Considering the Paradoxes, Perils, and Purposes of Conceptualizing Teacher Development

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CONSIDERING THE PARADOXES, PERILS, AND PURPOSES OF CONCEPTUALIZING TEACHER DEVELOPMENT

by

Thomas J. Cooney

University of Georgia

The business of teacher education has many purposes. On the one hand, teacher educators are expected to educate teachers who can survive if not thrive in today’s classrooms with all the complexity and turbulence that entails. As such, the task is essentially one of promoting the status quo, keeping society and education on an even keel. Witness the large amounts of time spent on acclimating preservice teachers to the conditions of the schools and of life in the classroom. Further, the school-based components of teacher education programs are the most popular among the participant preservice teachers. It is also the component of teacher education that has the most validity among those who create policies that impact teacher education. On the other hand, teacher educators are expected to educate teachers so that they can become reformers of the teaching of mathematics. Usually this reform has its roots in a more process-oriented instructional style in which considerable emphasis is placed on conceptual understanding and problem solving. This polarization of perspectives provides a sort of continuum on which most teacher education programs fall.

With respect to inservice teacher education, the scene is somewhat different in that familiarity of the classroom is assumed, a familiarity that can be a double-edged sword. Familiarity helps provide continuity with professional development programs but it can also narrow the vision of what might be. Myopia is not a friend of reform. Teacher educators and teachers live in different worlds. In some sense, the role of the teacher educator is to reveal and make evident the complexity of teaching and then propose alternatives for dealing with that complexity. Teachers, on the other hand, live in a very practical world. They do not have the luxury, nor the resources, to experiment, to fantasize a different school environment. Indeed, in most schools, the teacher’s job is to stay within certain boundaries, boundaries that are determined by school authorities who have the power to hire and fire. Reform becomes an issue to those outside the field of mathematics education when it is perceived that reform could alter the status quo. Today’s students and tomorrow’s workers need problem-solving skills and a flexibility of thinking that allow for changing conditions in an ever increasingly technologically oriented society. But just as often, the pendulum swings the other way in that the time-honored basics are seen as the cure that solves educational ills. Witness the back-to-basic movements in the United States during the 1970s and the 1980s and the strong emphasis on basic skills that is not far below the surface in most school programs today. It was out of this concern for basic skills and accountability that led education to the notion of competency based education in which objectives detailing pedagogical skills were as prevalent in teacher education as was skill development in school programs.

For preservice teachers, reform is more of an intellectual exercise in which they have the opportunity to grapple with interesting problems. The risk is very low for they will learn the real art of teaching during student teaching. For the inservice teacher there is considerable peril. Teachers, like the rest of us, strive to make sense of their lives and to find a comfort level that allows them to function in a reasonably orderly fashion. But reform is not always consistent with order as problems and perturbations, both essential components of reform-oriented teaching, often promote uncertainties in the teaching process. The question then becomes one of how much uncertainty teachers or students, both operating under an assumed didactical contract, can reasonably tolerate. The clever teacher educator is the one who envisions a different world of teaching but does so in a manner that honors the existing world of the teacher. Similarly, the clever teacher is the one who envisions a different world and searches for ways to realize that world within the usual classroom constraints. In some sense, we might think of teacher education as the process by which we develop clever teachers so defined.

Perhaps it is the case that reform is not for everyone, albeit we seldom talk or act that way for fear of sounding like elitists. But reform can be conceived in another way, one that sees reform as a form of liberation rather than as a movement toward something perceived to be better. This paper is about conceiving teacher development as a personal journey from a static world to one in which exploration and reflection are the norm. I will begin by considering the notion of teacher change.

Examining the Notion of Teacher Change and Its Moral Implications

The obvious question associated with the notion of teacher change is, “Change from what to what?” That is, what compass defines change? Often discussions about reform become polarized in the sense that traditional teaching is contrasted with reform-oriented teaching. But what is it that constitutes traditional teaching? Typically, traditional teaching is equated with telling which—as some assume--leads to rote learning with a heavy reliance on memorization. Although this view has considerable currency in the literature, it is not commonplace among teachers. I have never met a teacher who believed that he/she was teaching for rote learning. Teachers talk of enabling their students to solve problems and develop reasoning skills. Nevertheless, the evidence clearly shows that lecture is the dominant means of teaching in most school settings. Davis (1997) found that teachers’ views of their own teaching were not dramatically different from positions reflected in the NCTM Standards. Yet, observations of their teaching revealed a heavy reliance on telling and lecturing. This discrepancy results, no doubt, from a difference as to what constitutes meaningful learning. Teachers live in a practical and parochial world as they are necessarily commissioned to deal with specific students in specific classrooms in a specific cultural setting. For most teachers, order is important—both in the sense of order from a management perspective and from an intellectual perspective. It is no accident that teachers often use the words “step-by-step” to describe their teaching of mathematics, a connotation that necessarily evokes procedural knowledge. Such an orientation is the frame in which their professional lives exist.

If traditional teaching refers to what teachers traditionally do in some normative sense, then a case can be made that traditional teaching involves a kind of teaching in which the teacher informs students about mathematics through the primary scheme of telling and showing. Knowledge is presented in final form. What kind of learning results from this, meaningful or otherwise, is an empirical question not a definitional one. Traditional teaching, so conceived, allows us to consider a different kind of teaching, one which involves less telling and showing and more creating mathematical communities in which process and communication transcend product. We can call this kind of teaching reform teaching, and we can conceive of teacher change as moving from the traditional mode to the reform mode. Again, it remains an empirical question as to what kind of learning results from this kind of change although educators frequently speculate that students become more conceptual and adept at solving problems. Although I acknowledge the legitimacy of the empirical nature of connecting learning outcomes to any kind of teaching, I suggest that there remains a philosophical perspective that suggests a reform-oriented classroom is more consistent with the kind of society most of us would embrace. I do so under the assumption that the teaching of mathematics, or any subject for that matter, is ultimately a moral undertaking.

The Moral Dimension of Reform Teaching

The history of teacher change has many roots and can often be traced to scholars who see education in its broadest sense. Dewey (1916), for example, examined the purpose of education in a democratic society. His use of the word transmission might seem limited when he writes, “Society exists through a process of transmission quite as much as biological life. This transmission occurs by means of communication of habits of doing, thinking, and feeling from the older to the younger” (p. 3). But we see a much deeper meaning of transmission when he continues, “Society not only continues to exist by transmission, by communication, but it may fairly be said to exist in communication (emphasis in original)” (p. 4). Dewey’s emphasis on reflective activity is one of the hallmarks of his philosophy of education. We begin to sense the immense complexity of Dewey’s ideas when he defines education as the “reconstruction or reorganization of experience which adds to the meaning of experience, and which increases ability to direct the course of subsequent experience” (p. 76). Later he adds, “The other side of an educative experience is an added power of subsequent direction or control. To say that one knows what he is about or can intend certain consequences, is to say, of course, that he can better anticipate what is going to happen; that he can, therefore, get ready to prepare in advance so as to secure beneficial consequences and avert undesirable ones” (p. 77).

From Dewey’s perspective (1916), “Democracy cannot flourish where the influences in selecting subject matter of instruction are utilitarian ends narrowly conceived for the masses, and, for the higher education of the few, the traditions of a specialized cultivated class. The notion that the ‘essentials’ of elementary education are the three R’s mechanically treated, is based upon ignorance of the essentials needed for realization of democratic ideals” (p. 192). When education is seen as the backbone of democracy, education takes on a certain moral dimension. Moral education, according to Dewey, involves providing the means by which the educated can best control their own destiny and that of society. We often mistake, I believe, moral education as prescriptions of the sort “Johnnie be good,” rather than the fusion of knowledge and conduct in which the former informs the latter.

From this perspective, Green’s (1971) distinction between indoctrination and teaching seems quite relevant. Both seek to inform but only the latter informs with evidence. We must keep in mind that the teaching of mathematics, or any subject for that matter, educates the learner in two ways. First, it provides the learner with access to what Schön (1983) called technical knowledge. Second, the learning process is also a learning outcome whether that outcome is learning by reasoning or learning by imitation. Although we might not feel comfortable thinking about the teaching of mathematics as indoctrination, the reality is that this is exactly the kind of teaching we often criticize and characterize as traditional teaching.

Ball and Wilson (1996) echoed Dewey when they conclude, with respect to teaching, that the intellectual and the moral are inseparable. In what sense are the intellectual and the moral inseparable? Because of its inherent abstractness and certainty, mathematics is often seen as the sine qua non of ammorality. But we can ask the question of what makes any subject moral, immoral, or amoral. Given the often perceived ammorality of mathematics, the leap is often taken that its teaching, then, is largely an ammoral activity as well. But if examine the question of what it means to know, then we have a different slant that suggests the teaching of any content area is subject to the question of whether or not it is a moral activity. The issue centers on what kind of evidence supports one’s knowing. The presence of evidence is what fuses the intellectual and the moral.

What is our rationale for teaching functions, congruence, or literary classics? The answer lies not in the information itself, although that is not inconsequential, but in the underlying reasoning processes that allow students to make connections and reasoned judgments. Those reasoning processes are what distinguish knowledge from information. A student may know the Quadratic Equation in the sense of being able to apply it in given and predetermined setting. But it would seem strange to say that a student knows the Quadratic Equation if he/she has no idea how it is developed or in what contexts it can be used. Information is not to be confused with knowledge.

Rokeach (1960) used the term closed mind to describe situations in which what one knows or believes is based on other beliefs that are impermeable to change. Green (1971) called beliefs that are impermeable to conflicting evidence nonevidentially held beliefs. These two constructs are closely related and speak directly to the importance of students having experiences with processing different kinds of evidence. The encouragement of students to acquire information in the absence of evidence and reasoning is not what I would call a moral activity. The challenge, then, becomes one of educating teachers so that they can provide contexts for students to experience the processing of evidence. Professional development, then, can be conceived of the ability of the teacher to promote such experiences and to engage students in the kind of reasoning that reflects the essence of most reform movements in mathematics education.

There is a certain moral dilemma associated with acknowledging a student’s reasoning process when, in fact, that process leads to a mathematically incorrect statement. Ball and Wilson (1996) addressed this point. Teachers are usually reluctant to honor such reasoning processes particularly if they hold a product-oriented view of teaching and learning. Therein lies the dilemma. If only those reasoning processes that lead to correct results are appreciated, then, in some sense, process and product become fused and inseparable. If teaching is viewed from a constructivist perspective in which teaching is based on students’ mathematical understanding wherein that understanding and the so-called curriculum are one and the same, then there is no dilemma because there is no absolute to which understanding can be compared. Most teachers feel uncomfortable with this perspective if for no other reason than the curriculum becomes entirely problematic. Indeed, few classrooms are organized from a constructivist perspective. Witness, for example, teachers’ emphasis on objective tests and the paucity of alternative assessment items on those tests (Cooney, Badger, & Wilson, 1993; Senk, Beckmann, & Thompson, 1997).

A related issue is what students learn to value. Glasser (1990) observed that students’ responses to the question, “Where in school do you feel important?” inevitably evokes responses that entail extracurricular activities such as sports, music, or drama; rarely mentioned are experiences with academic subjects. Glasser’s observation paints a rather bleak picture that captures the failure of the classroom to create an intellectual community in which students are honored as much for their thinking as for their doing. Unfortunately, I suspect his conclusions are not specific to any particular school or subject. This, again, suggests that students fail to see their reasoning processes honored as an intellectual activity in and of itself.

The Notion of Good Teaching

What circumstances lead to a product-oriented view of teaching? Teachers often see themselves as wanting to provide an environment free of anxiety, one in which fear of the subject is neutralized or at least minimized. Cooney, Wilson, Chauvot, and Albright (1998) found that teachers’ beliefs about teaching often center on the notion of caring and telling. One preservice teacher, Brenda, wrote in a journal entry, “A good mathematics teacher explains material as clearly as possible and encourages his students to ask questions.” When preservice teachers are asked to select an analogy that best represents teaching (choices consist of newscaster, missionary, social worker, orchestra conductor, gardener, entertainer, physician, coach, and engineer), a popular choice is coach because a coach must establish fundamentals, show, cheer on, and explain. Another popular choice is gardener because gardeners nurture, provide support, and facilitate growth. When preservice teachers are asked what famous person they would like to be as a teacher of mathematics, a fairly common response is the identification of a comedian. The rationale they provide is based on the assumption that mathematics itself is a rather dry subject and hence it takes a special personality to make it interesting. These and other metaphorical descriptions reveal the various forms that telling and caring take. What these descriptions do not suggest is a kind of teaching in which students grapple with problematic situations or engage questions of context and what might be. If we think of mathematics as the science of creating order out of chaos or as pattern recognition as suggested by Steen (1988), then it follows that a reductionist view of mathematics is inappropriate.

I recall a conversation with one of my advisees that went something like this.

TC: How is this term going?

ST: My math professor is great this term.

TC: Wonderful. Why is he great?

ST: He is clear. He goes at a reasonable pace. He answers our questions.

This exchange conveys something about what this student considers good teaching to be, viz., be clear and present material at the students’ level. The anecdote is consistent with the way preservice teachers speak of coach, gardener, and other metaphorical selections. As laudable as being clear and teaching at the students’ level may be, they hardly constitute the kind of process or reform-oriented teaching advocated in most teacher education programs.