Social affordances in students’ mathematical modelling with digital tools
DOI:
https://doi.org/10.7146/nomad.v30i4.164209Keywords:
mathematicsAbstract
This study explores the social affordances that emerge from group interactions when students use digital tools in mathematical modelling activities. Drawing on video recordings and screen-capture data, we analyzed the collaborative work of four groups of 14-17-year-old students as they engaged with two mathematical modelling tasks. Using Gibson’s Affordance Theory as an analytical lens, we identified three key social affordances of digital tools: common focus, observing and improving strategies, and authority of the digital tool. These social affordances shaped collaboration, though some were not completely actualized due to constraints that hindered the students’ working process. The findings demonstrate how digital tools mediate social interaction in mathematical modelling, highlighting the interplay between affordances, constraints and the learning context.
References
Afram, O. O. (2023). An activity theory analysis of group interactions in mathematical modelling with the aid of digital technologies. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 1103–1110). Alfréd Rényi Institute of Mathematics and ERME.
Afram, O. O. (2024). Students’ mathematical modelling with the aid of digital technologies: An Activity and Affordance Theory perspective [Doctoral dissertation]. University of Agder Theses and Dissertations Archive.
Anderson, C., & Robey, D. (2017). Affordance potency: Explaining the actualization of technology affordances. Information and Organization, 27(2), 100–115. https://doi.org/10.1016/j.infoandorg.2017.03.002
Bærentsen, K. B., & Trettvik, J. (2002). An activity theory approach to affordance. In O. W. Bertelsen, S. Boedker, & K. Kuutti (Eds.), Proceedings of the Second Nordic Conference on Human-Computer Interaction, (pp. 51–60). Association for Computing Machinery.
https://doi.org/10.1145/572020.572028
Berget, I. K. L. (2022). Mathematical modelling in textbook tasks and national examination in Norwegian upper secondary school. Nordic Studies in Mathematics Education, 27(1), 51–70.
https://doi.org/10.7146/nomad.v27i1.149184
Bernhard, E., Recker, J., & Burton-Jones, A. (2013). Understanding the actualization of affordances: A study in the process modeling context. In M. Chau, & R. Baskerville (Eds.), Proceedings of the 34th International Conference on Information Systems (pp. 1–11). Association for Information Systems.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do?. In S. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Springer.
https://doi.org/10.1007/978-3-319-12688-3_9
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics-ICTMA 12, (pp. 222–231). Horwood Publishing.
https://doi.org/10.1533/9780857099419.5.221
Borba, M. C., & Villarreal, M. E. (2006). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, visualization and experimentation (Vol. 39). Springer Science & Business Media. https://doi.org/10.1007/b105001
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.
https://doi.org/10.1191/1478088706qp063oa
Caviola, S., Carey, E., Mammarella, I. C., & Szucs, D. (2017). Stress, time pressure, strategy selection and math anxiety in mathematics: A review of the literature. Frontiers in Psychology, 8, 1488.
https://doi.org/10.3389/fpsyg.2017.01488
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109, 205–236.
https://doi.org/10.1007/s10649-021-10104-6
Chiappini, G. (2013). Cultural affordances of digital artifacts in the teaching and learning of mathematics. In E. Faggiano, & A. Montone (Eds.), Proceedings of ICTMT11 (pp. 95–100). University of Bari (Università degli Studi di Bari).
Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Cambridge: Cambridge University Press.
English, L. D., Ärlebäck, J. B., & Mousoulides, N. (2016). Reflections on progress in mathematical modelling research. In Á. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 383–413). Brill.
https://doi.org/10.1007/978-94-6300-561-6_11
Esmonde, I. (2009). Mathematics learning in groups: Analyzing equity in two cooperative activity structures. The Journal of the Learning Sciences, 18(2), 247–284. https://doi.org/10.1080/10508400902797958
Geiger, V., Faragher, R., & Goos, M. (2010). CAS-enabled technologies as ’agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms. Mathematics Education Research Journal, 22(2), 48–68. https://doi.org/10.1007/BF03217565
Geiger, V., & Frejd, P. (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In G. Stillman, W. Blum, & M. Salett Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 161–171). Springer.
https://doi.org/10.1007/978-3-319-18272-8_12
Gibson, J. J. (1977). The theory of affordances. In R. Shaw, & J. Bransford (Eds.), Perceiving, acting and knowing. Lawrence Erlbaum.
Gibson, J. J. (2014). The ecological approach to visual perception: Classic edition. Psychology Press.
Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49(2), 193–223.
https://doi.org/10.1023/A:1016209010120
Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. The Journal of Mathematical Behavior, 22(1), 73–89.
https://doi.org/10.1016/S0732-3123(03)00005-1
Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48–62. https://doi.org/10.1016/j.jmathb.2014.11.001
Greefrath, G., Hertleif, C., and Siller, H.-S. (2018). Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software. ZDM – Mathematics Education, 50(1), 233–244.
https://doi.org/10.1007/s11858-018-0924-6
Greefrath, G., & Siller, H. S. (2017). Modelling and simulation with the help of digital tools. In G. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications (pp. 529–539). Springer.
https://doi.org/10.1007/978-3-319-62968-1_44
Hadjerrouit, S. (2017). Assessing the affordances of SimReal+ and their applicability to support the learning of mathematics in teacher education. Issues in Informing Science & Information Technology, 14, 121–138. SciTePress.
Hadjerrouit, S. (2019). Investigating the affordances and constraints of SimReal for mathematical learning: A case study in teacher education. In H. Lane, S. Zvacek & J. Uhomoibhi (Eds.), Proceedings of the 11th International Conference on Computer Supported Education, 2, 27–37. SciTePress.
https://doi.org/10.5220/0007588100270037
Hadjerrouit, S. (2020). Using Affordances and Constraints to Evaluate the Use of a Formative e-Assessment System in Mathematics Education. In H. Lane, S. Zvacek & J. Uhomoibhi (Eds.), Proceedings of the 12th International Conference on Computer Supported Education, 1, 366–373.
https://doi.org/10.5220/0009352503660373
Hankeln, C. (2020). Validating with the Use of Dynamic Geometry Software. In G. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 277–286). Springer.
https://doi.org/10.1007/978-3-030-37673-4_24
Hernandez-Martinez, P., & Harth, H. (2015). An activity theory analysis of group work in mathematical modelling. In T. Muir, J. Wells, & K. Beswick (Eds.), Proceedings of 39th Psychology of Mathematics Education Conference (Volume 3) (pp. 57–64). PME.
Jacinto, H., & Carreira, S. (2017). Mathematical problem solving with technology: The techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15(6), 1115–1136. https://doi.org/10.1007/s10763-016-9728-8
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM – Mathematics Education, 38(3), 302–310. https://doi.org/10.1007/BF02652813
Kirschner, P., Strijbos, J. W., Kreijns, K., & Beers, P. J. (2004). Designing electronic collaborative learning environments. Educational Technology Research and Development, 52(3), 47–66.
https://doi.org/10.1007/BF02504675
Leonardi, P. M. (2013). When does technology use enable network change in organizations? A comparative study of feature use and shared affordances. MIS Quarterly, 749–775.
Lowrie, T. (2011). ”If this was real”: Tensions between using genuine artefacts and collaborative learning in mathematics tasks. Research in Mathematics Education, 13(1), 1–16. https://doi.org/10.1080/14794802.2011.550707
Markus, M. L., & Silver, M. S. (2008). A foundation for the study of IT effects: A new look at DeSanctis and Poole’s concepts of structural features and spirit. Journal of the Association for Information Systems, 9(10), 5.
https://doi.org/10.17705/1jais.00176
Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. (2019). Research trends in digital technologies and modeling in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), 1–13. https://doi.org/10.29333/ejmste/108438
Mousoulides, N. G. (2011). GeoGebra as a conceptual tool for modeling real-world problems. In L. Bu, & R. Schoen (Eds.), Model-Centered Learning. Modeling and Simulations for Learning and Instruction, 6, 105–118. Brill.
https://doi.org/10.1007/978-94-6091-618-2_8
Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge. https://doi.org/10.4324/9781315189314
Pedersen, S., & Bang, J. (2016). Historicizing affordance theory: A rendezvous between ecological psychology and cultural-historical activity theory. Theory & Psychology, 26(6), 731–750.
https://doi.org/10.1177/0959354316669021
Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1(6), 3–21.
Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematical Learning, 15(1), 1–20. https://doi.org/10.1007/s10758-010-9158-6
Roschelle, J., & Teasley, S. D. (1995). The construction of shared knowledge in collaborative problem solving. In C. O’Malley (Ed.), Computer Supported Collaborative Learning. NATOASI Series, vol 128, 69–97. Springer.
https://doi.org/10.1007/978-3-642-85098-1_5
Siller, HS., Geiger, V., Greefrath, G. (2023). The role of digital resources in mathematical modelling in extending mathematical capability. In B. Pepin, G. Gueudet, & J. Choppin. (Eds.), Handbook of digital resources in mathematics education Springer international handbooks of education (pp. 1–24). Springer. https://doi.org/10.1007/978-3-030-95060-6_18-1
Stillman, G. A. (2019). State of the art on modelling in mathematics education—Lines of inquiry. In G. Stillman, & J. Brown (Eds.), Lines of inquiry in mathematical modelling research in education, ICME-13 Monographs, 1–20. Springer. https://doi.org/10.1007/978-3-030-14931-4_1
Strong, D. M., Volkoff, O., Johnson, S. A., Pelletier, L. R., Tulu, B., Bar-On, I., Trudel, J., & Garber, L. (2014). A theory of organization-EHR affordance actualization. Journal of the Association for Information Systems, 15(2), 53–85. https://doi.org/10.17705/1jais.00353
Turner, P., & Turner, S. (2002). An affordance-based framework for CVE evaluation. In X. Faulkner, J. Finlay, & F. Détienne (Eds.), People and Computers XVI-Memorable Yet Invisible (pp. 89–103). Springer, London. https://doi.org/10.1007/978-1-4471-0105-5_6
Volkoff, O., & Strong, D. M. (2013). Critical realism and affordances: Theorizing IT-associated organizational change processes. MIS Quarterly, 37(3), 819–834. https://www.jstor.org/stable/43826002
Volkoff, O., & Strong, D. M. (2017). Affordance theory and how to use it in IS research. In R. D. Galliers, & M.-K. Stein (Eds.), The Routledge Companion to Management Information Systems (pp. 232–245). Routledge.
https://doi.org/10.4324/9781315619361.ch16
Vos, P., & Frejd, P. (2022). The modelling cycle as analytic research tool and how it can be enriched beyond the cognitive dimension. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Twelfth Congress of the European Society for Research in Mathematics Education. (pp. 1185–1192). Free University of Bozen-Bolzano and ERME.
Wang, H., Wang, J., & Tang, Q. (2018). A review of application of affordance theory in information systems. Journal of Service Science and Management, 11(1), 56–70. https://doi.org/10.4236/jssm.2018.111006
Wertsch, J. V. (1998). Mind as action. Oxford University Press.
Yerushalmy, M. (2000). Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra. Educational Studies in Mathematics, 43(2), 125–147.
https://doi.org/10.1023/A:1017566031373
Zengin, Y. (2021). Students’ understanding of parametric equations in a collaborative technology-enhanced learning environment. International Journal of Mathematical Education in Science and Technology, 54(5), 740–766. https://doi.org/10.1080/0020739X.2021.1966848
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
