National Council of Teachers of Mathematics 2012 Research Presession

Please note: The NCTM conference program is subject to change.

1452-

Wednesday, April 25, 2012: 1:15 PM
Franklin Hall 1 (Philadelphia Marriott Downtown)
Lindsay M. Umbeck , Purdue University, West Lafayette, IN

Mathematics Teachers Exploring Reasoning and Sense Making Through Action Research

The National Council of Teachers of Mathematics published Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009) to address the need for mathematics programs to encourage students' reasoning and sense making abilities in order to develop mathematically literate citizens.  This study investigated the experiences of seven teachers responding to these recommendations and incorporating them into their teaching through action research.  Teacher action research (Carr & Kemmis, 1986) values the ‘insider' stance that teachers hold in their classroom and positions teachers as knowledge generators (Cochran-Smith & Lytle, 2009) as they examine recommendations generated by outsiders (Stenhouse, 1975).  Knowledge that is generated and incorporated into curricular reform proposals is not widely being applied to classroom practice (Atweh, 2004), and teacher action research contributes to bridging this divide between knowledge generation and knowledge application. 

Seven mathematics teachers met regularly throughout the school year with the researcher/facilitator to learn about action research and collaboratively examine recommendations for Reasoning and Sense Making (NCTM, 2009).  Subsequently, teachers individually selected specific actions to incorporate these recommendations into their practice, and meetings served as a space for them to discuss their ongoing work with colleagues.  The purpose of this study was to understand the experiences of mathematics teachers examining current recommendations for mathematics teaching and incorporating them into their practice.  Additionally, the following research sub-questions were explored: How do teachers conceptualize NCTM's curricular recommendations for reasoning and sense making? How do teachers choose to incorporate these recommendations into their practice? How do teachers interpret the impact of their actions on their students' reasoning and sense making practices? What are the challenges and opportunities that teachers encounter as they attempt to incorporate reasoning and sense making into their practice?  The research method of narrative inquiry (Connelly & Clandinin, 1990) was selected in order to illustrate the phenomenon studied through developing narratives of participants' experiences.  Data collected to inform this research consisted of audio recordings of teachers' conversations, the researcher's journal, teachers' written reflections, field notes from classroom observations, and open-ended interviews. 

Narrative inquiry allows the voices of teachers to be heard and develops an understanding of what the experience is like from the perspective of the teacher (Connelly & Clandinin, 1990).  Narrative inquiry is a “field in the making” (Chase, 2005, p. 651) that has recently received wider attention in the field of education.  Clandinin and Connelly (2000) describe narrative inquiry as “a collaboration between researcher and participants, over time, in a place or series of places, and in social interaction with milieus” (p. 20).  Narrative inquiry complements the teachers' use of action research, because both aim to give voice to teachers and status to their previously absent practical knowledge (Barone, 2010).  Narrative analysis consists of “emplotment and narrative configuration” (Polkinghorne, 1995), in which the researcher seeks to create a storied account of the experience.  Individual data pieces, or field texts, were pieced together to develop a plot (Polkinghorne, 1995) and create unified, coherent narratives that convey meaning to the reader about what the experience is like for each teacher.  This analysis process is one of “a synthesizing of the data rather than a separation of it into its constituent parts” (Polkinghorne, 1995, p. 15). 

Findings reveal that teachers incorporated these recommendations into their teaching in very individual ways.  Narratives reveal that their choices are a reflection of those aspects of the recommendations that held meaning for them within the context of their teaching and their visions for their practice.  While teachers used common language to describe their goals for reasoning and sense making, classroom observations revealed distinct ways that the recommendations were put into practice.  A common challenge that teachers faced was persisting in and refining their actions in the face of student resistance to changes being made in the classroom culture.  The variety of ways that teachers incorporated the recommendations into their teaching, the challenges and opportunities they faced, and the ways they interpreted the results of their actions will be shared.  The speaker will use the 15 minutes presentation time in the following ways: to briefly describe the study's theoretical perspective, purpose, design and analysis (5 min), develop the audience's understanding of abbreviated narratives of three of the teachers that were selected as representative (6 min), and describe commonalities and differences among participants with respect to the research questions (4 min).  During roundtable discussion I will engage the audience in responding to the findings and discussing the implications for future research and practice.

            This study has educational importance as it advances our understanding of teacher change in response to the current reform proposals.  Narrative inquiry offers an alternative perspective as it reveals teachers' experiences and allows their voices to be heard.  This study informs mathematics teacher educators of the diverse ways that teachers interpret Reasoning and Sense Making how it takes shape in their teaching practice.

             

References

Atweh, B. (2004). Understanding for changing and changing for understanding. In P. Valero & R. Zevenbergen (Eds.), Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology (pp. 187-205): Kluwer Academic Publishers.

Barone, T. (2010). Commonalities and variegations: Notes on the maturation of the field of narrative research. The Journal of Educational Research, 103(2), 149-153.

Carr, W., & Kemmis, S. (1986). Becoming critical: Education, knowledge and action research. London: Falmer.

Chase, S. E. (2005). Narrative inquiry: Multiple lenses, approaches, voices. In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (3rd ed., pp. pp. 651-679). Thousand Oaks, CA: Sage Publications.

Clandinin, D. J., & Connelly, F. M. (2000). Narrative inquiry: Experience and story in qualitative research. San Francisco: Jossey-Bass.

Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: Practitioner research for the next generation. New York: Teachers College Press.

Connelly, F. M., & Clandinin, D. J. (1990). Stories of experience and narrative inquiry. Educational Researcher, 19(5), 2-14.

National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: NCTM.

Polkinghorne, D. E. (1995). Narrative configuration in qualitative analysis. In J. A. Hatch & R. Wisniewski (Eds.), Life history and narrative (pp. 5-23). London: The Falmer Press.

Stenhouse, L. (1975). An introduction to curriculum research and development. London: Heinemann.