Research shows that mathematics teachers’ ability to connect content and pedagogy is a crucial factor contributing to their effectiveness in the classroom (Ball & Bass, 2000; Conference Board of the Mathematical Sciences [CBMS], 2001).  However, prospective secondary mathematics teachers (PSMTs) often experience a disjointed education, taking mathematics content courses in one department, mathematics methods/pedagogy courses in a different department, and finding it difficult to make meaningful connections between content and pedagogy throughout their teacher preparation program (Williams, 2005).  Given this disconnect between content and pedagogy in many mathematics teacher preparation programs and the importance of teachers’ ability to make connections between the two, numerous calls have been made for collaborations between mathematicians and mathematics teacher educators (MTEs), the two main groups responsible for educating and preparing PSMTs (CBMS, 2001; Ferrini-Mundy & Findell, 2001; McCallum, 2003; Wu, 2006).  However, collaborations between mathematicians and MTEs have historically been infrequent, and relationships between members of these two communities are often strained and characterized by a lack of trust and respect (Ferrini-Mundy & Findell, 2001).  Therefore, it is important to investigate existing efforts at collaboration in order to better understand and improve the nature of collaborative work between members of the mathematics and mathematics education communities. 

In this interactive paper session, we will present an overview of the results from an interpretive phenomenological case study in which we aimed to gain an understanding of the lived experiences of a mathematician and a MTE as they engaged in a team-teaching collaboration within the context of prospective secondary mathematics teacher preparation. The following research question served as the overarching question guiding the inquiry:

In what ways do mathematician (M) and mathematics teacher educator (E) make sense of their experiences engaging in a team-teaching collaboration within a mathematics content course (i.e., Geometry) and a mathematics methods course (i.e., Teaching Senior High School Mathematics) for prospective secondary mathematics teachers?

 In comparison to more traditional approaches to phenomenology (e.g., Husserl, 1970; van Manen, 1990), in which phenomenological research is conceptualized as “the study of the lifeworld—the world as we immediately experience it pre-reflectively rather than as we conceptualize, categorize, or reflect on it” (van Manen, 1990, p. 9), interpretive phenomenological analysis is focused on lived experiences of individuals within a particular context as those experiences are reflected on and interpreted by the individuals themselves (Smith, Flowers, & Larkin, 2009).  Throughout the duration of their team-teaching collaboration, M and E frequently engaged in reflective discussions in which it was clear the two instructors were attempting to make sense of their experiences.  Moreover, the phenomenon of interest in this study is situated in a particular context (i.e., a teacher preparation program for PSMTs) and is focused on the particular meaning that M and E make out of their experiences in that context. Therefore, the proposed study is particularly suited for an interpretive phenomenological analysis.

The selection of M and E for this study makes use of what Flyvbjerg (2006) referred to as a paradigmatic sampling strategy.  Flyvbjerg described paradigmatic cases as “cases that highlight more general characteristics of the societies in question” (p. 232), and that have “metaphorical and prototypical value” (p. 232).  M and E demonstrated considerable differences in their ideas about the teaching and learning of mathematics, as evidenced by their first team-teaching collaboration in Spring 2010. We had numerous insightful conversations with both instructors about their collaborative experiences, and it was clear that their contradictory perspectives on the teaching and learning of mathematics paralleled the salient literature in this area. 

The data we collected to inform the inquiry consisted of the following six sources: (1) field notes from observations within all class sessions and instructor planning sessions, (2) one-on-one interviews conducted with each instructor (two times each semester), (3) group interviews with both instructors together (one time each semester), (4) audio-recordings of all instructor planning sessions, (5) video-recordings of class sessions (2.5 hours each semester), and (6) a researcher reflective journal. 

We are currently in the data analysis stage of the project, employing a four-step interpretive phenomenological analysis procedure, as outlined by Smith et al. (2009).  Initial themes have emerged in relation to how M and E made sense of their collaborative experiences.  Of particular significance in M and E’s collaboration were their perceived differences with respect to assessment practices, technology use, pedagogical style, and focus on content/process.  For example, with respect to assessment practices, M and E found that they differed in terms of their expectations for student achievement, the purposes they attributed to formal assessment, and their actual grading practices.

During the proposed interactive paper session, we will present an overview of the study as described above together with the final themes that emerge from our analysis.  We hope to engage the audience in a reflective discussion about how their own experiences as members of the mathematics or mathematics education communities are similar or different from the experiences of M and E during their team-teaching collaboration.   We expect that this discussion will provoke members of the audience to think deeply about their own educational experiences, their assumptions about the teaching and learning of mathematics that stem from those experiences, and how those assumptions might help or hinder progress in the education of PSMTs at their own institutions. As suggested by Barritt (1986), “By heightening awareness and creating dialogue, it is hoped research can lead to better understanding of the way things appear to someone else and through that insight lead to improvements in practice” (p. 20).

Our session will specifically address the NCTM research presession priority area of “professional learning.”  One of the most salient outcomes of M and E’s team-teaching collaboration was that through reflective discussions about their instruction, both M and E believed that they grew significantly in their role as educators.  Moreover, because the context of this study was situated within a mathematics teacher preparation program, we will also discuss the ways in which M and E’s collaboration spurred professional learning amongst the PSMTs in their courses.

References

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83– 104). Westport, CT: Ablex.

Barritt, L. (1986).  Human sciences and the human image.  Phenomenology and Pedagogy, 4(3), 14-22.Conference Board of the Mathematical Sciences (2001). The mathematical education of teachers. Washington, DC: American Mathematical Society.

Ferrini-Mundy, J., & Findell, B. (2001). The mathematical education of prospective teachers of secondary school mathematics: Old assumptions, new challenges. In CUPM discussion papers about mathematics and the mathematical sciences in 2010: What should students know? (pp. 31–41). Washington, DC: Mathematical Association of America.

Flyvbjerg, B. (2006).  Five misunderstandings about case-study research.  Qualitative Inquiry, 12(2), 219-245.

Husserl, E. (1970).  The crisis of European sciences and transcendental phenomenology (D. Carr, Trans.). Evanston: Northwestern University Press.

McCallum, W. (2003). Promoting work on education in mathematics departments. Notices of the American Mathematical Society, 50(9), 1093-1098.

Smith, J. A., Flowers, P., & Larkin, M. (2009). Interpretive phenomenological analysis: Theory, method, and research.  London: Sage.

van Manen, M. (1990). Researching lived experience: Human science for an action sensitive pedagogy. Albany: State University of New York Press.

Williams, S. T. (2005).  Merging content and pedagogy: An investigation of the specific factors of an innovative master's degree program for secondary mathematics teachers that contribute to reported changes in beliefs and instructional practices (Doctoral dissertation, Kent State University). Available from ProQuest Dissertations and Theses database. (Publication No. AAT 3203437)

Wu, H. (2006). How mathematicians can contribute to K–12 mathematics education. In M.S. Sole, J. Soria, J. L. Varona, & J. Verdera (Eds.), Proceedings of the International Congress of Mathematics, Madrid 2006, Vol. 3 (pp.1676–1688). Zurich, Switzerland: European Mathematical Society