Analyzing elementary students’ access to cognitive-oriented positions in mathematics

Tye Campbell; Haleigh Sears

doi:10.29333/iejme/14191

Full Text (PDF)

Tye Campbell ¹ ^* , Haleigh Sears ²

More Detail

¹ Utah State University, Logan, UT, USA² Crandall University, Moncton, NB, CANADA^* Corresponding Author

Abstract

The effectiveness of group problem-solving in mathematics depends on the extent to which meaningful participation is distributed across all group members. One way to explore how participation is distributed within groups is by examining how students are positioned within group interactions. In this study, we explore the social instructional factors that cause elementary students to move in and out of positions that support cognitive engagement during collaborative problem-solving in mathematics. Using a case study analysis of three elementary students working in a group, we found five social instructional factors that caused students to move in and out of cognitive-oriented positions during group work in mathematics: (1) building an ally through common language, (2) physical access to the chalkboard and resources, (3) tone of voice, (4) teacher intervention, and (5) contestation from peers. The findings promote implications for effectively facilitating group work in mathematics.

Keywords

positioning theory
mathematics
group work
collaborative learning

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 19, Issue 1, February 2024, Article No: em0769

https://doi.org/10.29333/iejme/14191

Publication date: 10 Feb 2024

Article Views: 769

Article Downloads: 538

Open Access References How to cite this article

References

Barnes, M. (2004). The use of positioning theory in studying student participation in collaborative learning activities [Paper presentation]. The Annual Meeting of the Australian Association for Research in Education.
Barron, B. (2003). When smart groups fail. The Journal of the Learning Sciences, 12, 307-359. https://doi.org/10.1207/S15327809JLS1203_1
Barwell, R. (2005). Working on arithmetic word problems when English is an additional language. British Educational Research Journal, 31(3), 329-348. https://doi.org/10.1080/01411920500082177
Bishop, J. P. (2012). “She’s always been the smart one. I’ve always been the dumb one”: Identities in the mathematics classroom. Journal for Research in Mathematics Education, 43(1), 34-74. https://doi.org/10.5951/jresematheduc.43.1.0034
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. https://doi.org/10.1177/016146810811000302
Campbell, T. G., & Hodges, T. S. (2020). Using positioning theory to examine how students collaborate in groups in mathematics. International Journal of Educational Research, 103, 1-13. https://doi.org/10.1016/j.ijer.2020.101632
Capar, G., & Tarim, K. (2015). Efficacy of the cooperative learning method on mathematics achievement and attitude: A meta-analysis research. Educational Sciences: Theory and Practice, 15(2), 553-559.
Chan, M. C. E., Clarke, D., & Cao, Y. (2018). The social essentials of learning: An experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China. Mathematics Education Research Journal, 30(1), 39-50. https://doi.org/10.1007/s13394-017-0209-3
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
Dekker, R., & Elshout-Mohr, M. (2004). Teacher interventions aimed at mathematical level raising during collaborative learning. Educational Studies in Mathematics, 56(1), 39-65. https://doi.org/10.1023/B:EDUC.0000028402.10122.ff
Engle, R. A., Langer-Osuna, J. M., & McKinney de Royston, M. (2014). Toward a model of influence in persuasive discussions: Negotiating quality, authority, privilege, and access within a student-led argument. Journal of the Learning Sciences, 23(2), 245-268. https://doi.org/10.1080/10508406.2014.883979
Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79(2), 1008-1043. https://doi.org/10.3102/0034654309332562
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), 288-315. https://doi.org/10.5951/jresematheduc.44.1.0288
Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. Second Handbook of Research on Mathematics Teaching and Learning, 1(1), 225-256.
Kniffin, K. M., & Hanks, A. S. (2018). The trade-offs of teamwork among STEM doctoral graduates. American Psychologist, 73(4), 420. https://doi.org/10.1037/amp0000288
Kotsopoulos, D. (2010). When collaborative is not collaborative: Supporting student learning through self-surveillance. International Journal of Educational Research, 49(4-5), 129-140. https://doi.org/10.1016/j.ijer.2010.11.002
Kotsopoulos, D. (2014). The case of Mitchell’s cube: Interactive and reflexive positioning during collaborative learning in mathematics. Mind, Culture, and Activity, 21(1), 34-52. https://doi.org/10.1080/10749039.2013.790905
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practces for enhancing learning. Corwin.
Merriam, S. B. (1998). Qualitative research and case study applications in education. Jossey-Bass.
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Nieminen, J. H., Chan, M. C. E., & Clarke, D. (2022). What affordances do open-ended real-life tasks offer for sharing student agency in collaborative problem-solving? Educational Studies in Mathematics, 109(1), 115-136. https://doi.org/10.1007/s10649-02110074-9
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis: Striving to meet the trustworthiness criteria. International Journal of Qualitative Methods, 16(1), 1609406917733847. https://doi.org/10.1177/1609406917733847
OECD. (2017). PISA 2015 results: Collaborative problem solving. OECD Publishing. https://doi.org/10.1787/9789264285521-en
Powell, A. B., Fransciso, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435. https://doi.org/10.1016/j.jmathb.2003.09.002
Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76. https://doi.org/10.1207/S15327884MCA0801_04
Tait-McCutcheon, S. L., & Loveridge, J. (2016). Examining equity of opportunities for learning mathematics through positioning theory. Mathematics Education Research Journal, 28(2), 327-348. https://doi.org/10.1007/s13394-016-0169-z
van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional action (pp. 14-31). Wiley-Blackwell.
Wagner, D., & Herbel-Eisenmann, B. (2009). Re-mythologizing mathematics through attention to classroom positioning. Educational Studies in Mathematics, 72(1), 1-15. https://doi.org/10.1007/s10649-008-9178-5
Weissglass, J. (2000). No compromise on equity in mathematics education: Developing an infrastructure. In W. Secada (Ed.), Changing the faces of mathematics: Multiculturalism and gender equity (pp. 5-24). National Council of Teachers of Mathematics.
Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775-808. https://doi.org/10.5951/jresematheduc.44.5.0775
Wood, M. B., & Kalinec, C. A. (2012). Student talk and opportunities for mathematical learning in small group interactions. International Journal of Educational Research, 51, 109-127. https://doi.org/10.1016/j.ijer.2011.12.008
Yin, R. K. (2009). Case study research: Design and methods. SAGE.
Zhang, S., Cao, Y., Chan, M. C. E., & Wan, M. E. V. (2022). A comparison of meaning negotiation during collaborative problem solving in mathematics between students in China and Australia. ZDM-Mathematics Education, 54(2), 287-302. https://doi.org/10.1007/s11858-022-01335-9

How to cite this article

APA

Campbell, T., & Sears, H. (2024). Analyzing elementary students’ access to cognitive-oriented positions in mathematics. International Electronic Journal of Mathematics Education, 19(1), em0769. https://doi.org/10.29333/iejme/14191

Vancouver

Campbell T, Sears H. Analyzing elementary students’ access to cognitive-oriented positions in mathematics. INT ELECT J MATH ED. 2024;19(1):em0769. https://doi.org/10.29333/iejme/14191

AMA

Campbell T, Sears H. Analyzing elementary students’ access to cognitive-oriented positions in mathematics. INT ELECT J MATH ED. 2024;19(1), em0769. https://doi.org/10.29333/iejme/14191

Chicago

Campbell, Tye, and Haleigh Sears. "Analyzing elementary students’ access to cognitive-oriented positions in mathematics". International Electronic Journal of Mathematics Education 2024 19 no. 1 (2024): em0769. https://doi.org/10.29333/iejme/14191

Harvard

Campbell, T., and Sears, H. (2024). Analyzing elementary students’ access to cognitive-oriented positions in mathematics. International Electronic Journal of Mathematics Education, 19(1), em0769. https://doi.org/10.29333/iejme/14191

MLA

Campbell, Tye et al. "Analyzing elementary students’ access to cognitive-oriented positions in mathematics". International Electronic Journal of Mathematics Education, vol. 19, no. 1, 2024, em0769. https://doi.org/10.29333/iejme/14191