larger five-year research project entitled Learning to Teach Elementary Mathematics. The overall goal of
Learning to Teach as Assisted Performance 1463
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 experiences, and teacher education programs. The data reported in this manuscript were collected
during the first mathematics methods course taken by the participants
during their undergraduate program. The data are supplemented by
interviews conducted at subsequent points in the teacher education
program.
Setting
The project began in the context of the first mathematics methods
course in the teacher education program for elementary education
majors (certification Pre-K–5) at the University of Georgia. Prior to entering the teacher education program, students completed a 60-hour liberal
arts curriculum, including a mathematics content course designed specifically for elementary education majors. The teacher 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 (nonmathematics) methods courses and student teaching.
The first author was the mathematics methods instructor for all of the
participants in the project. The mathematics methods course focused on
eliciting, understanding, and crafting teaching practices based on children’s mathematical thinking. The course included both on-campus
instruction and an off-campus field experience. The goal of the instructor’s teaching was to not only help novice teachers craft practices that
were consistent with current reform efforts in mathematics education
(cf. NCTM, 1989, 1991, 1995, 2000), but also practices that were respectful of their personal theories and the institutional constraints of their
teaching situations. The instructor’s goals were to help novice 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).
The preservice teachers’ experiences with children in the field were
coupled with an examination of appropriate research and theoretical literature (e.g., constructivism, children’s solutions to addition and subtrac-
1464 Teachers College Record
tion word problems, and children’s fraction knowledge). Preservice
teachers 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 them with opportunities to examine their
personal theories in light of actual teaching practices and research-based
theories. In short, instruction in the mathematics methods course, rather
than dichotomizing theory and practice, provided opportunities for
novices to see that theory and practice are inextricably linked.
Participants
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. This manuscript is based on
data from a further subset of 7 participants—two from Group A and five
from Group B. This set of participants consisted of six Caucasian females
and one Caucasian male, which is representative of the student population in the elementary education program at the University of Georgia.
Data from these seven participants were selected for this manuscript
because they revealed the clearest evidence of the preservice teachers’
learning in and from their teacher education program.
Data Collection
For research studies in the interpretivist tradition, Eisenhart (1988) advocated the use of ethnographic methods of data collection. This project
made use of all four methods of data collection attributed to ethnographic research: artifact collection, participant observation, ethnographic interviewing, and researcher introspection. The data used for
this manuscript came from the participants’ written course assignments
produced during their first elementary mathematics methods course and
the transcriptions of their first four interviews. The written assignments
included a brief autobiography, a critique of an essay (discussed later in
the manuscript), personal reflections on working one-on-one with a
Learning to Teach as Assisted Performance 1465
student in mathematics (also discussed later in the manuscript), and an
end-of-course portfolio.
The four interviews were conducted once per semester and used a
semi-structured, traditional, question-and-answer protocol (Hollway &
Jefferson, 2000). The first interview was conducted near the end of the
first mathematics methods course and focused on eliciting autobiographical data from the participants regarding their views of mathematics and
their prior experiences as mathematics learners. They were also asked to
reflect on their experiences working one-on-one with a student in mathematics during the methods course. The second and third interviews
occurred at the end of the second and third semesters of the teacher education program and asked participants to reflect on their practicum field
experiences and how these experiences differed (or not) from their oneon-one teaching experience and from what they had learned in their
mathematics methods course. The fourth interview, conducted after the
conclusion of student teaching, focused on their reflections about their
various teaching experiences during their teacher education program
and the changes (if any) in their conceptions about mathematics and
mathematics teaching and learning from the beginning to the end of
their teacher education program.
Data Analysis
The data were analyzed using the methods of grounded theory (Glaser &
Strauss, 1967) and grounded interpretivism (Addison, 1989), as the
larger project attempts to build a theory of how preservice teachers learn
how to teach mathematics. Grounded theory and interpretive research
methods are both constant comparative methods in which the researcher
is constantly looking for and questioning “gaps, omissions, inconsistencies, misunderstandings, and not-yet understandings” (Addison, 1989, p.
41). Both methods also emphasize the importance of context and social
structures in research settings, and in both methods data collection, coding, and analysis continue throughout the research process.
The research team, which included both authors and a project
research assistant, used line-by-line qualitative methods of coding data as
a “progressive process of sorting and defining and defining and sorting”
(Glesne, 1999, p. 135). We coded data that reflected beliefs, prior experiences, teacher education experiences, and concerns that the preservice
teachers identified. We subsequently refined these codes to delineate, for
example, beliefs about mathematics, about students, about teaching, and
about self as a learner and teacher. All coding was done using the
1466 Teachers College Record
computer program Atlas.ti 4.2, which facilitated assigning codes to the
data and sorting data by the codes it had been assigned.
We coded each participant’s data in chronological order (the order in
which it was collected) with different researchers coding data for different participants and then writing a summary of each participant, called a
“data story.” Sharing the data stories among researchers facilitated refinement of codes, development of common ideas and language, and comparison and contrast of the participants. The methodology for developing the data stories served as a form of triangulation and assisted the
research team in developing hypotheses about the events that took place
in the participants’ mathematics methods courses that most impacted
their learning of how to teach mathematics. These hypotheses were compared and contrasted with the current literature regarding initial-preparation teacher education programs.
FINDINGS
We identified three components of the mathematics methods course that
provided preservice teachers with an opportunity to become aware of
and articulate their beliefs about teaching and learning mathematics. We
describe each one in turn and provide data from the participants to indicate the ways in which these components of the course helped them
learn about mathematics teaching and learning. We begin 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 Alex
and Jayne from Group A; and Eileen, Jennifer, Heather, Laura, and
Shelly from Group B. 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 illustrated 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. Alex 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
Learning to Teach as Assisted Performance 1467
purpose to the math, except to get a certain grade.” Jayne, 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.” Shelly 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, Eileen said, “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.” Laura 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. The participants, however,
did report several examples of caring teachers who made mathematics
learning fun.
The importance of caring teachers who make learning fun was echoed
throughout their descriptions of ideal teachers and their reasons for
wanting to teach. Eileen remarked, “In my opinion, the most important
qualities [of an ideal teacher] are being kind and creative.” Jennifer
described a former teacher whom she considered the ideal teacher
because she made “math fun, interesting, and beneficial for everyone in
the class” and was “compassionate, intelligent, honest, fair, fun loving,
energetic, and caring.” Laura said the ideal teacher should “focus on creating an environment where children look forward to learning and being
challenged.” Jayne described a teacher who turned her on to mathematics in middle school as “clear, concise, and to the point. If there ever
came a time that we didn’t understand a problem, she would go over it
again and again until we did. She never talked down to us or made us feel
stupid.”
Many of these preservice teachers entered the program with some
sense of the importance of listening to children and allowing children to
think for themselves. For example, Jennifer noted that the teacher
should provide the students with the basics, “the things to get going and
let them work with it and figure it out.” Jayne said that the ideal teacher
“is a listener who cares about what their children think and feel. She must
take the time to listen, not just hear.” Shelly said that in her experience
teaching in a preschool she “tried to turn a child’s idea into a learning
experience,” which helped her realize how challenging it is to “process in
your mind how to respond to what children are saying and to react
1468 Teachers College Record
quickly to it before the moment is lost.” Although most of these comments are not specific, Heather did provide a more detailed description
of why it is important to listen to children. She wrote, “Teachers need to
listen and find out what students do not understand, why they don’t
understand, and how the explanations affect the student. Every student
is different; therefore, it is very important for teachers to listen to each
one.”
The participants’ initial comments suggest that at the beginning of
their mathematics methods courses they were aware of the role that children’s thinking and actions could play in shaping instruction. Their
views, however, lacked depth or specificity of what it meant to apply this
notion to the teaching and learning of mathematics.
Participants’ Learning To Teach Elementary Mathematics
We now turn our attention to how specific components of the preservice
teachers’ initial mathematics methods course engaged the preservice
teachers in assisted performance, helping them add more depth to their
ideas about using children’s mathematical thinking and actions in
instructional decision-making. This discussion is organized (roughly
chronologically) around three specific components of that course: critiquing an essay written by a teacher as she reflected on her teaching
practice; working one-on-one with a child for an extended period of
time; and observing an experienced teacher teach an elementary mathematics lesson. Throughout the discussion, we draw parallels to three of
the five tasks that Feiman-Nemser (2001) argued are components that
“form a coherent and dynamic agenda for initial preparation” (p. 1016):
(a) analyzing beliefs and forming new visions, (b) developing understandings of learners and learning, and (c) developing the tools to study
teaching.
Critiquing an essay by Vivian Paley. Early in the semester of the first mathematics methods course, preservice teachers were asked to read and
respond in writing to a book chapter titled “On Listening to What the
Children Say” by Vivian Paley (Paley, 1987). Paley’s chapter is her firstperson account of how she became aware of the importance of listening
to the children in her kindergarten classroom in order to uncover the
meaning behind their words. The chapter does not address mathematics
teaching; rather it describes classroom activities such as show-and-tell and
the housekeeping center. Throughout the chapter, Paley provides
numerous examples of things she heard children say, how she initially
interpreted their words, and what she learned about the children’s
Learning to Teach as Assisted Performance 1469
meaning when she continued to listen to and probe the children for
further explanation.
One particularly vivid example of listening and probing that Paley
recounted involved a discussion of birthdays in which a child claimed
that his mother no longer had birthdays. This claim would be an easy
comment for the teacher to dismiss or respond to by saying, “Of course
your mother has a birthday. Everyone has a birthday.” Paley, however,
asked the child with genuine sincerity why his mother did not have a
birthday. The child replied that when it is your birthday, your mother
bakes you a cake. Given that his mother’s mother was no longer alive,
there was no one to bake her a cake, so she could not have a birthday. By
probing the child’s statement and by listening carefully and sincerely to
the child’s response, Paley uncovered a very logical, but incorrect, conception the child had about birthdays.
In the methods course, the students and instructor had a lively discussion about the chapter. Some students thought that Paley had gone to
extremes to make her point, and they noted that it is simply not possible
or desirable to probe every single thing that each child says. Many students, however, found the chapter very enlightening because it provided
specific examples of situations in which an adult had the potential to
underestimate, misinterpret, or dismiss a child’s reasoning. But because
Paley took the time to listen to the child, she came away with a much better understanding of and appreciation for the child’s thinking. Following
the discussion in class, students wrote reflective commentaries on the
chapter.2 These commentaries provide the first evidence of the preservice
teachers’ deepening understanding of what it might mean to listen to
children in an instructional setting. It is especially notable that many of
the teachers related the Paley chapter to their prior or current teaching
experiences.
Heather’s initial reaction to the birthday story was that Paley was wasting valuable class time, and she should just tell the child that everyone
has a birthday. After the class discussion, Heather reflected on the birthday story differently, however. She noted that if Paley had tried to explain
to the child why his mother does have a birthday without understanding
the child’s reasoning, her explanation likely would not have made sense
to the child or changed his views because it did not connect to what the
child was thinking. Although Heather wrote in her autobiography at the
beginning of the semester that it was important for teachers to listen to
students, her reflections on the Paley chapter suggest that she did not
have a very robust idea of what it meant to listen to children. Heather
described the influence the chapter had on her this way:
1470 Teachers College Record
When we discussed this topic in class, it helped open my eyes
even further. I realized that students have their own point of
view. I know this sounds ridiculous, that this realization had
never occurred to me. I always thought of children as empty
sponges ready to be filled with new knowledge. I never thought
about them having already formed their own definitions and
opinions. I just thought students would take the information I
gave them and soak every bit of it up. I did understand not every
student would grasp this information, but now I see that in some
cases, it is because they already have a different understanding
about the information I am presenting to them.
Heather went on to say that it is important that teachers not get “stuck”
in their lesson plans because it is the teacher’s responsibility to “see the
world through [the child’s] eyes and attack problems and questions as if
you were in the mind of that child.”
Jennifer also initially dismissed Paley’s ideas, thinking they were
extreme and that the message was that children should discover everything on their own. After a second reading of the chapter and the class
discussion, however, Jennifer said she realized that Paley was simply
reminding teachers of the importance of allowing children to learn from
themselves. She said that the impact of Paley’s chapter became clearer to
her when she was observing a first-grade classroom as part of an assignment for another course. As she reflected on that experience, Jennifer
noted:
As I began watching the teacher, I immediately found myself feeling critical of the way that she was simply telling her students how
to solve the math problem. I just wanted to jump up and say,
“Please, just let the children experiment first and see if they can
solve the problem on their own! Let them see how far they can
get without being forced to do it your way!”
Jennifer then turned the mirror back on herself, wondering how many
times someone had observed her working with children and thought the
very same thing about her interactions. Jennifer concluded her essay by
stating new goals for her teaching:
I want my students to know that I am listening to them, and I also
want them to listen to themselves and each other. I hope to be
able to have class discussions and lessons filled with open-ended
questions and multiple right answers.
Learning to Teach as Assisted Performance 1471
Laura connected the Paley chapter to both her previous experience
working in a pre-kindergarten classroom and her experience in the
methods class working one-on-one with a child (discussed later in this
manuscript). Regarding her experience with Pre-K children, Laura said
that she often walked away from interactions with children wondering if
she had caused more confusion. She said the children often did not seem
to understand her answers to their questions, which puzzled her because
she knew her answers were “correct.” She said the Paley chapter helped
her realize that her answers did not fit with the children’s existing ideas,
so the children could not “work what I said into the thought processes
they already had going in their minds.”
Laura also related the Paley chapter to her first-hand experience with
teaching mathematics to a child, noting that one of her goals for the
teaching experience was to “keep my mouth shut” and “stay out of the
problem-solving process.” Laura quickly discovered that this was easier
said than done for her, both because she wanted to jump in and “give”
the child the solution and because she had a hard time adjusting her
thinking to the child’s thinking. In her final portfolio, recounting her
field experiences Laura wrote:
When we were discussing teachers who just jumped right in and
gave a child the answer, or one who only responded positively to
correct answers, I knew I had that problem. I have the one right
answer in my mind, and that’s the only answer for which I’m
looking. I also have a bad habit of leading children to the answer
instead of letting them discover their own way. I also want to
jump right in with my own suggestions during the problemsolving process.
Shelly said the Paley chapter challenged her to put more effort into trying to understand children’s thinking by interacting with them and asking open-ended questions. Shelly said that in the past she had often dismissed children’s ideas as cute or funny, and now realized that these ideas
generally spring from a well-formed web of logical ideas. In her commentary about the chapter, Shelly admitted to having beliefs about the value
of directive teaching at the beginning of her mathematics methods
course and said that the Paley chapter challenged these beliefs. In
response to the chapter she wrote:
Sometimes when I interact with students, I find myself teaching
as I have been taught. It is a hard habit to break because for some
reason it feels natural. Paley talks about, as a teacher, she wanted
1472 Teachers College Record
to supply students with knowledge and correct answers because
it gave her the surest feeling that she was teaching. . . . So many
times, we are so wrapped up in successfully teaching a lesson that
we are not truly observing the thoughts our students are concluding on their own.
As is clear from the excerpts presented above, the preservice teachers
became aware of and explicitly analyzed their beliefs about mathematics
teaching and learning in light of Paley’s descriptions of children’s thinking and its impact on her instruction. In some cases, these analyses were
more thorough and well-connected to the participants’ teaching experiences. In other cases, these analyses were more of a surface-level nature,
making it difficult to determine whether the participants had actually
developed “visions of what is possible” (Feiman-Nemser, 2001, p. 1017).
The specific examples provided in Paley’s chapter, however, seemed to
present the preservice teachers with “compelling alternatives” and “powerful images of good teaching” (p. 1017).
The ideas contained in the Paley chapter laid the groundwork for the
preservice teachers to better understand learners and learning in their
subsequent field experiences, particularly their work with their Barrow
Buddies (discussed later in this manuscript). Although reading the chapter, per se, did not help them develop a better understanding of children’s learning in mathematics, it did seem to provide a concrete example of what the instructor meant by her continuous references to listening to students’ thinking and building instruction on that basis.
The experience of reading the Paley chapter and discussing it with
peers also provided the preservice teachers with an opportunity to
develop the tools to study teaching. The chapter gave the preservice
teachers an example of how one studies one’s own teaching and that of
others. Paley’s open and explicit reflection on her own teaching exemplified the manner in which one can deliberately observe one’s own teaching and analyze it later. Although some preservice teachers initially dismissed what they had read, discussing the chapter with peers—with support from the instructor—helped them take a more open-minded
approach to the text of the essay, to find something of value in the chapter, and to relate it to their own experiences. It is this interactive aspect
of the experience that can be viewed as assisted performance. Left on
their own to read the chapter and write a reflection, many preservice
teachers were not yet ready to take Paley’s ideas seriously. But with assistance from their peers and the instructor, the preservice teachers were
able to engage in a meaningful discussion of what Paley meant, how it
worked in her classroom, and the implications for mathematics teaching
Learning to Teach as Assisted Performance 1473
and learning. The fact that the preservice teachers continued to refer to
the Paley chapter in subsequent assignments and in their interviews suggests that this course task was a powerful learning experience for them.
Barrow Buddy Field Experience. Approximately 4 weeks into the mathematics methods course, each preservice teacher began to work one-onone with an elementary school-aged child in mathematics once a week
for 8 weeks. The field experience took place at Barrow Elementary
School and is hereafter referred to as the Barrow Buddy (BB) field experience.3 The goal of the field experience was for the preservice teachers
to learn to listen to and assess children’s mathematical thinking and to
plan subsequent instruction based on this assessment. The preservice
teachers were encouraged to engage the children in problem solving
rather than in computational work. Accordingly, the children who were
selected for the experience were working at or above grade level so that
the preservice teachers would not feel pressure to “cover” certain mathematical content.
Throughout the BB field experience, as the preservice teachers were
working with the children, the instructor/researcher and two
teaching/research assistants moved from pair to pair using a coaching
model to provide input. For example, if a child solved a problem correctly and the preservice teacher was ready to move on to the next problem, the instructor interjected and asked the child to explain her/his
solution method. In this manner, the instructor was able to model for the
preservice teachers what she was teaching in the university classroom:
The importance of uncovering children’s mathematical thinking in
order to inform subsequent instruction. Moreover, because the instructor and her assistants observed each preservice teacher in an instructional setting each week, they were able to tailor classroom instruction on
campus to reflect and enhance what happened at Barrow Elementary
School. The BB field experience was deliberately set up to be an opportunity for assisted performance.
For Jayne, the BB field experience motivated a critical examination of
her beliefs about children and their capabilities. In an interview shortly
after the field experience ended, Jayne made the following statement
regarding her newfound understanding of children:
I’ve never really understood how much kids can understand at
such a young age. I was just amazed to watch Sion [her Barrow
Buddy]. He was actually thinking in his little head, and I just
somehow looked at him in awe. He was just so bright, and if
something didn’t work, he’d try another way, and he’d try
another way. They’re just so persistent, and I just never realized
1474 Teachers College Record
kids could grasp that much. I mean, they were at such an
advanced level for how old they were. They’re just like miniature
adults, I guess. It was really, that just shocked me.
Jayne remarked that she learned a great deal about herself and her
style of teaching from the BB field experience. She believed that the
experience taught her the importance of being “ready to adjust what I
had planned at anytime during my lesson” in order to capitalize on the
understanding, thinking, and persistence of children.
The BB field experience also helped Jayne develop an appreciation for
the value of questioning students. In her final portfolio for the course she
noted:
I learned how to ask better questions. I learned that sometimes
the way a problem is phrased is the only thing keeping a child
from solving it. I learned that if you just rearrange the wording
of some questions, a child would understand it more clearly. . . .
We need to build off of what they already know and understand.
So often, all a child needs is a little hint. My Barrow Buddy
helped me learn how to give better hints. He helped me to see
that sometimes all it takes is a little help (from the teacher) to
make the problem “click.”
Coming to see the value of effective questioning and how it can help
the teacher build instruction from the child’s existing knowledge base
was a recurring result of the BB field experience for Jayne, and most of
the project participants. Throughout her written assignments from the
first mathematics methods course and during her initial interviews, Jayne
made several references to the BB field experience and how it changed
her attitudes about children and children’s learning and her conceptions
of teaching and planning.
The BB field experience affected Alex’s conceptions of mathematics
teaching and learning—particularly the value of multiple solution strategies. On several occasions when Alex presented his Barrow Buddy with a
mathematics problem, he was amazed by the solution strategies used by
the student because they were ones that had not occurred to Alex in his
planning. In an interview, Alex remarked that when he posed a mathematics problem for his Barrow Buddy he had in mind “pretty much a set
pattern” of how to do the problem; however, his Barrow Buddy would “do
it a completely different way.”
Alex articulated how he developed a better understanding of learners
from working with his Barrow Buddy. He noted that the experience
Learning to Teach as Assisted Performance 1475
allowed him “to visualize first-hand how children solve problems and
where difficulty may lie.” He also came to recognize that children could
work independently to successfully solve problems using their own strategies and not those imposed by the teacher. Alex became more aware of
the limiting effects of making assumptions about what students could or
could not do mathematically, recognizing that students could teach
teachers as much as teachers could teach the students.
The BB field experience prompted Shelly to shift her focus as a teacher
from what she was teaching to what the student was learning. Shelly initially began planning for her BB field experience sessions by seeking
“first-grade activities” from books and internet sites because she held
some stereotypes about what children of a particular age could do mathematically. Her first-grade Barrow Buddy surprised her with what she was
able to do, however:
Maria used her basic knowledge of counting, adding, and subtracting to do the higher math that she had not learned yet, such
as place value, multiplying, and dividing. The thing that was
amazing was that I did not even instruct her on how to use her
basic skills to do the higher math. She figured it out on her own.
After Shelly realized the thinking of which her Barrow Buddy was capable, she shifted her planning from searching for first-grade activities to
building her next lesson based on the child’s learning from the previous
lesson. In addition, Shelly noted that she sought to give hints “without
giving [the answer] away.”
The BB field experience caused Laura to shift her focus from her
thinking to her Barrow Buddy’s thinking. After reading the Paley chapter, Laura said that she wanted to base her teaching on children’s ways of
thinking, but she found it very difficult to listen to her Barrow Buddy and
respond accordingly. Laura said that figuring out students’ thinking was
difficult “because I have a hard time seeing things except in the way that
I would have done it.” She acknowledged that it was important to be able
to approach a problem “from another angle” if children did not understand the first approach. But her ability to foster multiple approaches was
a significant concern for Laura: “I could only think of my way, one way. I
don’t know how to do math from any other angle.”
Laura’s initial focus on her way of thinking resulted in problematic
interactions with her Barrow Buddy. She became fixated on “getting
through” her plans and on helping her Barrow Buddy get the correct
answer to the problems she posed. She was not very patient and tended
to interject suggestions at the first sign that her Barrow Buddy did not
1476 Teachers College Record
know exactly how to proceed with a problem. The instructor and assistants gave Laura a great deal of feedback, both in the form of written
feedback on her plans and in the form of coaching during her lessons, to
alert her to these tendencies. She was very receptive to this feedback and
was already somewhat aware of these tendencies. She made a deliberate
effort to “back off a little bit and let [the child] figure out problems on
her own.” Laura found this effort extremely difficult, however, and her
Barrow Buddy resisted Laura’s attempts to “back off.” Because of her earlier habit of providing directive feedback to her Barrow Buddy every time
she was stuck, Laura created the expectation that she would “give her the
answer,” and the child became upset, frustrated, and even withdrawn
when Laura tried to change tactics and withhold her input in favor of
allowing the child to explore solutions on her own. In some sense, Laura
went from one extreme—telling the child what to do at every turn—to
another—telling the child nothing. This second extreme was reflected in
Laura’s comment: “It was a lot easier to say that I was going to stay out of
the problem-solving process than it was to actually do it!”
Through instructor coaching and peer feedback, Laura came to understand that her goal was to find a middle ground in which she could provide encouragement, hints, and suggestions without railroading the child
into her way of thinking. Laura’s final reflection on her BB field experience showed that she began to mediate the extremes of “backing off” and
directing the child’s thinking. She wrote, “I learned from working with
my Buddy to keep my mouth shut! It took a while, and it was difficult, but
I think I’m better about not giving so many suggestions. I think I am realizing when my Buddy needs help and when she really just needs me to let
her think.”
Jennifer developed a deeper understanding of student motivation and
the pedagogy of questioning by working with a Barrow Buddy who was
not particularly motivated. Jennifer initially struggled with finding mathematical problems that were both accessible and challenging for her
Barrow Buddy. In order to motivate her Barrow Buddy, Jennifer began by
playing mathematical games. Her Barrow Buddy, however, was fixated on
winning and lost interest in the game if he did not win. Consequently,
Jennifer began letting him win in order to keep him engaged. She summarized this experience by writing, “This was probably not the best
approach to take, but I am struggling to find a way to make my meeting
with Terrence a fun, positive, learning experience.” The instructor suggested that Jennifer should make the mathematical game playing less
competitive by explaining the strategy that she was using while playing
the game. Jennifer began to develop an appreciation for the complexity
Learning to Teach as Assisted Performance 1477
of student motivation as evidenced by her reflections upon implementing this approach:
I tried to be more interactive with him. I asked lots of questions
about why he did things the way he did, and I tried to get him to
see the endless extensions and connections of everything we did
together. I learned to allow Terrence to discover the answers on
his own, but I also learned how to effectively ask him questions
that would make him think and go that next step…This “new”
way of solving problems made both Terrence and me feel much
more successful. Terrence felt more confident because he knew
that he could apply strategies that were familiar to him from previous problems, and he became more comfortable experimenting with manipulatives and different ideas.
Through this approach, Jennifer also began to see the link between
effective questioning and student engagement. One year later, Jennifer
was still reflecting on the effect of the BB field experience:
Towards the end of last year [her second semester in the program], it was “Wow, questioning is really important.” And I was
really seeing the benefits of it. Whereas with my Barrow Buddy,
I’m not quite sure I knew then what I was looking for when I was
questioning. I was like “Okay, I’ll ask lots of questions and listen
to his answers,” but I didn’t really realize as much why or what to
do with it, I guess. I think, personally I grew, like, as a teacher in
that aspect, if that makes sense.
As the data reported suggest, the Barrow Buddy field experience provided preservice teachers with ongoing and sustained opportunities to
analyze their beliefs about teaching and learning and to develop understandings of learning and learners (Feiman-Nemser, 2001). Because the
preservice teachers worked weekly with the same child for a period of 2
months, with on-campus class sessions interspersed with the fieldwork,
they had an opportunity to engage in a protracted and deliberate study
of the mathematical thinking and learning of a single child with support
from their instructor. By writing weekly plans, enacting them, and writing
a reflection on the session (that was shared with the classroom mentor
teacher and university instructor), the future teachers gained experience
with designing appropriate instructional tasks, justifying pedagogical
actions, assessing student learning, and communicating with other
1478 Teachers College Record
educators. The teaching sessions themselves, coupled with the support
and challenge from the instructor and teaching assistants, enabled the
preservice teachers to experiment with various methods of teaching,
questioning, and assessing student learning in order to develop a preliminary understanding of what works best under what conditions.
The Barrow Buddy field experience provided a deliberate forum for
assisted performance in the areas of linking theory and practice, for
developing teaching skills and pedagogical strategies, and for learning to
analyze and reflect upon student learning and teaching. The preservice
teachers were assisted in their performance by their Barrow Buddies,
their peers, and their instructor.
Observing an Experienced Teacher. Toward the end of the first mathematics methods course, preservice teachers were given an opportunity to
observe a mathematics lesson taught by a mathematics specialist in a local
school. In some cases, the preservice teachers were able to discuss the lesson with the teacher afterward, but in other cases, this discussion was not
possible. Observing the teacher was one of several options for a particular assignment, and all but two of the participants (Alex and Jayne) chose
to observe the teacher, Patti Huberty.
Ms. Huberty had been identified as an exemplary mathematics teacher
by university faculty and by fellow teachers in the school district. (See
Mewborn, 1998, Mewborn & Huberty, 1999 for a description of this
teacher’s practice.) The purpose of having the preservice teachers
observe Ms. Huberty was to offer them an example of how the things they
were learning in their mathematics methods course and with their
Barrow Buddies might be implemented with a full classroom of diverse
learners. The specific assignment that was given to the preservice teachers was to observe a lesson and write a 500-word paper about the
teacher’s actions, the students’ learning, and the connections between
the two.
While reflecting on Ms. Huberty’s lesson, Jennifer wrote, “The entire
lesson was filled with questions for the students, [Ms. Huberty] was constantly asking about [the students’] thought processes, their ideas, and
even their behavior.” Jennifer made a connection to student behavior by
noting, “The classroom environment seemed so student-centered and
productive that there was very little need for discipline.”
Observing Ms. Huberty teach demonstrated to Laura how the teacher
can use the thinking and actions of the children to develop the mathematics lesson:
I was shocked by how little [Ms. Huberty] said while the children
were trying to decide what to do. I’m sure I would have jumped
Learning to Teach as Assisted Performance 1479
in there and tried to give them a hint and ruined the whole
process!
Because Laura was struggling with her role as a teacher in her BB field
experience, the observation of Ms. Huberty seemed to reinforce her selfawareness. Furthermore, Laura had an opportunity to see the rich thinking of which children are capable—something that she did not experience much with her Barrow Buddy because she fluctuated between
telling her what to do and telling her nothing. Laura noted: “The depth
and clarity of the children’s explanations [in Ms. Huberty’s class] were
amazing! . . . Without her explaining much, they picked up the concepts
and basically taught one another.” Laura explicitly contrasted Ms.
Huberty’s teaching with her own: “I benefited from watching [Ms.
Huberty teach] because I have a bad habit of leading students…to the
answer I’m thinking of, and I may be stifling their own ideas.”
Heather remarked she was impressed by how “Ms. Huberty took the
time to call on every student, even if the first person gave the correct
answer.” Heather believed the communication between Ms. Huberty and
the students “allowed Ms. Huberty to understand where the students
were coming from, and it encouraged the students to participate.”
Similarly, Shelly noted the value of listening to children’s ideas. She said
that during Ms. Huberty’s lesson, children “were able to learn about measurement from each other’s responses and mistakes.” She further
explained that the questions Ms. Huberty asked encouraged the children
to “use their common sense and reasoning skills” to arrive at answers.
Feiman-Nemser (2001) suggested that studying the ways in which different teachers work toward the same goal could help preservice teachers develop the tools to study teaching. In this case, the preservice teachers were able to compare and contrast their own teaching of one child
with Ms. Huberty’s teaching in a classroom setting. In fact, several of the
preservice teachers drew explicit connections between their teaching or
beliefs and what they observed in Ms. Huberty’s classroom. Also interesting to note is the fact that approximately half of the preservice teachers’
comments in their write-ups about their observation of Ms. Huberty pertained to the teacher’s actions while the other half pertained to student
learning. This balance of attention suggests that the preservice teachers
were beginning to appreciate the synergistic relationship between
teacher actions and student learning.
We view the observation of Ms. Huberty as an example of assisted performance because the preservice teachers were assisted in developing
and articulating their ideas about the role of the teacher. They were
not yet capable of explicating the relationship between teaching and
1480 Teachers College Record
learning on their own because of their limited teaching experiences and
observations. The assistance in this case came from the experienced
teacher, who was carefully selected, and from the students in the classes
that were observed. The observation and the assignment that went with
it were carefully structured by the instructor to facilitate this kind of
assisted performance. This course task is certainly a less robust type of
assisted performance than the two examples noted earlier, but it is,
nonetheless, suggestive of the ways in which preservice teachers can
stretch their thinking with assistance.
DISCUSSION
The three components of the mathematics methods course illustrated—
reading the Paley chapter, the Barrow Buddy field experience, and
observing an experienced teacher—supported the preservice teachers’
learning about children’s mathematical thinking, which was the central
focus of the course. The Paley chapter gave the future teachers an opportunity to read about children’s thinking, while the Barrow Buddy field
experience gave them a chance to experiment with eliciting children’s
mathematical thinking. Observing Ms. Huberty enabled the preservice
teachers to extend these experiences by seeing what it might look like for
a teacher to orchestrate a classroom so as to build instruction on children’s mathematical thinking. These three components dovetail with
three of the central tasks of teaching advocated by Feiman-Nemser
(2001)—analyzing beliefs and forming new visions, developing understandings of learners and learning, and developing the tools to study
teaching.
We believe that these three course components provide images of what
assisted performance might look like in a preservice methods course.
Although Feiman-Nemser (2001) used “performance” to mean tasks of
teaching such as planning and lesson implementation, we have expanded
the notion of performance to include such things as analyzing one’s own
teaching and that of others. In different ways, each of the course components helped preservice teachers do something that they were not ready
to do on their own when they started the program. The assistance part of
assisted performance came from a variety of sources. In reading and
reflecting on the Paley chapter, the assistance came mostly from peers
and somewhat from the instructor. In the Barrow Buddy field experience, the assistance came from the children and the instructor. And in
the teacher observation, the assistance came from the experienced
teacher and the children.
Feiman-Nemser (2001) reviewed case studies of teacher education
Learning to Teach as Assisted Performance 1481
programs from the report of the National Commission on Teaching and
America’s Future (1996) to identify promising practices in teacher education that may lead to preparation of teacher candidates who are able to
meet the challenges of the reform agenda. The three promising practices
identified by Feiman-Nemser are the conceptual coherence of the program; the use of purposeful, integrated field experiences; and attention
to teachers as learners. We believe that the mathematics methods course
we described provides an example of these ideas.
Although Feiman-Nemser’s quest is for entire teacher education programs that have a salient conceptual frame, it is logical to start at the level
of individual courses and ask what it would mean for a single course to be
conceptually coherent. We have described components of the course
that, we believe, show evidence of a conceptually coherent approach to
elementary mathematics teacher education. The course had a clear focus
on children’s mathematical thinking, and course activities were designed
with this goal in mind. Furthermore, the goal of the course was explicitly
stated in the syllabus and by the instructor on numerous occasions.
Preservice teachers also had repeated opportunities to articulate their
emerging understanding of the course goal throughout the semester.
The Barrow Buddy field experience is an example of a purposeful, integrated field experience. The field experience had a clear purpose that
was linked to the on-campus course: To provide preservice teachers with
an opportunity to learn to elicit and respond to children’s mathematical
thinking. The Barrow Buddy field experience was also integrated with
the coursework in that the instructor and assistants were actively present
in the field, using it as an extended instructional site, and the subsequent
class period on campus reflected events that happened in the schools.
The instructor of the course had an explicit commitment to viewing
preservice teachers as learners. She assumed that preservice teachers,
like children, had well-reasoned explanations behind the ideas they
brought with them to their mathematics methods courses. Thus, class sessions often included questions posed by the instructor, multiple answers
from students, followed by in-depth discussions of those answers. Rather
than dismissing preservice teachers’ prior experiences as simply leading
them toward more traditional views and practices of teaching, the
instructor used the aforementioned components of the course to help
preservice teachers examine the knowledge and beliefs that they brought
to the teacher education setting. Furthermore, class activities, such as the
Barrow Buddy field experience, provided preservice teachers with opportunities to engage in assisted performance—to do with help what they
were not yet ready to do on their own.
1482 Teachers College Record
IMPLICATIONS AND CONCLUSIONS
In this section, we consider further what it might mean to pay attention
to teachers as learners and to view teacher education as an opportunity
for assisted performance. To do so, we challenge some of the prevailing
practices in teacher education that are linked to an apprenticeship
model of learning to teach.
We echo Feiman-Nemser’s (2001) concern that instructors of both
content and methods courses often feel pressured to “cover” the curriculum so that future teachers will be prepared to teach any topic they may
encounter. Recognizing that it is not possible to provide preservice teachers with content knowledge, activities, and connections between every
important topic at every grade level, we generally confine ourselves to the
“big ideas,” which in elementary mathematics education typically include
such things as prenumber work, place value, the four basic operations
with whole and rational numbers, geometry, measurement, and data
analysis. As with K–12 teachers, there is an ever-increasing pressure to put
more and more content into this curriculum; the latest push is for algebraic thinking at the elementary level. What would it mean to free ourselves from any sense of having to cover the curriculum? What might a
course look like if it was not organized by content topics but instead by
aspects of teaching (such as planning and assessment) or processes in
which we want students to engage (such as conjecturing and generalizing) or by some other categorization and used examples from content to
illustrate these organizing ideas? Again, a look at what we want preservice
teachers to do while they are with us is in order. Do we want them to practice the things they will be doing when they leave us, or do we want them
to take advantage of the support they have from us in order to engage in
challenging tasks for which they may not have the resources to engage
after they leave us? How do we assist them in performing these tasks?
A second area to question is the tasks in which we typically engage preservice teachers. This questioning logically connects to the prior notion
of the goals and topics around which our courses revolve. For example,
if a central course goal is for future teachers to understand the link
between instruction and assessment, what kinds of tasks would we provide for them? What kinds of tasks would qualify as assisted performance
in this arena? A first step would be to consider the purpose of the myriad
typical tasks in which we engage preservice teachers, such as finding or
writing activities, lesson plans, and unit plans; writing reflections; critiquing textbooks; and peer teaching or microteaching.
Field experiences provide a rich ground for questioning why we do the
things we do and how we might do them differently if we are serving the
Learning to Teach as Assisted Performance 1483
goal of creating opportunities for preservice teachers to engage in
assisted performances. For example, we might investigate such practices
as only assigning one preservice teacher to one mentor teacher, using
only experienced teachers as mentor teachers, and staying with the same
mentor teacher for an extended period of time. We might investigate the
affordances and limitations of a field experience that is conducted for
full days during a 1-month block in comparison to weekly field experience on Tuesday and Thursday mornings. Beyond the configuration of
field experiences, we could also question the tasks in which preservice
teachers engage in the field, such as observation, teaching small groups,
and teaching the whole class. We might look to co-teaching (with peers
or with mentor teachers or with university faculty) as a form of assisted
performance. We might consider having preservice teachers co-teach different subjects with different teachers because not all teachers are equally
strong in all content areas. Or we might consider having a preservice
teacher observe and co-teach with several different teachers—all in one
subject area. Co-planning is another avenue for assisted performance. A
mentor teacher and preservice teacher might co-plan a lesson that is
then implemented by the mentor teacher. Or a university supervisor and
a preservice teacher might co-plan a lesson that is implemented by the
preservice teacher with support from the university supervisor.
We might also question the role of the university supervisor in field
experiences. The role is typically one of evaluation and supervision. But
if field experiences are an opportunity for assisted performance, we
could consider the possibility that an observation is not a chance to sink
or swim but a chance to be coached. Similar to our description of the
Barrow Buddy experience, the mentor teacher and/or university supervisor might intervene in a lesson to ask a question that better reveals student thinking, to offer a management suggestion, or to make a connection to the previous day’s lesson. Rather than teaching entire lessons, preservice teachers might teach portions of lessons, such as the introduction
and connection to yesterday’s lesson or the main body of the lesson, or
the summary and wrap-up of the topic. On a grander scale, we might ask
why we have a semester devoted to student teaching. Is the typical 2
weeks of “solo teaching” a sacred cow whose time has come for reconsideration?
Freeing ourselves from the idea that teacher preparation is just that—
preparation for the future in the form of practice—and opening ourselves to the idea that teacher education is about structuring learning
opportunities for future teachers, using the same principles we use to
design educational opportunities for children, provides a wide variety of
interesting avenues for future scholarly work. The unarticulated and
1484 Teachers College Record
untested assumption within the idea of assisted performance, however, is
that somehow the teachers will be able to “pull it all together” when they
leave us in order to do the things that teachers do. Feiman-Nemser
(2001) takes the next step in her article by suggesting what the central
tasks of the induction years and professional development are and identifying key features of successful programs. Similarly, we plan to follow
the participants in this study in order to develop robust descriptions of
their learning trajectories and to ascertain the staying power of the teaching practices they began to develop with assistance in their preservice
program.
Notes
1 We use the terms “personal theories” and “beliefs” interchangeably throughout the
manuscript. The term “beliefs” is not well defined in the mathematics education literature
and often encompasses the additional elements included in Tann’s (1993) definition.
2 I (first author) made a deliberate pedagogical decision to have the students write their
commentaries after the class discussion rather than before it. I wanted the students to hear
their peers’ reactions to the chapter and to have an opportunity to articulate their own
views before writing the commentary. I believe that the commentary had a more reflective
nature to it because of this sequence.
3 See Mewborn, 2000 for more details about this field experience.
References
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DENISE S. MEWBORN is a Professor of Mathematics Education and
Head of the Department of Mathematics and Science Education at the
University of Georgia where she teaches mathematics methods courses
for prospective elementary school teachers. Her research interests
include how preservice teachers make sense of classroom events, how
teaching practice develops across time, and teachers’ beliefs. She is a coauthor of “Research on teaching mathematics: The unsolved problem of
teachers’ mathematical knowledge,” which appeared in the Fourth
Handbook of Research on Teaching. She is also serving as the series editor for
the four-volume series title Teachers Engaged in Research: Inquiry into
Mathematics, which is to be published by the National Council of Teachers
of Mathematics and InfoAge Publishing in 2006.
Learning to Teach as Assisted Performance 1487
DAVID W. STINSON is an Assistant Professor of Mathematics Education
at Georgia State University. His research interests are examining how
mathematics teachers incorporate the philosophical and theoretical
underpinnings of postmodern critical theory into their education
philosophies and classroom practices and how students who are constructed outside the White, Christian, heterosexual male of bourgeois
privilege successfully accommodate, resist, or reconfigure the hegemonic
discourses of schooling, and of society generally. He is the author of
“Mathematics as ‘Gatekeeper’?: Three Theoretical Perspectives that Aim
Toward Empowering All Children with a Key to the Gate.” This essay,
after verifying mathematics as a gatekeeper, explores the empowering
tenets of the situated, culturally relevant, and critical theoretical perspectives on the teaching and learning of mathematics.