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Increasing awareness of practice through interaction across communities: the lived experiences of a mathematician and mathematics teacher educator

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Abstract

Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of collaboration. In this article, I present the results of an interpretative phenomenological analysis investigating the lived experiences of a mathematician and a mathematics teacher educator as they team-taught a mathematics content and mathematics methods course for prospective secondary mathematics teachers. I present extracts from interviews to illustrate the instructors’ perceptions that through collaboration and participation in the practice of the “other,” they were able to increase the awareness of their own practice and the practices characterizing their respective communities. The results of this study illustrate the potential of collaboration across these communities as a form of professional development for mathematics and mathematics education faculty.

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Notes

  1. For the purposes of this research, I use the term “mathematician” to refer to an individual who holds a terminal degree in the subject matter of mathematics and has little formal training in pedagogy or teacher preparation. I use the term “mathematics teacher educator” (MTE) to refer to an individual who holds a terminal degree in mathematics or education, and who has extensive training in pedagogy and/or teacher preparation within the discipline of mathematics. In general, the distinction between these two groups is not always clear, and individuals may refer to themselves under both titles (Even 2008; Millman et al. 2009).

  2. This material is based upon work supported by the National Science Foundation under Grant No. 0821996, Principal Invesitagor, Rebecca McGraw, University of Arizona.

  3. I limit the discussion here to these two themes for two reasons. One, in the presentation of the results, it is important to provide the reader with sufficient exposure to the instructors’ voices, so as to “communicate a sense of what the data are like” (Smith et al. 2009, p. 109). These excerpts from the instructors serve as the basis of evidence in this qualitative study. Moreover, in remaining true to IPA as a methodology, it is important for me to focus on the depth of analysis in this case and explore fully the interpretation of these emergent themes.

References

  • Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270–296.

    Google Scholar 

  • Albrecht, N. M. R. (2003). University faculty collaboration and its impact on professional development (Doctoral dissertation, Kansas State University.) Available from ProQuest Dissertations and Theses database (Publication No. AAT 3090338).

  • Association of Public and Land-grant Universities. (2012). Mathematics teacher education partnership: Guiding principles for secondary mathematics teacher preparation programs (Revised working draft—August 23, 2012). Retrieved May 27, 2013, from http://www.aplu.org/page.aspx?pid=2184.

  • 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.

    Google Scholar 

  • Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In E. Simmt, & B. Davis (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton, AB: Canadian Mathematics Education Study Group.

  • Ball, D. L., Ferrini-Mundy, J., Kilpatrick, J., Milgram, R. J., Schmid, W., & Schaar, R. (2005). Reaching for common ground in K-12 mathematics education. Notices of the American Mathematical Society, 52(9), 1055–1058.

    Google Scholar 

  • Bass, H. (1997). Mathematicians as educators. Notices of the American Mathematical Society, 44(1), 18–21.

    Google Scholar 

  • Bass, H. (2005). Mathematics, mathematicians, and mathematics education. Bulletin of the American Mathematical Society, 42(4), 417–430.

    Article  Google Scholar 

  • Beckmann, S. (2011). The community of math teachers, from elementary school to graduate school. Notices of the American Mathematical Society, 58(3), 368–371.

    Google Scholar 

  • Bleiler, S. K. (2012). Team-teaching experiences of a mathematician and a mathematics teacher educator: An interpretative phenomenological case study. (Doctoral dissertation, University of South Florida). Retrieved from ProQuest Dissertations and Theses database (3504993).

  • Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121–143.

    Article  Google Scholar 

  • Burton, L. (2002). Recignising commonalities and reconciling differences in mathematics education. Educational Studies in Mathematics, 50, 157–175.

    Article  Google Scholar 

  • Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. Boston, MA: Kluwer.

    Book  Google Scholar 

  • Cheng, S. (2006). The role of mathematicians in K-12 education: A personal perspective. In M. S. Sole, J. Soria, J. L. Varona, & J. Verdera (Eds.), Proceedings of the international congress of mathematics, Madrid 2006 (vol. 3, pp. 1688–1690). Zurich, Switzerland: European Mathematical Society.

  • Common Ground Conference Report. (2006). Reports from Finding Common Ground, Indianapolis, March, 2006. Retrieved June 14, 2010, from Mathematical Association of America. http://www.maa.org/common-ground/.

  • Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers. Washington, DC: American Mathematical Society.

    Google Scholar 

  • Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. Providence, RI/Washington, DC: American Mathematical Society and Mathematical Association of America.

    Google Scholar 

  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Crow, J., & Smith, L. (2005). Co-teaching in higher education: Reflective conversation on shared experience as continued professional development for lecturers and health and social care students. Reflective Practice, 6(4), 491–506.

    Article  Google Scholar 

  • Darling-Hammond, L., Pacheco, A., Michelli, N., LePage, P., Hammerness, K., & Youngs, P. (2005). Implementing curriculum renewal in teacher education: Managing organizational and policy change. In L. Darling-Hammond & J. Bransford (Eds.), Preparing teachers for a changing world (pp. 442–479). San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Dörfler, W. (2003). Mathematics and mathematics education: Content and people, relation and difference. Educational Studies in Mathematics, 54, 147–170.

    Article  Google Scholar 

  • Eaton, P. T., & Carbone, R. E. (2008). Asking those who know: A collaborative approach to continuing professional development. Teacher Development, 12(3), 261–270.

    Article  Google Scholar 

  • Even, R. (2008). Facing the challenge of educating educators to work with practicing mathematics teachers. In B. Jaworski, & T. Wood (Eds.), The international handbook of mathematics teacher education, vol. 4: The mathematics teacher educator as a developing professional (pp. 57–74). Rotterdam: Sense.

  • 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.

    Article  Google Scholar 

  • Goldin, G. A. (2003). Developing complex understandings: On the relation of mathematics education research to mathematics. Educational Studies in Mathematics, 54, 171–202.

    Article  Google Scholar 

  • Goos, M., & Geiger, V. (2010). Theoretical perspectives on mathematics teacher change. Journal of Mathematics Teacher Education, 13, 499–507.

    Article  Google Scholar 

  • Grassl, R., & Mingus, T. T. Y. (2007). Team teaching and cooperative groups in abstract algebra: Nurturing a new generation of confident mathematics teachers. International Journal of Mathematical Education in Science and Technology, 38(5), 581–597.

    Article  Google Scholar 

  • Hanks, W. F. (1991). Foreward. In J. Lave & E. Wenger (Eds.), Situated learning: Legitimate peripheral participation (pp. 13–24). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Heaton, R. M., & Lewis, W. J. (2011). A mathematician–mathematics educator partnership to teach teachers. Notices of the American Mathematical Society, 58(3), 394–400.

    Google Scholar 

  • Hemmi, K. (2006). Approaching proof in a community of mathematical practice (Doctoral dissertation, Stockholm University). Available from WorldCat Dissertations and Theses database.

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Hodge, A. M., Gerberry, C. V., Moss, E. R., & Staples, M. E. (2010). Purposes and perceptions: What do university mathematics professors see as their role in the education of secondary mathematics teachers? PRIMUS, 20(8), 646–663.

    Article  Google Scholar 

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

  • Kahan, J. A., Cooper, D. A., & Bethea, K. A. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6(3), 223–252.

    Article  Google Scholar 

  • Kehle, P., Maki, D., Norton, A., & Nowlin, D. (2005). Design and implementation of linking courses: Connecting college mathematics with high school mathematics for pre-service teachers. Paper presented at the Joint Meeting of the American Mathematical Society and the Mathematical Association of America, Atlanta, GA.

  • Koirala, H. P., Davis, M., & Johnson, P. (2008). Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills. Journal of Mathematics Teacher Education, 11(2), 127–138.

    Article  Google Scholar 

  • Krainer, K. (2008). Researchers and their roles in teacher education. Journal of Mathematics Teacher Education, 11, 253–257.

    Article  Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Lester, J. N., & Evans, K. R. (2009). Instructors’ experiences of collaboratively teaching: Building something bigger. International Journal of Teaching and Learning in Higher Education, 20(3), 373–382.

    Google Scholar 

  • Madison, B. L. (2006). Tensions and tethers: Assessing learning in undergraduate mathematics. In L. A. Steen (Ed.), Supporting assessment in undergraduate mathematics (pp. 3–10). Washington, DC: Mathematical Association of America.

    Google Scholar 

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

    Google Scholar 

  • McGraw, R., Lynch, K., Koc, Y., Budak, A., & Brown, C. A. (2007). The multimedia case as a tool for professional development: An analysis of online and face-to-face interaction among mathematics pre-service teachers, in-service teachers, mathematicians, and mathematics teacher educators. Journal of Mathematics Teacher Education, 10, 95–121.

    Article  Google Scholar 

  • Millman, R., Iannone, P., & Johnston-Wilder, P. (2009). Educators and the teacher training context. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics (pp. 127–133). New York, NY: Springer.

    Chapter  Google Scholar 

  • Nardi, E. (2008). Amongst mathematicians: Teaching and learning mathematics at university level. New York, NY: Springer.

    Book  Google Scholar 

  • Nardi, E., Jaworski, B., & Hegedus, S. (2005). A spectrum of pedagogical awareness for undergraduate mathematics: From “tricks” to “techniques”. Journal for Research in Mathematics Education, 36(4), 284–316.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Retrieved June 11, 2010, from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.

  • National Research Council. (2003). Evaluating and improving undergraduate teaching in science, technology, engineering, and mathematics. Washington, DC: National Academy Press.

    Google Scholar 

  • Patterson, K. B., Syverud, S. M., & Seabrooks-Blackmore, J. (2008). A call for collaboration: Not jack of all trades. Kappa Delta Pi Record, 45(1), 16–21.

    Article  Google Scholar 

  • Potari, D., Sakonidis, H., Chatzigoula, R., & Manaridis, A. (2010). Teachers’ and researchers’ collaboration in analyzing mathematics teaching: A context for professional reflection and development. Journal of Mathematics Teacher Education, 13, 473–485.

    Article  Google Scholar 

  • Ralston, A. (2004). Research mathematicians and mathematics education: A critique. Notices of the American Mathematical Society, 51(4), 403–411.

    Google Scholar 

  • Sanchez, M. (2011). A review of research trends in mathematics teacher education. PNA, 5(4), 129–145.

    Google Scholar 

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

    Google Scholar 

  • Smith, J. A., & Osborn, M. (2008). Interpretative phenomenological analysis. In J. A. Smith (Ed.), Qualitative psychology: A practical guide to research methods (pp. 53–80). London: Sage.

    Google Scholar 

  • Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook for research on mathematics teaching and learning (pp. 157–223). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Steele, M. D. (2005). Comparing knowledge bases and reasoning structures in discussions of mathematics and pedagogy. Journal of Mathematics Teacher Education, 8, 291–328.

    Article  Google Scholar 

  • Steen, L. A. (2006). Asking the right questions. In L. A. Steen (Ed.), Supporting assessment in undergraduate mathematics (pp. 11–18). Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Sultan, A., & Artzt, A. F. (2005). Mathematicians are from Mars, math educators are from Venus: The story of a successful collaboration. Notices of the American Mathematical Society, 52(1), 48–53.

    Google Scholar 

  • Thompson, D. R., Beneteau, C., Kersaint, G., & Bleiler, S. K. (2012). Voices of mathematicians and mathematics teacher educators co-teaching prospective secondary teachers. In J. M. Bay-Williams (Ed.), Professional collaborations in mathematics teaching and learning: Seeking success for all—74th yearbook (pp. 229–242). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

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

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Wenger, E. (2006). Communities of practice: A brief introduction. Retrieved January 1, 2013, from http://www.ewenger.com/theory/communities_of_practice_intro.htm.

  • 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). Retrieved from ProQuest Dissertations and Theses database (Publication No. AAT 3203437).

  • Wood, L. N., Petocz, P., & Reid, A. (2012). Becoming a mathematician: An international perspective. Dordrecht: Springer.

    Book  Google Scholar 

  • 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.

  • Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7, 5–32.

    Article  Google Scholar 

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  1. Department of Mathematical Sciences, KOM 263, Middle Tennessee State University, 1301 E. Main St., Murfreesboro, TN, 37132, USA

    Sarah K. Bleiler

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  1. Sarah K. Bleiler
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Correspondence to Sarah K. Bleiler.

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Bleiler, S.K. Increasing awareness of practice through interaction across communities: the lived experiences of a mathematician and mathematics teacher educator. J Math Teacher Educ 18, 231–252 (2015). https://doi.org/10.1007/s10857-014-9275-6

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