Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

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Margaret Rathouz University of Michigan–Dearborn, MI

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Nesrin Cengiz-Phillips University of Michigan–Dearborn, MI

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Angela S. Krebs University of Michigan–Dearborn, MI

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Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

Contributor Notes

Margaret Rathouz, University of Michigan–Dearborn, MI 48128; rathouz@umich.edu

Nesrin Cengiz-Phillips, University of Michigan–Dearborn, MI 48128; nesrinc@umich.edu

Angela S. Krebs, University of Michigan–Dearborn, MI 48128; askrebs@umich.edu

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Mathematics Teacher Educator
  • 1.

    Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Available online at https://amte.net/standards.

    • Search Google Scholar
    • Export Citation
  • 2.

    Asterhan, C. S. C., & Eisenmann, T. (2011). Introducing synchronous e-discussion tools in co-located classrooms: A study on the experiences of ‘active’ and ‘silent’ secondary school students. Computers in Human Behavior, 27(6), 21692177. https://doi.org/10.1016/j.chb.2011.06.011

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 3.

    Barnes, D. (2008). Exploratory talk for learning. In N. Mercer & S. Hodgkinson (Eds.), Exploring talk in school: Inspired by the work of Douglas Barnes (pp. 115). Sage.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 4.

    Brown, A., Thomas, K., & Tolias, G. (2002). Conceptions of divisibility: Success and understanding. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (Vol. 2, pp. 4182). Greenwood Publishing Group.

    • Search Google Scholar
    • Export Citation
  • 5.

    Chapin, S. H., O’Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K–6. Math Solutions Publications.

    • Search Google Scholar
    • Export Citation
  • 6.

    Chapin, S. H., O’Connor, C., & Anderson, N. C. (2013). A teacher’s guide for using talk moves to support the common core and more, grades K–6 (3rd ed.). Math Solutions Publications.

    • Search Google Scholar
    • Export Citation
  • 7.

    Cioe, M., King, S., Ostien, D., Pansa, N., & Staples, M. (2015). Moving students to “the why”? Mathematics Teaching in the Middle School, 20(8), 484491. https://doi.org/10.5951/mathteacmiddscho.20.8.0484

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 8.

    Dixon, J. K., Andreasen, J. B., & Stephan, M. (2009). Establishing social and socio-mathematical norms in an undergraduate mathematics content course for prospective teachers: The role of the instructor. In D. S. Mewborn & H. S. Lee (Eds.), AMTE monograph 6: Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 4366). AMTE.

    • Search Google Scholar
    • Export Citation
  • 9.

    Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79(2), 10081043. https://doi.org/10.3102/0034654309332562

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 10.

    Esmonde, I., & Langer-Osuna, J. M. (2013). Power in numbers: Student participation in mathematical discussions in heterogeneous spaces. Journal for Research in Mathematics Education, 44(1), 288315. https://doi.org/10.5951/jresematheduc.44.1.0288

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 11.

    Feldman, Z. (2014). Rethinking factors. Mathematics Teaching in the Middle School, 20(4), 230236. https://doi.org/10.5951/mathteacmiddscho.20.4.0230

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 12.

    Franke, M. L., Turrou, A. C., Webb, N. M., Ing, M., Wong, J., Shin, N., & Fernandez, C. (2015). Student engagement with others’ mathematical ideas: The role of teacher invitation and support moves. The Elementary School Journal, 116(1), 126148. https://doi.org/10.1086/683174

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13.

    Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2009). Constructing competence: An analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematics, 70(1), 4970. https://doi.org/10.1007/s10649-008-9141-5

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 14.

    Gutiérrez, R. (2007). Context matters: Equity, success, and the future of mathematics education. In T. Lamberg & L. R. West (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 118). University of Nevada, Reno.

    • Search Google Scholar
    • Export Citation
  • 15.

    Gutiérrez, R. (2012). Context matters: How should we conceptualize equity in mathematics education? In B. Herbal-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies (pp. 1733). Springer Science & Business. Mathematics Education Library 55. https://doi.org/10.1007/978-94-007-2813-4_6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 16.

    Gutiérrez, R. (2018). Rehumanizing mathematics: A vision for the future [Video]. YouTube. https://youtu.be/D266LYIigS0

  • 17.

    Horn, I. S. (2008). Accountable argumentation as a participation structure to support learning through disagreement. Journal for Research in Mathematics Education, Monograph, 14, 97126.

    • Search Google Scholar
    • Export Citation
  • 18.

    Inagaki, K., Hatano, G., & Morita, E. (1998). Construction of mathematical knowledge through whole-class discussion. Learning and Instruction, 8(6), 503526. https://doi.org/10.1016/S0959-4752(98)00032-2

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 19.

    Jansen, A. (2009). Prospective elementary teachers’ motivation to participate in whole-class discussions during mathematics content courses for teachers. Educational Studies in Mathematics, 71(2), 145160. https://doi.org/10.1007/s10649-008-9168-7

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20.

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

  • 21.

    Jansen, A., Cooper, B., Vascellaro, S., & Wandless, P. (2016/2017). Rough-draft talk in mathematics classrooms. Mathematics Teaching in the Middle School, 22(5), 304307. https://doi.org/10.5951/mathteacmiddscho.22.5.0304

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 22.

    Kantamneni, N. (2020). The impact of the COVID-19 pandemic on marginalized populations in the United States: A research agenda. Journal of Vocational Behavior, 119, 103439. https://doi.org/10.1016/j.jvb.2020.103439

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 23.

    Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Stenhouse Publishers.

  • 24.

    Langer-Osuna, J. M. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107124. https://doi.org/10.1080/10986065.2016.1148529

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25.

    Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014). Prime time. Pearson.

  • 27.

    Martin, D. B., Gholson, M. L., & Leonard, J. (2010). Mathematics as gatekeeper: Power and privilege in the production of knowledge. Journal of Urban Mathematics Education, 3(2), 1224. https://doi.org/10.21423/jume-v3i2a95

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 28.

    Matthews, L. E., Jessup, N. A., & Sears, R. (2021). Looking for “us”: Power reimagined in mathematics learning for Black communities in the pandemic. Educational Studies in Mathematics, 108(1–2), 333350. https://doi.org/10.1007/s10649-021-10106-4

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 29.

    McDuffie, A. R., & Slavit, D. (2003). Utilizing online discussion to support reflection and challenge beliefs in elementary mathematics methods classrooms. Contemporary Issues in Technology and Teacher Education [Online serial], 2(4). https://citejournal.org/volume-2/issue-4-02/mathematics/utilizing-online-discussion-to-support-reflection-and-challenge-beliefs-in-elementary-mathematics-methods-classrooms

    • Search Google Scholar
    • Export Citation
  • 30.

    Moschkovich, J. (2012). How equity concerns lead to attention to mathematical discourse. In B. Herbal-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies (pp. 89105). Springer Science & Business. Mathematics Education Library 55. https://doi.org/10.1007/978-94-007-2813-4_6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 31.

    National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. http://doi.org/10.1787/9789264207585-en

    • Search Google Scholar
    • Export Citation
  • 32.

    O’Connor, C., Michaels, S., Chapin, S., & Harbaugh, A. G. (2017). The silent and the vocal: Participation and learning in whole-class discussion. Learning and Instruction, 48, 513. https://doi.org/10.1016/j.learninstruc.2016.11.003

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 33.

    Riggs, S. A., & Linder, K. E. (2016). Actively engaging students in asynchronous online classes (IDEA Paper #64). The IDEA Center.

  • 34.

    Ruef, J. L., Willingham, C. J., & Ahearn, M. R. (2022). Math and equity in the time of COVID: Teaching challenges and successes. International Electronic Journal of Mathematics Education, 17(2), em0681. https://doi.org/10.29333/iejme/11818

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 35.

    Thanheiser, E., & Jansen, A. (2016). Inviting prospective teachers to share rough draft mathematical thinking. Mathematics Teacher Educator, 4(2), 145163. https://doi.org/10.5951/mathteaceduc.4.2.0145

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 36.

    Van Dorn, A., Cooney, R. E., & Sabin, M. L. (2020). COVID-19 exacerbating inequalities in the US. The Lancet, 395(10232), 12431244. https://doi.org/10.1016/S0140-6736(20)30893-X

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 37.

    Webb, N. M., Franke, M. L., Ing, M., Turrou, A. C., Johnson, N. C., & Zimmerman, J. (2019). Teacher practices that promote productive dialogue and learning in mathematics classrooms. International Journal of Educational Research, 97, 176186. https://doi.org/10.1016/j.ijer.2017.07.009

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 38.

    Webb, N. M., Franke, M. L., Ing, M., Wong, J., Fernandez, C. H., Shin, N., & Turrou, A. C. (2014). Engaging with others’ mathematical ideas: Interrelationships among student participation, teachers’ instructional practices, and learning. International Journal of Educational Research, 63, 7993. https://doi.org/10.1016/j.ijer.2013.02.001

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 39.

    Yackel, E. (2001). Explanation, justification, and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 924). PME.

    • Search Google Scholar
    • Export Citation
  • 40.

    Yackel, E., & Cobb, P. (1996). Socio-mathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458477. https://doi.org/10.5951/jresematheduc.27.4.0458

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 41.

    Yeh, C. (2018). Democratic accountability in the neoliberal era: The politics of teaching and teacher education in mathematics classrooms. Policy Futures in Education, 16(6), 764780. https://doi.org/10.1177/1478210318776470

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 42.

    Yeh, C., & Otis, B. M. (2019). Mathematics for whom: Reframing and humanizing mathematics. Bankstreet Occasional Paper Series, 2019 (41). https://educate.bankstreet.edu/occasional-paper-series/vol2019/iss41/8

    • Search Google Scholar
    • Export Citation
  • 43.

    Zazkis, R. (2011). Divisibility and transparency of number representations. In C. Rasmussen & M. P. Carlson (Eds.), Making the connection: Research to practice in undergraduate mathematics education (pp. 8191). The Mathematical Association of America.

    • Search Google Scholar
    • Export Citation
  • 44.

    Zazkis, R. (1998). Odds and ends of odds and evens: An inquiry into students’ understanding of even and odd numbers. Educational Studies in Mathematics, 36(1), 7389. https://doi.org/10.1023/A:1003149901409

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 45.

    Zazkis, R., & Campbell, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers’ understanding. Journal for Research in Mathematics Education, 27(5), 540563. https://doi.org/10.5951/jresematheduc.27.5.0540

    • Crossref
    • Search Google Scholar
    • Export Citation
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