Cognitive and social skills in collaborative solution of mathematical problems

Keywords: Collaborative Problem Solving, mathematical tasks, social skills, cognitive skills, graph theory

Abstract

[Objective] The objective of this study was to analyze the cognitive and social skills of a group of students and their teacher in an exercise based on Collaborative Problem Solving (CPR) in Mathematics. [Methodology] A study was carried out by selecting one of the 8 groups of 4 students randomly assigned in a non-curricular exercise scheduled in 24 biweekly sessions of 90 minutes. The group selected consisted of 4 female students. The sessions were recorded, and data on the interactions between subjects (students and teacher) were coded at the beginning and at the end of the exercise for factors including skills of representation, regulation, communication and roles assumed in group work, and interaction with the teacher. The coded data were subsequently analyzed using asymmetric graph analysis techniques to measure the intensity of interactions, and correspondence analysis to determine the significance of relationships between the sub-skills involved. Rstudio software was used to carry out the analysis. [Results] A significant change in the intensity of interactions between participants was observed throughout the implementation with respect to the centrality and closeness indices associated with the graphs obtained. [Conclusions] The systematic CPR work in mathematics carried out in the exercise promotes and modifies social and cognitive skills and their interaction.

References

Araujo, R. C., & Gadanidis, G. (2020). Online collaborative mind mapping in a mathematics teacher education program: a study on student interaction and knowledge construction. ZDM, 52(5), 943-958. https://doi.org/10.1007/s11858-019-01125-w
Andrews-Todd, J., & Forsyth, C. M. (2020). Exploring social and cognitive dimensions of collaborative problem solving in an open online simulation-based task. Computers in human behavior, 104, 105-759. https://doi.org/10.1016/j.chb.2018.10.025
Brodbeck, F. C., & Greitemeyer, T. (2000). Effects of individual versus mixed individual and group experience in rule induction on group member learning and group performance. Journal of Experimental Social Psychology, 36(6), 621-648. https://doi.org/10.1006/jesp.2000.1423
Camacho-Morles, J., Slemp, G. R., Oades, L. G., Morrish, L., & Scoular, C. (2019). The role of achieve- ment emotions in the collaborative problem-solving performance of adolescents. Learning and Individual Differences, 70, 169–181. https://doi.org/10.1016/j.lindif.2019.02.005
Care, E. (2018). Twenty-first century skills: From theory to action. Educational Assessment in an Information Age, 3-17. https://doi.org/10.1007/978-3-319-65368-6_1
Care, E., Griffin, P., Scoular, C., Awwal, N., & Zoanetti, N. (2015). Collaborative problem solving tasks. Educational Assessment in an Information Age, 85-104. https://doi.org/10.1007/978-94-017-9395-7_4
Carlana, M. (2019). Implicit Stereotypes: Evidence from Teachers’ Gender Bias. The Quarterly Journal of Economics, 134(3), 1163–1224, 10.1093/qje/qjz008
Chan, M. Ch. E., & Clarke, D. (2017). Structured affordances in the use of open-ended tasks to facilitate collaborative problem solving. ZDM Mathematics Education, 49, 951–963. https://doi.org/10.1007/s11858-017-0876-2
Chung, Y., Yoo, J., Kim, S., Lee, H., & Zeidler, D. L. (2016). Enhancing students’ communication skills in the science classroom through socioscientific issues. International Journal of Science and Mathematics Education, 14, 1-27. https://doi.org/10.1007/s10763-014-9557-6
Clark, H. H. (1996). Using language. Cambridge MA: Cambridge University Press.
Cooke, N. J., Kiekel, P. A., Salas, E., Stout, R., Bowers, C., & Cannon-Bowers, J. (2003). Measuring team knowledge: A window to the cognitive underpinnings of team performance. Group Dynamics: Theory, Research, and Practice, 7(3), 179–199. https://doi.org/10.1037/1089-2699.7.3.179
Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Palo Alto, CA: Learning Policy Institute. https://doi.org/10.54300/122.311
DiDonato, N. C. (2013). Effective self- and co-regulation in collaborative learning groups: An analysis of how students regulate problem solving of authentic interdisciplinary tasks. Instructional Science, 41, 25–47. https://doi.org/10.1007/s11251-012-9206-9
Dowell, N. M., Lin, Y., Godfrey, A., & Brooks, C. (2020). Exploring the Relationship between Emergent Sociocognitive Roles, Collaborative Problem-Solving Skills, and Outcomes: A Group Communication Analysis. Journal of Learning Analytics, 7(1), 38-57. https://doi.org/10.18608/jla.2020.71.4
Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88, 89–114. https://doi.org/10.1007/s10649-014-9577-8
Erduran, S., Simon, S., & Osborne, J. (2004). TAPping into Argumentation: Developments in the Application of Toulmin’s Argument Pattern for Studying Science Discourse. Science Education, 88(6), 915-933. https://doi.org/10.1002/sce.20012
Fiore, S. M., Carter, D. R., & Asencio, R. (2015). Conflict, trust, and cohesion: Examining affective and attitudinal factors in science teams. In E. Salas, W. B. Vessey & A. X. Estrada (Eds.), Team Cohesion: Advances in Psychological Theory, Methods and Practice, 271-301. Emerald Group Publishing Limited. https://doi.org/10.1108/s1534-085620150000017011
Gentrup, S., & Rjosk, C. (2018). Pygmalion and the gender gap: do teacher expectations contribute to differences in achievement between boys and girls at the beginning of schooling? Educational Research and Evaluation, 24(3-5), 295-323, https://doi.org/10.1080/13803611.2018.1550840
Goffman, E. (1972). Interaction ritual: Essays on face-to-face behavior. Harmondsworth, Middlesex: Penguin University Books.
Graesser, A. C., Fiore, S. M., Greiff, S., Andrews-Todd, J., Foltz, P. W., & Hesse, F. W. (2018). Advancing the science of collaborative problem solving. Psychological Science in the Public Interest, 19(2), 59-92. https://doi.org/10.1177/1529100618808244
Griffin, P., & Care, E. (2015). Assessment and teaching of 21st century skills: Methods and approach. Educational Assessment in an Information Age. https://doi.org/10.1007/978-94-017-9395-7
Gu, X., Chen, S., & Zhu, W. (2015). An intervention framework designed to develop the collaborative problem-solving skills of primary school students. Education Tech Research Dev, 63, 143–159. https://doi.org/10.1007/s11423-014-9365-2
Hesse, F., Care, E., Buder, J., Sassenberg, K., & Griffin, P. (2015). A framework for teachable collaborative problem solving skills. In P. Griffin and E. Care (Eds.), Assessment and teaching of 21st century skills: Methods and approach. Educational Assessment in an Information Age, 37-56. https://doi.org/10.1007/978-94-017-9395-7_2
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
Laughlin, P. R. (2013). Group problem solving. Princeton University Press.
Law, V., Ge, X., & Eseryel, D. (2016). The Development of a Self-regulation in a Collaborative Context Scale. Tech Know Learn, 21, 243–253. https://doi.org/10.1007/s10758-016-9274-z
Linzer, D. A., & Lewis, J. B. (2011). An R package for polytomous variable latent class analysis. Journal of statistical software, 42(10), 1-29. https://doi.org/10.18637/jss.v042.i10
Marchant, P., Cornejo, C., & Felmer, P. (2022). Student Insights in Mathematics Problem Solving: Cognition, Affect, and Gesture. Int J of Sci and Math Educ. https://doi.org/10.1007/s10763-022-10270-w
Mayer, R. E. (1992). Thinking, problem solving, cognition. WH Freeman/Times Books/Henry Holt & Co.
Müller, A., Bellhäuser, H., Konert, J., & Röpke, R. (2021). Effects of group formation on student satisfaction and performance: a field experiment. Small Group Research, (2), 244-273. https://doi.org/10.1177/1046496420988592
OCDE. (2017). PISA 2015 Collaborative problem solving Framework, PISA, OCDE Publishing, Paris. https://www.oecd.org/pisa/pisaproducts/Draft%20PISA%202015%20Collaborative%20Problem%20Solving%20Framework%20.pdf
Pekrun, R. (2019). Achievement emotions: A control-value theory perspective. In R. Patulny, A. Bellocchi, R. E. Olson, S. Khorana, J. McKenzie. & M. Peterie (Eds.), Emotions in late modernity,142–157. Routledge/Taylor & Francis Group. https://doi.org/10.4324/9781351133319-13
Peterson, R. S., & Behfar, K. J. (2004). Leadership as group regulation. In The psychology of leadership, 157-178. Psychology Press.
Pruner, M., & Liljedahl, P. (2021). Collaborative problem solving in a choice-affluent environment. ZDM–Mathematics Education, 1-18. https://doi.org/10.1007/s11858-021-01232-7
Recber, S., Isiksal, M., & Koc, Y. (2017). Investigando la autoeficacia, la ansiedad, las actitudes y los logros de las matemáticas con respecto al género y el tipo de escuela. Anales de Psicología, 34(1), 41–51. https://doi.org/10.6018/analesps.34.1.229571
Roschelle, J. & Teasley, S. D. (1995). The Construction of Shared Knowledge in Collaborative Problem Solving. Computer Supported Collaborative Learning, 69–97. https://doi.org/10.1007/978-3-642-85098-1_5
Saadati, F., Chandia, E., Cerda, G. (2021). Self-efficacy, practices, and their relationships; the impact of a professional development program for mathematics teachers. J Math Teacher Educ. https://doi.org/10.1007/s10857-021-09523-2
Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. Liberal education in a knowledge society, 97, 67-98.
Smith, J. M., & Mancy, R. (2018). Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean by collaborative metacognition?. Research in Mathematics Education, 20(1), 14-36. https://doi.org/10.1080/14794802.2017.1410215
Scoular, C., & Care, E. (2020). Monitoring patterns of social and cognitive student behaviors in online collaborative problem solving assessments. Computers in Human Behavior, 104, 105-874. https://doi.org/10.1016/j.chb.2019.01.007
Stadler, M., Herborn, K., Mustafić, M. & Greiff, S. (2020). The assessment of collaborative problem solving in PISA 2015: An investigation of the validity of the PISA 2015 CPS tasks. Computers & Education, 157, 103-964. https://doi.org/10.1016/j.compedu.2020.103964
Stasser, G., & Abele, S. (2020). Collective choice, collaboration, and communication. Annual Review of Psychology, 71, 589-612. https://doi.org/10.1146/annurev-psych-010418-103211
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: An International Journal, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
Tang, P., Liu, H., & Wen, H. (2021, April). Factors Predicting Collaborative Problem Solving: Based on the Data From PISA 2015. In Frontiers in Education, 6, 130. Frontiers. https://doi.org/10.3389/feduc.2021.619450
Trilling, B., & Fadel, C. (2009). 21st century skills: Learning for life in our times. John Wiley & Sons.
Trötschel, R., Hüffmeier, J., Loschelder, D. D., Schwartz, K., & Gollwitzer, P. M. (2011). Perspective taking as a means to overcome motivational barriers in negotiations: When putting oneself into the opponent's shoes helps to walk toward agreements. Journal of personality and social psychology, 101(4), 771. https://doi.org/10.1037/a0023801
UNESCO. (2017). Report E2030: Education and skills for the 21st century. Regional Meeting of Ministers of Education of Latin America and the Caribbean, Buenos Aires, Argentina. http://www.unesco.org/new/fileadmin/MULTIMEDIA/FIELD/Santiago/pdf/Meeting-Report-Buenos-Aires-2017-E2030-LAC-ENG.pdf
Van Knippenberg, D., & Schippers, M. C. (2007). Work group diversity. Annual Review of Psychology, 58, 515–541. https://doi.org/10.1146/annurev.psych.58.110405.085546
Von Davier, A. A., Zhu, M. & Kyllonen, P. C. (Eds.). (2017). Innovative assessment of collaboration. Springer.
Webb, N. M., Ing, M., Burnheimer, E., Johnson, N. C., Franke, M. L., & Zimmerman, J. (2021). Is there a right way? Productive patterns of interaction during collaborative problem solving. Education Sciences, 11(5), 214. https://doi.org/10.3390/educsci11050214
Zhuang, X., MacCann, C., Wang, L., Liu, L., & Roberts, R. D. (2008). Development and validity evidence supporting a teamwork and collaboration assessment for high school students. ETS Research Report Series, (2), i-51. https://doi.org/10.1002/j.2333-8504.2008.tb02136.x
Published
2022-11-01
How to Cite
Chandia, E., Huencho, A., Pérez, C., Ortiz, A., & Cerda, G. (2022). Cognitive and social skills in collaborative solution of mathematical problems. Uniciencia, 36(1), 1-26. https://doi.org/10.15359/ru.36-1.50
Section
Original scientific papers (evaluated by academic peers)

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