A Methodology That Does Not Break the Complexity in Noticing

• In Event: 30.067 - New Perspectives on Teacher Noticing in Mathematics Education

Abstract

A review of research on noticing in mathematics education with a focus on the theoretical foundations reveals a nominal recognition that the phenomenon of interest is complex. However, such recognition devolves into a “manageable” complexity as these studies assume that noticing—similar to other phenomena relevant to the teaching practice—can be decomposed for analytical purposes (Grossman, et al, 2009). Decomposing a complex phenomenon into parts to be studied resonates with “a stable, unchanging reality that can be studied with the empirical methods of objective social science” (Denzin, Lincoln, & Giardina, 2006, pp. 771-772). The focus on a component of a phenomenon creates, inevitably, a defocus. In this presentation I will discuss the seriousness of this defocus, particularly how teacher noticing has been separated from student noticing. At the axiological level, studies on teacher noticing articulate an important reminder that there is something to be valued and to be noticed, namely student reasoning, particularly in mathematics classrooms. What keeps us from valuing student noticing? At the ontological level, the reality of the phenomenon studied is fractured by the fact that teacher noticing is isolated from student noticing. What do we gain by studying a fractured reality? At the epistemological level, the way the field is moving its understanding of noticing focuses on the teacher as the primary agent who notices. Why not connecting teacher noticing to student noticing? In this presentation, I will share an emerging methodology that I am currently developing in classrooms with non-dominant students. Examples of the complex reciprocity in noticing from my research project will be discussed. This methodology is a radical elaboration on current research, particularly in the area of teacher noticing.
Following the distinction between complicated and complex phenomena (Davis & Sumara, 2006), my proposal is not to take a complex systems apart, because the results can be catastrophic (Bateson, 2011). A methodology that does not break the complexity in noticing challenges linear development, separation, and analysis and makes room for the importance of fractal growth, connections, and synthesis.

Author

• Higinio Dominguez, Michigan State University