Mathematics Teachers’ Use of Content-specific Data for Dialogic Grouping
Keywords:
group learning, personal example space, personal and interpersonal, teachers’ grouping considerations, learning analyticsAbstract
Group composition affects learning by individuals. Dialogic pedagogy approaches demonstrate that this is particularly true when each grouped student knows something others do not (i.e., mutuality grouping). Learning analytics can help grouping by providing teachers with data on students’ content-specific learning. What are mathematics teachers’ considerations in grouping students based on such data? We analysed fifty-three acts of grouping by nine mathematics teachers, who used data about students’ solutions to a mathematical task on linear functions to group students into pairs. We propose a schematic model including two types of considerations: interpersonal (here, mutuality, encompassing, and similarity) and content-specific (here, methods of construction, function orientation, and correctness). In this study, encompassing was the leading interpersonal characteristic, and function orientation was the leading content-specific characteristic. Moreover, different teachers formed the same groups using various considerations. The teachers utilised learning analytics to group students, and we modelled their grouping considerations.
References
Abdu, R., Schwarz, B., & Mavrikis, M. (2015). Whole-class scaffolding for learning to solve mathematics problems together in a computer-supported environment. ZDM Mathematics Education, 47(7), 1163–1178. https://doi.org/10.1007/s11858-015-0719-y
Abdu, R., van Helden, G., Alberto, R., & Bakker, A. (2021). Multimodal dialogue in small-group mathematics learning. Learning, Culture and Social Interaction, 29, Article 100491. https://doi.org/10.1016/j.lcsi.2021.100491
Abdu, R., Olsher, S., & Yerushalmy, M. (2022). Pedagogical considerations for designing automated grouping systems: The case of the parabola. Digital Experiences in Mathematics Education, 8(1), 99–124. https://doi.org/10.1007/s40751-021-00095-7
Asterhan, C. S., Howe, C., Lefstein, A., Matusov, E., & Reznitskaya, A. (2020). Controversies and consensus in research on dialogic teaching and learning. Dialogic Pedagogy, 8. https://doi.org/10.5195/dpj.2020.312
Azmitia, M., & Montgomery, R. (1993). Friendship, transactive dialogues, and the development of scientific reasoning. Social Development, 2(3), 202–221. https://doi.org/10.1111/j.1467-9507.1993.tb00014.x
Barron, B. (2003). When smart groups fail. The Journal of the Learning Sciences, 12(3), 307–359. https://doi.org/10.1207/S15327809JLS1203_1
Calor, S. M., Dekker, R., van Drie, J. P., & Volman, M. L. (2022). Scaffolding small groups at the group level: Improving the scaffolding behavior of mathematics teachers during mathematical discussions. Journal of the Learning Sciences, 31(3), 369-407. https://doi.org/10.1080/10508406.2021.2024834
Chapman, O. (2012). Challenges in mathematics teacher education. Journal of Mathematics Teacher Education, 15(4), 263–270. https://doi.org/10.1007/s10857-012-9223-2
Chapman, K. J., Meuter, M., Toy, D., & Wright, L. (2006). Can’t we pick our own groups? The influence of group selection method on group dynamics and outcomes. Journal of Management Education, 30(4), 557–569. https://doi.org/10.1177/1052562905284872
Chen, C. M., & Kuo, C. H. (2019). An optimized group formation scheme to promote collaborative problem-based learning. Computers & Education, 133, 94–115. https://doi.org/10.1016/j.compedu.2019.01.011
Chen, L., Yoshimatsu, N., Goda, Y., Okubo, F., Taniguchi, Y., Oi, M., Konomi, S., Shimada, A., Ogata, H., & Yamada, M. (2019). Direction of collaborative problem-solving-based STEM learning by learning analytics approach. Research and Practice in Technology Enhanced Learning, 14(1), Article 24. https://doi.org/10.1186/s41039-019-0119-y
Cohen, E. G. (1994). Restructuring the classroom: Conditions for productive small groups. Review of Dducational Research, 64(1), 1–35. https://doi.org/10.3102/00346543064001001
Connor, C. M., Morrison, F. J., Fishman, B., Crowe, E. C., Al Otaiba, S., & Schatschneider, C. (2013). A longitudinal cluster-randomized controlled study on the accumulating effects of individualized literacy instruction on students’ reading from first through third grade. Psychological Science, 24(8), 1408–1419. https://doi.org/10.1177/0956797612472204
D’angelo, C. M., Roschelle, J., & Bratt, H. (2015). Using students’ speech to characterize group collaboration quality. In proceedings of the11th International Conference on Computer Supported Collaborative Learning: Exploring the Material Conditions of Learning, CSCL 2015 (pp. 819–820). International Society of the Learning Sciences (ISLS).
Dar, Y. (1985). Teachers' attitudes toward ability grouping: Educational considerations and social and organizational influences. Interchange,16(2), 17–38. https://doi.org/10.1007/BF01807206
Dekker, R., & Elshout-Mohr, M. (2004). Teacher interventions aimed at mathematical level raising during collaborative learning. Educational Studies in Mathematics, 56(1), 39–65.
Dillenbourg, P. (1999). What do you mean by collaborative learning? In P. Dillenbourg (Ed.), Collaborative learning: Cognitive and computational approaches (pp. 1–19). Elsevier.
Fagen, A. P., Crouch, C. H., & Mazur, E. (2002). Peer instruction: Results from a range of classrooms. The Physics Teacher, 40(4), 206–209. https://doi.org/10.1119/1.1474140
Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194. https://doi.org/10.1007/s10649-008-9143-3
Gutierrez-Santos, S., Mavrikis, M., Geraniou, E., & Poulovassilis, A. (2016). Similarity-based grouping to support teachers on collaborative activities in an exploratory mathematical microworld. IEEE Transactions on Emerging Topics in Computing, 5(1), 56–68. https://doi.org/10.1109/TETC.2016.2533318
Hopfenbeck, T. N., Zhang, Z., Sun, S. Z., Robertson, P., & McGrane, J. A. (2023). Challenges and opportunities for classroom-based formative assessment and AI: A perspective article. Frontiers in Education, 8, Article 1270700. https://doi.org/10.3389/feduc.2023.1270700
Hohenwarter, J., Hohenwarter, M., & Lavicza, Z. (2009). Introducing dynamic mathematics software to secondary school teachers: The case of GeoGebra. Journal of Computers in Mathematics and Science Teaching, 28(2), 135–146. https://www.learntechlib.org/p/30304/
Hoyles, C., Healy, L., & Sutherland, R. (1991). Patterns of discussion between pupil pairs in computer and non‐computer environments. Journal of Computer Assisted Learning, 7(4), 210–228. https://doi.org/10.1111/j.1365-2729.1991.tb00253.x
Johnson, D. W. & Johnson, R. T. (1989). Cooperation and competition: Theory and research. Interaction.
Johnson, D. W., & Johnson, R. T. (2002). Learning together and alone: Overview and meta‐analysis. Asia Pacific Journal of Education, 22(1), 95–105. https://doi.org/10.1080/0218879020220110
Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-2), 55–85. https://doi.org/10.1023/A:1012789201736
Kaddoura, M. (2013). Think pair share: A teaching learning strategy to enhance students' critical thinking. Educational Research Quarterly, 36(4), 3–24.
Koedinger, K. R., McLaughlin, E. A., & Heffernan, N. T. (2010). A quasi-experimental evaluation of an on-line formative assessment and tutoring system. Journal of Educational Computing Research, 43(4), 489–510. https://doi.org/10.2190/EC.43.4.d
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. https://doi.org/10.1016/j.jmathb.2011.11.002
Kop, P. M., Janssen, F. J., Drijvers, P. H., & van Driel, J. H. (2017). Graphing formulas: Unraveling experts’ recognition processes. The Journal of Mathematical Behavior, 45, 167–182. https://doi.org/10.1016/j.jmathb.2017.01.002
Kutnick, P., & Kington, A. (2005). Children's friendships and learning in school: Cognitive enhancement through social interaction? British Journal of Educational Psychology, 75(4), 521–538. https://doi.org/10.1348/000709904X24591
Lei, S. A., Kuestermeyer B. N., & Westmeyer, K. A. (2010). Group composition affecting student interaction and achievement: Instructors' perspectives. Journal of Instructional Psychology, 37(4), 317–325.
Lou, Y., Abrami, P. C., Spence, J. C., Poulsen, C., Chambers, B., & d’Apollonia, S. (1996). Within-class grouping: A meta-analysis. Review of Educational Research, 66(4), 423–458. https://doi.org/10.3102/00346543066004423
Lyman, F. (1981). The responsive classroom discussion. In A. S. Anderson (Ed.), Mainstreaming Digest (pp. 109–113). University of Maryland College of Education.
Maqtary, N., Mohsen, A., & Bechkoum, K. (2019). Group formation techniques in computer-supported collaborative learning: A systematic literature review. Technology, Knowledge and Learning, 24(2), 169–22.
Moschkovich, J. N. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239–277. https://doi.org/10.20935/AcadMatSci6212
Olsher, S., Yerushalmy, M., & Chazan, D. (2016). How might the use of technology in formative assessment support changes in mathematics teaching? For the Learning of Mathematics, 36(3), 11–18.
Olsher, S. (2022). Te (a) Ching to collaborate: Automatic assessment-based grouping recommendations and implications for teaching. In Proceedings of the 15th International Conference on Technology in Mathematics Teaching (p. 214). Aarhus University.
Olsher, S., Abdu, R., & Shalata, M. (2025). The relationships between student content-specific grouping and teachers-students’ interactions during online collaborative mathematical task solving. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-024-10382-w
Raković, M., Gašević, D., Hassan, S. U., Ruipérez Valiente, J. A., Aljohani, N., & Milligan, S. (2023). Learning analytics and assessment: Emerging research trends, promises and future opportunities. British Journal of Educational Technology, 54(1). 10–18.
Schwarz, B. B., De Groot, R., Mavrikis, M., & Dragon, T. (2015). Learning to learn together with CSCL tools. International Journal of Computer-Supported Collaborative Learning, 10(3), 239–271. https://doi.org/10.1007/s11412-015-9216-0
Schwarz, B. B., Neuman, Y., & Biezuner, S. (2000). Two wrongs may make a right...If they argue together! Cognition and Instruction, 18(4), 461–494. https://doi.org/10.1207/S1532690XCI1804_2
Schwartz, D. L. (1999). The productive agency that drives collaborative learning. In P. Dillenbourg (Ed.), Collaborative learning: Cognitive and computational approaches (p. 197–218). Elsevier.
Sinclair, N., Watson, A., Zazkis, R., & Mason, J. (2011). The structuring of personal example spaces. The Journal of Mathematical Behavior, 30(4), 291–303. https://doi.org/10.1016/j.jmathb.2011.04.001
Segal, A., Hindi, S., Prusak, N., Swidan, O., Livni, A., Palatnic, A., & Schwarz, B. (2017, June). Keeping the teacher in the loop: Technologies for monitoring group learning in real-time. In International Conference on Artificial Intelligence in Education (pp. 64–76). Springer.
Slavin, R. E. (1980). Cooperative learning. Review of Educational Research, 50(2), 315–342. https://doi.org/10.3102/00346543050002315
Slavin, R. E. (1987). Ability grouping and student achievement in elementary schools: A best-evidence synthesis. Review of Educational Research, 57(3), 293–336. https://doi.org/10.3102/00346543057003293
Stacey, K., Price, B., Steinle, V., Chick, H., & Gvozdenko, E. (September 28–October 1, 2009). SMART assessment for learning. Paper presented at the Conference of the International Society for Design and Development in Education, Cairns, Australia.
Stacey, K., & Wiliam, D. (2012). Technology and assessment in mathematics. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung, F. (Eds.),Third international handbook of mathematics education (pp. 721–751). Springer. https://doi.org/10.1007/978-1-4614-4684-2_23
Stanja, J., Gritz, W., Krugel, J., Hoppe, A., & Dannemann, S. (2023). Formative assessment strategies for students' conceptions—The potential of learning analytics. British Journal of Educational Technology, 54(1), 58–75. https://doi.org/10.1111/bjet.13288
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
Van den Bossche, P., Gijselaers, W., Segers, M., Woltjer, G., & Kirschner, P. (2011). Team learning: Building shared mental models. Instructional Science, 39(3), 283–301. https://doi.org/10.1007/s11251-010-9128-3
Webb, N. M. (2009). The teacher’s role in promoting collaborative dialogue in the classroom. The British Journal of Educational Psychology, 79 (1), 1–28.
Webb, N. M., Baxter, G. P., & Thompson, L. (1997). Teachers' grouping practices in fifth-grade science classrooms. The Elementary School Journal, 98(2), 91–113. https://doi.org/10.1086/461886
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, 79–93. https://doi.org/10.1016/j.ijer.2013.02.001
Wegerif, R. (2011). Towards a dialogic theory of how children learn to think. Thinking Skills and Creativity, 6(3), 179–190. https://doi.org/10.1016/j.tsc.2011.08.002
Wegerif, R., & Major, L. (2019). Buber, educational technology, and the expansion of dialogic space. AI & Society, 34, 109–119.
Wichmann, A., Hecking, T., Elson, M., Christmann, N., Herrmann, T., & Hoppe, H. U. (2016, August). Group formation for small-group-learning: Are heterogeneous groups more productive? In Proceedings of the 12th International Symposium on Open Collaboration, Article 14. https://doi.org/10.1145/2957792.2965662
Wise, A. F., Knight, S., & Ochoa, X. (2021). What makes learning analytics research matter. Journal of Learning Analytics, 8(3), 1–9. https://doi.org/10.18608/jla.2021.7647
Wise, A. F., & Schwarz, B. B. (2017). Visions of CSCL: Eight provocations for the future of the field. International Journal of Computer-Supported Collaborative Learning, 12(4), 423–467. https://doi.org/10.1007/s11412-017-9267-5
Yerushalmy, M., Nagari-Haddif, G., & Olsher, S. (2017). Design of tasks for online assessment that supports understanding of students’ conceptions. ZDM Mathematics Education, 49, 701–716. https://doi.org/10.1007/s11858-017-0871-7
Yerushalmy, M. (2020). Seeing the entire picture with STEP: An example-eliciting approach to online formative assessment. In B. Barzel & F. Schacht (Eds.), Proceedings of the 14th International Conference on Technology in Mathematics Teaching, Essen, Germany, July 2019. https://nbn-resolving.org/urn:nbn:de:hbz:464-20191119-153831-9
Zhang, P., Ding, L., & Mazur, E. (2017). Peer instruction in introductory physics: A method to bring about positive changes in students’ attitudes and beliefs. Physical Review Physics Education Research, 13(1), Article 010104. https://doi.org/10.1103/PhysRevPhysEducRes.13.010104
