The recent past has seen an increasing frequency of calls for teachers to implement "evidence-based" practices (Davies, 1999; U.S. Department of Education, 2002). At the same time, it has been noted that teachers see research as largely irrelevant to practice (Lester & William, 2002; Steen, 1999). If one accepts the premise that research holds value for educational practice (Margolinas, 1998; NCTM Research Committee, 2006; Silver, 1990), it is important for teacher educators to develop instructional experiences that bring teachers into the discourse surrounding educational research. At the present time, communities of teachers and researchers are often largely separated by communication-related barriers (Sowder, 2000; Silver, 2003).
Lesh and Lovitts (2000) observed the following about the relationship between research and practice:
In mathematics and science education, the flow of information
between researchers and practitioners is not the kind of one-way
process that is suggested by such terms as information
dissemination. Instead, to be effective, the flow of information
usually must be cyclic, iterative, and interactive (p. 53).
An implication of this statement is that a "transmission" view of familiarizing teachers with research is naive, just as mathematical pedagogy based on such a view is misguided (Kline, 1977). Lesh and Lovitts (2000) went on to state, "Although simpleminded, 'delivery-and-reception' metaphors are recognized widely now as being inappropriate for describing the development of students, teachers, or other complex systems, these same machine-based metaphors continue to be applied to the development of programs of instruction" (p. 57).
Teachers' Conversations as Complex Systems
Complexity science provides a framework for designing and analyzing the types of complex systems for the development of teachers mentioned by Lesh and Lovitts (2000). Davis and Simmt (2003) provided a discussion of the implications of complexity science for mathematics education. They defined complex phenomena in the following manner:
First, each of these phenomena is adaptive. That is, a complex
system can change its own structure ... Second, a complex phenomenon
is emergent, meaning that it is composed of and arises in the
complicated activities of individual agents. In effect, a complex
system is not just the sum of its parts, but the product of the
parts and their interactions (Davis & Simmt, 2003, p. 138).
These two defining characteristics also apply to complex systems that arise in other disciplines, such as cells, bodily organs, cultures, economics, and ecosystems (Johnson, 2001).
Literature pertaining to mathematics teacher education contains empirical examples of complex systems emerging among teachers as they converse with one another. Davis and Simmt (2003) characterized a study group of teachers trying to solve mathematics problems as a complex system. The structure of the conversations among the study group changed as individuals each brought unique contributions to the solutions of problems to the conversation. Smitherman (2005) described similar dynamics among a group of pre-service teachers discussing fraction concepts. She described how she conducted a classroom conversation among pre-service teachers by asking them to share their thoughts on the fraction one-third. By the end of the conversation, many of the aspects in the NCTM (2000) standards connected to fractions had been considered by the group. In each complex system, knowledge was constructed in a non-linear fashion as individuals contributed their perspectives on the objects of study at hand to the conversation.
In studying teachers' interactions within complex systems, it is important to keep in mind that complexity science provides a framework for analyzing human interactions, which are never devoid of contextual peculiarities (Stacey, 2003). …