CHANGING BELIEFS
AND TEACHING PRACTICES: AN ILLUSTRATION OF A REFLECTIVE CONNECTIONIST
Denise S. Mewborn
University of Georgia
dmewborn@coe.uga.edu
Abstract: Carrie entered her preservice elementary
teacher education program professing a strong dislike for mathematics and a
desire to avoid teaching the subject.
Her beliefs about mathematics were in strong contradiction to her more
general beliefs about teaching and learning.
As a result of a field experience in which she observed an exemplary
mathematics teacher, Carrie was able to modify some of her beliefs about
mathematics and to craft her mathematics teaching practices to be consistent
with her beliefs about teaching and learning.
Theoretical work from the beliefs literature is used to explain how Carrie
was able to change her beliefs and actions.
In particular, the notion of a reflective connectionist, proposed by
Cooney, Shealy, and Arvold (1998) is elaborated.
The literature abounds with examples of preservice and
inservice mathematics teachers who hold less than desirable beliefs about
mathematics and who, despite a teacher education course or inservice
experience, fail to show evidence of substantial change in their beliefs. In this article, I present a preservice
teacher, Carrie, who showed evidence of some dramatic changes in her beliefs in
a relatively short period of time. I
contend that Carrie is an example of reflective connectionist as described by
Cooney, Shealy, and Arvold (1998), and I elaborate on what it might mean to be
a reflective connectionist.
Theoretical
Framework
Cooney et al. (1998) presented the case of a preservice secondary mathematics teacher who held a coherent set of beliefs about teaching mathematics and who modified his beliefs in the face of new experiences. They characterized the teacher as a reflective connectionist because he was able to mold his beliefs based on a careful analysis of the views of others (such as mentor teachers, peers, teacher educators). Because he engaged in this type of analysis, he was very committed to his beliefs and seemed inclined to act on those beliefs in the classroom. To amplify the notion of a reflective connectionist, I drew on the work of Green (1971) and Raths, Harmin and Simon (1987, as cited in Seah & Bishop, 2000). I propose that a reflective connectionist holds what Green termed an ideal belief system and goes through a process described by Raths et al. as valuation.
Green contended that the purpose of teaching is to modify not only the content but also the structure of students’ belief systems. He argued that the goal of teaching should be to help students develop belief systems in which “the number of core beliefs and belief clusters are [sic] minimized, the number of evidential beliefs are [sic] maximized, and the quasi-logical order of ... beliefs is made to correspond as closely as possible to their objective logical order” (p. 52). For a thorough description of each of these characteristics, see Green (1971).
Raths, Harmin and Simon (1987, as cited in Seah & Bishop, 2000) proposed that attitudes, beliefs, and interests go through a process of valuation in order to become part of one’s system of operating. They suggested that one must choose freely from among alternatives after careful consideration of the consequences of each alternative, that one must cherish one’s beliefs and affirm them to others, and that one must act in concert with one’s choices repeatedly to form a pattern in one’s life.
Methods
Data Collection
Carrie was one of four preservice teachers that I studied during a field-based mathematics methods course. Carrie and her peers were placed in a fourth-grade classroom with a teacher that was locally recognized as an exemplary mathematics teacher who was committed to teaching in a manner consistent with current reform recommendations. Data collected during this study included two individual interviews, Carrie’s journal, four audiotapes of Carrie conducting task-based interviews with individual children, three audiotapes of Carrie teaching mathematics to a small group, one videotape of her teaching a small group, field notes on eight observations of the classroom teacher, and audiotapes and field notes from eight discussions among the four preservice teachers, the mentor teacher, and me. See Mewborn (1999) for more details of the study. I kept anecdotal records of informal conversations with Carrie during the first two years of her teaching career, and I conducted a study of her teaching during the third year. Data from this study included weekly classroom observations, two individual interviews, and classroom artifacts such as lesson plans, classroom displays, and student work.
The data were analyzed from the perspective of the interpretive paradigm for teacher socialization (Zeichner & Gore, 1990) in an attempt to understand the nature of a social setting at the level of subjective experience. I hoped to gain an understanding of mathematics teaching and learning from Carrie’s perspective. The data were analyzed using the methods of grounded theory (Glaser & Strauss, 1967) and grounded interpretivism (Addison, 1989). Grounded theory and interpretive research methods are both constant comparative methods that emphasize the importance of context and social structure in research settings.
A Portrait of Carrie
Carrie’s
beliefs about teaching and learning were tightly clustered around her core
belief that teachers should treat children with love, compassion, and
respect. She believed that school
should be a place where children interact with adults who love and care about
them as human beings, and she saw school as a place that could rectify the
unpleasantness in some children’s lives.
From the beginning of her teacher education program Carrie exhibited a
strong care ethic and demonstrated concern for the societal and family
situations that impact negatively on children’s lives. Her core belief was held with passionate
conviction and formed a central aspect of who Carrie was as a person and a
teacher. She held beliefs about
students, learning, and teaching that were derived from her primary belief
about respecting children.
With regard to students, Carrie believed that children must have confidence in themselves as learners if they are to be successful in school and in life. She believed that learning is a process of understanding, not a means to a correct answer, and she believed that teachers should be role models for their students. These beliefs and her core belief about respecting students were all logically related and tightly clustered. Carrie’s beliefs were organized in a manner consistent with Green’s (1971) description of an ideal belief system.
However, as a preservice teacher Carrie held a cluster of beliefs about mathematics as a discipline, about herself as a learner of mathematics, and about herself as a teacher of mathematics that was in sharp contradiction to her general teaching and learning belief cluster. Carrie disliked mathematics and did not see herself as a competent mathematics student, despite earning good grades in four years of college preparatory mathematics in high school. Carrie did not see mathematics as engaging, interesting, logical, or meaningful. She described mathematics as “alphabet soup with numbers” and “a headache that won’t go away.” For her, learning mathematics was like “putting a puzzle together and finding one piece is missing.” Carrie’s experiences and beliefs about mathematics conflicted with her beliefs about teaching and learning, in general, and her belief that a teacher is a role model, in particular. This conflict was a significant source of concern for her because she knew that she was not able to model excitement and enthusiasm for learning mathematics. She did not want her students to have the same types of mathematical experiences that she had, so she was very concerned about her ability to teach mathematics.
Carrie’s initial reaction to this conflict was to say that she did not want to teach mathematics because she did not want to do a disservice to students. However, she soon realized that this was not a realistic solution as most elementary teachers are expected to teach mathematics. From this point forward, Carrie displayed a genuine desire to learn about teaching mathematics in a way that would help her overcome her negative experiences and enable her to be a competent teacher. She was open, willing, and eager to learn. In her first interview, Carrie said, “That’s why I volunteered for this study, because I want to see someone who really loves math teach it so that maybe I can see math differently.”
During the initial study, Carried was involved in a field experience in which she worked with a skilled mathematics teacher, and she saw that it was possible for students to experience mathematics as a dynamic, creative, fun, interesting discipline with opportunities for individual exploration and interpretation. At the end of the field experience Carrie said she had learned that “teaching math is nothing more than exploring math with your students. I’ve learned that ‘wrong answers’ are such a gift in the classroom because they open the doors for so much more understanding and exploration of math.” As a result of this experience, she was able to shape her mathematics teaching practice to be consistent with her other beliefs.
For example,
Carrie manifested her belief in children’s need for self-confidence by placing
a lot of emphasis on children’s mathematical thinking. She took every opportunity to praise and
reward children for their thinking.
Carrie thought it was important to find something of value in each
child’s thinking, regardless of the correctness of the response. She manifested her belief in learning as a
process by insisting that children explain their answers and by seeking and
rewarding multiple solution strategies.
She enacted her belief that a teacher is a role model by revealing her
mathematical thinking to students. She
also believed that it was important to “be human” and admit to making errors or
admit to not knowing all of the answers.
Discussion
The structure of Carrie’s belief system enabled her to change her actions and beliefs. She held one core belief about respecting children and held it with passionate conviction so that it was necessary for her to resolve any beliefs that conflicted with this core belief. She had a minimum number of belief clusters, and she was able to find a way to connect some of her beliefs about mathematics to her core belief cluster. All of her beliefs were held evidentially, which allowed her to modify beliefs in the face of new evidence. In particular, Carrie’s beliefs about mathematics were held evidentially because they were based on her experiences as a learner. Thus, when she saw evidence, in the form of her mentor teacher, that mathematics could be taught differently, she was able to use this evidence to modify her beliefs about mathematics. Then she was able to fold her belief cluster about mathematics into the cluster about teaching and learning, thus minimizing the conflict she had previously experienced.
The process by which Carrie altered her actions and beliefs is consistent with the description given by Cooney et al. (1998) and Raths et al. (1987, as cited in Seah & Bishop, 2000). A key element of the process proposed by both sets of authors is the notion of choice. Carrie deliberately chose her teaching actions from among alternatives presented by her past experience and her teacher education program (particularly the field experience). She was able to integrate her experiences as a learner with her experiences in her teacher education program, analyze the merits of various positions and shape her mathematics teaching practice to be consistent with her general beliefs cluster. During this process she also changed some of her beliefs about mathematics. She cherished her core belief, so she was able to become committed to beliefs that were consistent with that belief. Specifically, she was able to act consistently on beliefs within her core cluster, including her new beliefs about how mathematics should be taught.
The extent to which Carrie changed her beliefs about mathematics as a discipline and herself as a learner of mathematics is still an open question. She certainly changed her actions as a mathematics teacher, and it is plausible that she changed her beliefs about mathematics teaching. However, there is no evidence that Carrie now sees mathematics (beyond school mathematics) as a dynamic, meaningful, sensible discipline or that she sees herself as a competent learner of mathematics. It seems likely that because she was able to act as a mathematics teacher in a manner consistent with her beliefs about teaching and learning, she gave herself license to lock away her other beliefs about mathematics because they were no longer a source of conflict for her. This explanation resonates with Guskey's (1986) proposal that change in action precedes change in belief, a proposal that is worthy of further exploration by the mathematics teacher education community.
References
Addison, R. B. (1989). Grounded interpretive research: an investigation of physician socialization. In M. J. Packer, & R. B. Addison (Eds.), Entering the circle: Hermeneutic investigation in psychology (pp. 39-57). Albany: State University of New York Press.
Cooney, T. J., Shealy, B. E., & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29, 306-333.
Glaser, B. C. & Strauss, A. L. (1967). The discovery of grounded theory: Stategies for qualitative research. New York: Aldine.
Green, T. F. (1971).
The activities of teaching. New York: McGraw-Hill.
Guskey, T. R. (1986).
Staff development and the process of teacher change. Educational
Researcher, 15(5), 5-12.