Student or Teacher? A Look at How Students Facilitate Public Sensemaking During Collaborative Groupwork

Keywords: groupwork, authority, agency, positioning

Abstract

As institutions strive to improve teaching and learning for all, educators must consider equitable instruction. In particular, equitable distributions of authority and agency among students. The authors define distribution of authority as shared opportunities for decision-making in enacting mathematical tasks, and agency as the power to carry out these self-made decisions. Equitable distributions of authority and agency can be enhanced in mathematics public sensemaking classrooms where students participate in discourse as active members of the classroom. In public sensemaking classrooms, students understand and acknowledge one another's ideas, present and revise arguments, and take risks by sharing ideas. This study investigates one group of students and how they positioned one another during mathematical groupwork in a public sensemaking classroom, as well as how the positioning impacted the distribution of agency and authority. Analyses indicate that one student replicates the role of teacher by redistributing authority and agency back to other students. The findings intend to inform classroom teachers of the positioning patterns that may occur during groupwork, and the effectiveness of public sensemaking classrooms on distributing authority and agency equitably during groupwork.

References

Berry, M. (1981). Systemic linguistics and discourse analysis: A multi-layered approach to exchange structure. In M. Coulthard & M. Montgomery (Eds.), Studies in discourse analysis (pp. 120–145). Routledge & Kegan Paul.

Boaler, J. (2002). The development of disciplinary relationships: Knowledge, practice and identity in mathematics classrooms. For the Learning of Mathematics, 22(1), 42–47.

Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608–645.

Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43(1), 137–154. https://doi.org/10.3102/00028312043001105

Burris, C. C., Wiley, E., Welner, K., & Murphy, J. (2008). Accountability, rigor, and detracking: Achievement effects of embracing a challenging curriculum as a universal good for all students. Teachers College Record, 110(3), 571–607.

Cabana, C., Shreve, B., Woodbury, E., & Louie, N. (2014). Mathematics for equity: A frame-work for successful practice. 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, 40(1), 40–68.

Cohen, E. G., & Lotan, R. A. (2014). Designing Groupwork: Strategies for the Heterogeneous Classroom (3rd ed.). Teachers College Press.

Darling-Hammond, L. (1995). Inequality and access to knowledge. In J. A. Banks & C. A. M. Banks (Eds.), Handbook of research on multicultural education (pp. 465–483). Simon & Schuster Macmillan.

Davies, B., & Harré, R. (1999). Positioning and personhood. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional actions (pp. 32–52). Blackwell.

DeJarnette, A. F., & González, G. (2015). Positioning during group work on a novel task in Algebra II. Journal for Research in Mathematics Education, 46(4), 378–422. https://doi.org/10.5951/jresematheduc.46.4.0378

Dunleavy, T. (2015). Delegating mathematical authority as a means to strive toward equity. Journal of Urban Mathematics Education, 8(1), 62–82. https://doi.org/10.21423/jume-v8i1a242

Emerson, R. M., Fretz, R. I., & Shaw, L. L. (2011). Writing ethnographic fieldnotes. University of Chicago Press.

Esmonde, I. (2009). Mathematics learning in groups: Analyzing equity in two cooperative activity structures. Journal of the Learning Sciences, 18(2), 247–284. https://doi.org/10.1080/10508400902797958

Esmonde, I., Brodie, K., Dookie, L., & Takeuchi, M. (2009). Social identities and opportunities to learn: Student perspectives on group work in an urban mathematics classroom. Journal of Urban Mathematics Education, 2(2), 18–45. https://doi.org/10.21423/jume-v2i2a46

Gamoran, A. (2009). Tracking and Inequality: New Directions for Research and Practice. (WCER Working Paper No. 2009-6). Wisconsin Center for Education Research. https://wcer.wisc.edu/docs/working-papers/Working_Paper_No_2009_06.pdf

Gresalfi, M. S., & Cobb, P. (2006). Cultivating students' discipline-specific dispositions as a critical goal for pedagogy and equity. Pedagogies, 1(1), 49–57. https://doi.org/10.1207/s15544818ped0101_8

Gutiérrez, R. (2009). Framing equity: Helping students “play the game” and “change the game.” Teaching for Excellence and Equity in Mathematics, 1(1), 4–8.

Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 7–73.

Halliday, M. A. K. (1984). Language as code and language as behaviour: A systemic-functional interpretation of the nature and ontogenesis of dialogue. In R. Fawcett, M. A. K. Halliday, S. M. Lamb, & A. Makkai (Eds.), The semiotics of language and culture: Vol. 1. Language as social semiotic (pp. 3–35). Pinter.

Hand, V. M. (2010). The co-construction of opposition in a low-track mathematics classroom. American Educational Research Journal, 47(1), 97–132. https://doi.org/10.3102%2F0002831209344216

Horn, I. S. (2007). Fast kids, slow kids, lazy kids: Framing the mismatch problem in mathematics teachers' conversations. The Journal of the Learning Sciences, 16(1), 37–79. https://doi.org/10.1080/10508400709336942

Horn, I. S. (2012). Strength in numbers: Collaborative learning in secondary mathematics. National Council of Teachers of Mathematics.

Jackson, K. J. (2010). The social construction of youth and mathematics: The case of a fifth-grade classroom. In D. B. Martin (Ed.), Mathematics teaching, learning, and liberation in the lives of Black children (pp. 185–209). Routledge.

Jansen, A. (2020). Rough draft math: Revising to learn. Stenhouse.

Jett, C. C. (2019). Mathematical persistence among four African American male graduate students: A critical race analysis of their experiences. Journal for Research in Mathematics Education, 50(3), 311–340. https://doi.org/10.5951/jresematheduc.50.3.0311

Langer-Osuna, J. M. (2011). How Brianna became bossy and Kofi came out smart: Understanding the trajectories of identity and engagement for two group leaders in a project-based mathematics classroom. Canadian Journal of Science, Mathematics and Technology Education, 11(3), 207–225. https://doi.org/10.1080/14926156.2011.595881

Langer-Osuna, J. M. (2018). Exploring the central role of student authority relations in collaborative mathematics. ZDM, 50(6), 1077–1087. https://doi.org/10.1007/s11858-018-0965-x

Leonard, J., & Martin, D. B. (Eds.). (2013). The brilliance of Black children in mathematics. Information Age Publishing.

Martin, D. B. (2012). Learning mathematics while Black. Educational Foundations, 26, 47–66.

National Council of Teachers of Mathematics. (2018). Catalyzing change in high school mathematics: Initiating critical conversations.

National Research Council. (2011). Successful K-12 STEM education: Identifying effective approaches in science, technology, engineering, and mathematics. National Academies Press. https://www.nap.edu/resource/13158/dbasse_071100.pdf

Oakes, J. (1990). Multiplying inequalities: The effects of race, social class, and tracking on opportunities to learn mathematics and science. RAND Corporation.

Ruef, J. (2013). Mutability and resiliency of teacher beliefs and practices: A case study. In M. V. Martinez & A. C. Superfine (Eds.), Proceedings of the Thirty-Fifth Annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education (pp. 1069–1072). University of Illinois at Chicago. https://www.pmena.org/pmenaproceedings/PMENA%2035%202013%20Proceedings.pdf

Ruef, J. (2016). Building powerful voices: Co-constructing public sensemaking [Unpublished doctoral dissertation]. Stanford University.

Ruef, J. (in press). How Ms. Mayen and her students co-constructed "good at math." Journal of Research in Mathematics Education.

Tate, W. F., Anderson, C. R., & Tate, D. A. (2018). “SUM" is better than nothing: Toward a sociology of urban mathematics education. Journal of Urban Mathematics Education, 11(1&2), 31–34. https://doi.org/10.21423/jume-v11i1-2a356

van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional actions (pp.14–31). Blackwell.

Watanabe, M., & Evans, L. (2015). Assessments that promote collaborative learning. Mathematics Teacher, 109(4), 298–304.

Yin, R. K. (2017). Case study research and applications: Design and methods. SAGE.

Published
2020-04-30
How to Cite
Lo, M., & Ruef, J. (2020). Student or Teacher? A Look at How Students Facilitate Public Sensemaking During Collaborative Groupwork. Journal of Urban Mathematics Education, 13(1), 15–33. https://doi.org/10.21423/jume-v13i1a372
Section
RESEARCH ARTICLES