Practitioner Research: Reflecting on Minoritized Student Agency in a Reform-Based Secondary Mathematics Classroom
Keywords:
practitioner research, equitable whole-class mathematics discussions, agency, statusAbstract
There is a global demand for mathematics teachers to learn how to facilitate discussions where students make sense of mathematics via problem-solving and reasoning activities. Despite this call for meaningful discussions, they are rarely found in secondary instruction, especially in low-socioeconomic communities. A practitioner research approach was used to document the types of agency students and teacher employed during whole class discussions in a racially and socioeconomically diverse classroom in the United States. Cobb, Gresalfi and Hodge’s (2009) interpretive scheme was used to analyse the ways students chose to identify with the normative expectations of the classroom, documented in the daily field notes and audio recordings. In this paper, two transcripts were used to illustrate examples of student and teacher participation in a
9th–11th grade mathematics classroom. Findings from this research demonstrate the small shifts that occurred allude to the structural constraints of traditional school systems.
References
Allen, K., & Schnell, K. (2017). Mathography: A Tool for Fostering Mathematics Identity. In J. Carpenter, A. Lutz, L. Samek, M. M. Caskey, W. L. Greene, Y. M. Kim, J. Casbon, & M. Musser (Eds.), Imagine a place: stories from middle grades educators. The handbook of resources in middle level education (pp. 23-28). Information Age Publishing. https://books.google.com/books?id=EQ0oDwAAQBAJ
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397. https://doi.org/10.1086/461730
Bartle, S. (2012). Integrated Math I: A common core math program, student skill practice. Carnegie Learning. https://www.carnegielearning.com/
Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematical worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 45–82). Stamford, CT: Ablex.
Brantlinger, A. (2013). Between politics and equations: Teaching critical mathematics in a remedial secondary classroom. American Educational Research Journal, 50(5), 1050-1080. https://doi.org/10.3102/0002831213487195
Brenner, M. (1994). A communication framework for mathematics classrooms: Exemplary instruction for culturally and linguistically diverse students. In B. McLeod (Ed.), Language and Learning: Educating linguistically and culturally diverse students (pp. 233-268). SUNY.
Bunch, G. C. (2013). Pedagogical language knowledge: Preparing mainstream teachers for English learners in the new standards era. Review of Research in Education, 37(1), 298-341. https://doi.org/10.3102/0091732X12461772
Chapin, O’Connor, & Anderson (2013). Classroom discussions in math: A teacher's guide for using talk moves to support the common core and more grades K-6 (3rd ed.). Math Solutions. ISBN-13: 9781935099567
Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York, NY: Teachers College Press.
Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 39(0), 40-68.
Cobo, P. & Fortuny, J. (2000). Social interactions and cognitive effects in contexts of area-comparison problem solving. Educational Studies in Mathematics, 42(2), 115-140. https://doi.org/10.1023/A:1004187711956
Cohen, E. G., Lotan, R. A., Scarloss, B. A., & Arellano, A. R. (1999). Complex instruction: Equity in cooperative learning classrooms. Theory into practice, 38(2), 80-86. https://doi.org/10.1080/00405849909543836
Cope, B., & Kalantzis, M. (2009). “Multiliteracies”: New literacies, new learning. Pedagogies: An international Journal, 4(3), 164-195. https://doi.org/10.1080/15544800903076044
Enyedy, N., Rubel, L., Castellón, V., Mukhopadhyay, S., Esmonde, I., & Secada, W. (2008). Revoicing in a multilingual classroom. Mathematical Thinking and Learning, 10(2), 134-162. https://doi.org/10.1080/10986060701854458
Fendel, D., Resek, D., Alper, L., & Fraser, S. (2003). Interactive mathematics program. Key Curriculum Press.
Forman, E. A. (1996). Learning mathematics as participation in classroom practice: Implications of sociocultural theory for educational reform. In L. P. Steffe, P. Nesher, P. Cobb, B. Sriraman, & B. Greer (Eds.), Theories of mathematical learning (pp. 115-130). https://doi.org/10.4324/9780203053126
Forman, E., & Ansell, E. (2001). The multiple voices of a mathematics classroom community. Educational Studies in Mathematics, 46(1), 115-142. https://doi.org/10.1080/10508406.2002.9672139
Forman, E. A., McCormick, D., & Donato, R. (1998). Learning what counts as a mathematical explanation. Linguistics and Education, 9(4), 313–339. https://doi.org/10.1016/S0898-5898(97)90004-8
Frankenstein, M. (1990). Incorporating race, gender, and class issues into a critical mathematics literacy curriculum. The Journal of Negro Education, 59(3), 336-347. https://www.jstor.org/stable/2295568
Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37-73. https://www.jstor.org/stable/30034699
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York: Taylor & Francis.
Hammersley, M., & Atkinson, P. (1983). Ethnography: Principles in practice. London: Tavistock Publications.
Herbel-Eisenmann, B. A., Steele, M.D., & Cirillo, M. (2013). (Developing) teacher discourse moves: a framework for professional development. Mathematics Teacher Educator, 1(2), 181-196. https://www.jstor.org/stable/10.5951/mathteaceduc.1.2.0181
Herr, K., & Anderson, G. L. (2014). The action research dissertation: A guide for students and faculty. Thousand Oaks: Sage publications.
Holland, D., Lachicotte, W., Skinner, D. C., & Cain, C. C., (1998). Identity and agency in cultural worlds. Cambridge, MA: Harvard University.
Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116. https://www.jstor.org/stable/30034933
Hunter, R. (2010). Changing roles and identities in the construction of a community of mathematical inquiry. Journal of Mathematics Teacher Education, 13(5), 397–409. https://doi.org/10.1007/s10857-010-9152-x
Hunter, R., & Anthony, G. (2011). Forging mathematical relationships in inquiry-based classrooms with Pāsifika students. Journal of Urban Mathematics Education, 4(1), 98-119. http://education.gsu.edu/JUME
Johnson, C. C. (2012). Four Key Premises of STEM (Editorial). School Science and Mathematics, 112(1), 1-2. https://doi.org/10.1111/j.1949-8594.2011.00110.x
Kagan, S. (1989). The structural approach to cooperative learning. Educational Leadership, 47(4), 12-15. http://www.ascd.org/ASCD/pdf/journals/ed_lead/el_198912_kagan.pdf
Kamischke, E. & Murdock, J. (2007). Discovering Algebra: An investigative approach. New York: Key Curriculum Press. http://115.78.239.30:8080/dspace/handle/DNULIB_52011/3588
Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102(1), 59-80. https://doi.org/10.1177/0022057409189001-209
Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55(2), 178-195. https://doi.org/10.17763/haer.55.2.56142234616x4352
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63. https://doi.org/10.3102/00028312027001029
Lubienski, S. T. (2004). Traditional or standards-based mathematics? The choices of students and parents in one district. Journal of Curriculum and Supervision, 9, 338-365. https://doi.org/10.1007/s10857-006-9012-x
Martin, D. (2000). Mathematics success and failure among African-American youth: The roles of sociohistorical context, community forces, school influence, and individual agency. Mahwah, NJ: Lawrence Erlbaum Associates.
Martin, D. B. (2012). Learning mathematics while Black. Educational Foundations, 26, 47-66. https://doi.org/10.1080/13613324.2019.1592833
MCEECDYA. (2009). National report: Achievement in reading, writing, language conventions and numeracy 2009. Canberra: Australian Government.
Merriam, S. B. (1998). Qualitative research and case study applications in education. revised and expanded from “Case study research in education." Jossey-Bass Publishers, San Francisco, CA. www.josseybass.com
Ministry of Education. (2007). The New Zealand curriculum. Wellington: Learning Media. http://nzcurriculum.tki.org.nz/The-New-Zealand-Curriculum
Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics, 19(1), 11-19. https://www.jstor.org/stable/40248284
Moschkovich, J. N. & Zahner, W. (2018). Using the academic literacy in mathematics framework to uncover multiple aspects of activity during peer mathematical discussions. ZDM, The International Journal on Mathematics Education, 50(6), 999-1011. https://doi.org/10.1007/s11858-018-0982-9
Pickering, A. (1995). The mangle of practice. Chicago: University of Chicago Press.
Planas, N., & Gorgorió, N. (2004). Are different students expected to learn norms differently in the mathematics classroom? Mathematics Education Research Journal, 16(1), 19-40. https://doi.org/10.1007/BF03217389
Planas, N., & Setati-Phakeng, M. (2014). On the process of gaining language as a resource in mathematics education. ZDM, 46(6), 883-893. https://doi.org/10.1007/s11858-014-0610-2
Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. Oxford University Press. ISBN: 9780195070033
Secada, W. G. (1996). Urban students acquiring English and learning mathematics in the context of reform. Urban Education, 30(4), 422–448. https://doi.org/10.1177/0042085996030004004
Sherin, M. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205-233. https://doi.org/10.1023/A:1020134209073
Solórzano, D. G., & Bernal, D. D. (2001). Examining transformational resistance through a critical race and LatCrit theory framework: Chicana and Chicano students in an urban context. Urban education, 36(3), 308-342. https://doi.org/10.1177/0042085901363002
Spencer, J. A. (2009). Identity at the crossroads: Understanding the practices and forces that shape African American success and struggle in mathematics. In D. B. Martin (Ed.), Mathematics teaching, learning, and liberation in the lives of Black children (pp. 200- 230). New York: Routledge. Staples, M. E. (2008). Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom. Journal of Mathematics Teacher Education, 11(5), 349-371. https://doi.org/10.1007/s10857-008-9078-8
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. https://doi.org/10.3102/00028312033002455
Stephens, M., Landeros, K., Perkins, R., & Tang, J. H. (2016). Highlights from TIMSS and TIMSS Advanced 2015: Mathematics and Science Achievement of US Students in Grades 4 and 8 and in Advanced Courses at the End of High School in an International Context. NCES 2017-002. National Center for Education Statistics.
Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. SAGE Publications, Inc.
Turner, E. E. (2003). Critical mathematical agency: Urban middle school students engage in mathematics to investigate, critique, and act upon their world. Doctoral dissertation. http://hdl.handle.net/2152/1015
Vanneman, A., Hamilton, L., Baldwin Anderson, J., & Rahman, T. (2009). Achievement Gaps: How Black and White students in public schools perform in mathematics and reading on the National Assessment of Educational Progress (NCES 2009-455). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education.
Varelas, M., Martin, D. B., & Kane, J. M. (2013). Content learning and identity construction: A framework to strengthen African American students’ mathematics and science learning in urban elementary schools. Human Development, 55(5-6), 319-339. https://doi.org/10.1159/000345324
Varelas, M., Tucker‐Raymond, E., & Richards, K. (2015). A structure‐agency perspective on young children's engagement in school science: Carlos's performance and narrative. Journal of Research in Science Teaching, 52(4), 516-529. https://doi.org/10.1002/tea.21211
Wagner, D., & Herbal-Eisenmann, B. (2009). Re-mythologigzing mathematics through attention to classroom positioning. Educational Studies in Mathematics, 72, 1-15. https://doi.org/10.1007/s10649-008-9178-5
Watson-Gegeo K.A. (1997). Classroom Ethnography. In: Hornberger N.H., Corson D. (eds) Encyclopedia of language and education, vol 8. (pp. 135-144). Dordrecht: Springer. https://doi.org/10.1007/978-94-011-4535-0_13
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://www.jstor.org/stable/749877
Yonezawa, S. (2015). Student Voice and the Common Core. Teachers College Record, 117(13), 39-58. http://create.ucsd.edu/research/yonezawa_student-voice-and-the-common-core.pdf