Shulman’s (1986, 1987) work on pedagogical content knowledge (PCK) made a significant contribution to the field of teacher education by re-focusing attention on content knowledge during a time when the primary focus within teacher education research was on pedagogy. Since the construct of PCK was introduced to the field, work has been done to further explicate what PCK entails in various subject matter domains. Within the field of mathematics education, Ball and her colleagues’ work at Michigan and Rowland and his colleagues’ work at University of Cambridge have made significant contributions to teacher education and mathematics education (Ball, Thames & Phelps, 2008; Rowland et al., 2009). Both projects have yielded models of mathematical knowledge for teaching that explicates what elementary classroom teachers need to know and be able to do during mathematics planning and instruction.

Although it could be argued that there is growing consensus in the field as to the “types” of knowledge required to teach elementary mathematics, to date there has been little work done to describe the emergence and growth of this knowledge with novice or beginning teachers (Leinhardt, 1993).  Becoming clearer on expert knowledge is significantly different than becoming aware of how this knowledge comes to be, in the first place.  This has resulted in significant gaps in current scholarship surrounding theories about learning to teach elementary mathematics, where such theories tend to be oversimplified and underspecified (Feiman-Nemser & Remillard, 1996; Munby et al., 2001).  This lack of knowledge, in turn, is a problematic omission within teacher education because of the relative lack of theories and research on which to build courses, field work, and programs for preservice teachers.  Furthermore, just because courses and field placements should result in positive impacts on many domains, including the development of pedagogical content knowledge, does not mean that experiences will “stick” in the intended way or be translated into practice.  Therefore, considering how knowledge growth occurs over a preservice teacher education program addresses a significant gap in existing studies.

In addition to addressing gaps in the research of teacher knowledge, it was my intent to design a study with a substantial philosophical foundation.  The problematic nature of disconnects in teacher education between course work and field placements have been explained by researchers.  I perceive a similar problematic divide in content area research void of substantial philosophical grounding.  Therefore, Dewey’s (1916/1985; 1938/1963) philosophy of experience and distinctions between experiences that are educative, mis-educative, and non-educative was used as a way to frame content area research in teacher education while enhancing it with a substantial theoretical foundation.  Shulman, Ball, Rowland, and Dewey’s work was used in conjunction to make sense of the growth and development that occurred with preservice teachers: Shulman, Ball, and Rowland’s work was used to examine and explain the knowledge growth that occurred over the final year in a preservice teacher program and Dewey’s work was used to identify and describe the preservice teachers’ experiences that contributed to the growth of their knowledge.  

Lastly, this study also addressed a gap in current qualitative methodologies.  The phenomenon of preservice teachers’ knowledge development seemed best suited to a case study design, however case studies are intended to offer specific rather than general understanding of the phenomenon at hand (Grossman, 1990).  Given the significant gaps in current research I wanted to have a way to situate the specific understanding of a smaller group of preservice teachers I gained against a larger number of the other preservice teachers in the same cohort.  Therefore, I developed a new methodology that I termed “situated case studies” in which data is collected in a series of nested tiers, thus offering a broader scope of data in which to situate the focal case studies.  Developing this new methodology provided a way to research more participants and make more substantial suggestions for teacher education than would have been possible using a traditional case study design. 

Research Questions

            This study spanned the fields of mathematics education and teacher education and addressed gaps in content, theory, and methodology.  The dual purpose was to a) describe preservice teachers’ growth in mathematical knowledge for teaching and b) investigate what experiences contribute to preservice teachers’ development of mathematical knowledge for teaching.  Specifically, the research questions for the study were as follows: 

1.     To what extent does elementary preservice teachers’ mathematical knowledge for teaching develop over their last year in a teacher education program?

2.     What aspects of mathematical knowledge for teaching translate into elementary preservice teachers’ practices?

3.     What experiences are educative for elementary preservice teachers’ development of mathematical knowledge for teaching?

To address these research questions, data analysis included examining Preservice teachers’ written reflections, focus group interviews, individual interviews, teaching observations, post-observation interviews, and one quantitative measure, the MKT test (Learning Mathematics for Teaching, 2005).  The study design employed situated case studies, in which tiered participation resulted in extensive data for three focal preservice teachers as well as a comparison to larger groups of their peers through interviews (n=8), focus groups (n=11), and written reflections and the MKT test (n=35).  A new protocol for coding elementary pre-service teachers’ mathematics lessons was developed to extend Rowland et al.’s (2009) work on the Knowledge Quartet (KQ) model.  

The study investigated preservice teachers’ definitions of MKT, demonstrations of MKT in their teaching, and educative experiences that contributed to their development of MKT.  Insights were gained into preservice teachers’ definitions of MKT, the development of which was dynamic, non-linear, individual, and shared similarities to the aggregate definition only at the end of the year.  The KQ category of foundation tended to dominate the preservice teachers’ definitions of MKT, the transformation category remained vague, connection was an inconsistent category in their definition, and contingency arose late in the year and at a relatively small proportion.

Insights were also gained into preservice teachers’ demonstration of MKT in their teaching of mathematics.  Dimensions of MKT were most often demonstrated at a minimum level, growth on a dimension as indicated by scores that improved over time was extremely rare, scores were more variable than predicted across the four observed lessons, and the connection category was particularly challenging.

This study used the theoretical lenses of cognitive views of learning and Dewey’s (1904/1964; 1916/1985) philosophy of educative experiences.  These foundations enhanced this study and led to more substantial suggestions by which to improve teacher education in order to better facilitate preservice teachers’ development of MKT through the methods course, initial field placements, student teaching and content-based discussion groups such that pre-service teachers’ can better develop MKT via educative experiences that encourage conceptual rather than procedural teaching knowledge.  

In terms of a presentation time-line, the initial 15-minute presentation will be used to give an overview of the primary methods and results of the study.  The roundtable portion of the study will be used to provide more specific vignettes through excerpts from interviews, focus groups, and teaching observations.

REFERENCES

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makes it special? Journal of Teacher Education, 59(5), 389-407.

Dewey, J. (1916/1985). Democracy and education. In J. A. Boydston (Ed.), The middle

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Dewey, J. (1938/1963). Experience and education. New York: Macmillan.

Feinman-Nemser, S., & Remillard, J. (1996). Perspectives on learning to teach. In F. B.

Murray (Ed.), The teacher educator's handbook : Building a knowledge base for

the preparation of teachers (1st ed., pp. 63-91). San Francisco: Jossey-Bass.

Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher

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Leinhardt, G. (19993). On teaching. In R. Glaser (Ed.), Advances in instructional

psychology (pp. 1-54). Hillsdale, N.J.: L. Erlbaum Associates.

Munby, H., Russell, T., & Martin, A. K. (2001). Teachers' knowledge and how it

develops. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 877-904). Washington, D.C.: American Educational Research Association.

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Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching.

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