Abstract
Problem solving is a distinctive human activity that shapes and influences what individuals do when facing social, professional, or academic situations. Reflecting on what the process of identifying, formulating, and solving problems involves becomes a relevant task to understand how people develop resources, strategies, and ways of reasoning to solve problems in different domains. How are mathematical problems formulated? And what does the process of approaching and solving problems involve? How do students develop problem-solving competencies? How do teachers and students’ use of digital tools shape the ways they reason and solve mathematical problems? These questions have inspired mathematicians and mathematics educators to investigate what the process of formulating and solving mathematical problems entails and ways for students to understand mathematical concepts and to solve problems. In this chapter, some seminal conceptual frameworks are reviewed to shed light on principles and tenets to support and frame learning scenarios that foster students’ problem-solving competencies. Further, the consistent and systematic use of digital technologies becomes relevant for learners to enhance their ways of reasoning to work on mathematical tasks and to engage in and extend mathematical discussions beyond classrooms. Thus, digital tools provide a set of affordances for students to dynamically model tasks and rely on heuristic strategies such as orderly dragging objects, quantifying parameters, tracing loci, using sliders, etc. to work and solve the problems.
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Notes
- 1.
The term tool is used to refer to artefacts (concrete or symbolic ones) that individuals transform into an instrument to represent, explore, and solve mathematical problems.
References
Arcavi, A. (2020). From tools to resources in the professional development of mathematics teachers. In S. Llinares & O. Chapman (Eds.), International handbook of mathematics teacher education: Volume 2, tools and processes in mathematics teacher education (pp. 421–440). Koninklijke Brill NV. https://doi.org/10.1163/9789004418967_016
Arzarello, F., et al. (2021). Experimental approaches to theoretical thinking: Artefacts and proofs. In G. Hanna & M. de Villiers (Eds.), New ICMI Study Series. Proof and proving in mathematics education. https://doi.org/10.1007/978-94-007-2129-6_5
Atweh, B., Kaur, B., Nivera, G., Abadi, A., & Thinwiangthong, S. (2022). Futures for post-pandemic mathematics teacher education: Responsiveness and responsibility in the face of a crisis. ZDM Mathematics Education. https://doi.org/10.1007/s11858-022-01394-y
Berger, W. (2014). A more beautiful question. Bloomsbury Publishing. Kindle Edition.
Cai, J., & Hwang, S. (2019). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2019.01.001
Cropley, D. H. (2019). Homo Problematis Solvendis—Problem-solving Man. Springer. https://doi.org/10.1007/978-981-13-3101-5_13
Engelbrecht, J., & Oates, G. (2021). Student collaboration in blending digital technology in the learning of mathematics. In M. Danesi (Ed.), Handbook of cognitive mathematics (pp. 1–39). https://doi.org/10.1007/978-3-030-44982-7_37-1
English, L. (2019). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2019.06.014
Foster, C., Burkhardt, H., & Schoenfeld, A. (2022). Crisis-ready educational design: The case of mathematics. The Curriculum Journal, 00, 1–17. https://doi.org/10.1002/curj.159
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Information Age Publishing.
Li, Y., Silver, E. A., & Li, S. (2014). Transforming mathematics instruction: What do we know and what can we learn from multiple approaches and practices? In Y. Li et al. (Eds.), Advances in Mathematics Education. Transforming mathematics instruction: Multiple approaches and practices (pp: 1–12). Springer. https://doi.org/10.1007/978-3-319-04993-9_1
Liljedahl, P., & Santos-Trigo, M. (Eds.). (2019). Mathematical problem solving, current themes, trends, and research. ICME-13 monographs. Springer.https://doi.org/10.1007/978-3-030-10472-6_4
McKnight, K., O’Malley, K., Ruzic, R., Horsley, M. K., Franey, J. J., & Bassett, K. (2016). Teaching in a digital age: How educators use technology to improve student learning. Journal of Research on Technology in Education, 48(3), 194–211. https://doi.org/10.1080/15391523.2016.1175856
Monaghan, J., & Trouche, L. (2016). Introduction to the book. In J. Monaghan, et al. (Eds.), Mathematics Education Library. Tools and mathematics (pp. 3–12). Springer. https://doi.org/10.1007/978-3-319-02396-0_1
Polya, G. (1945). How to solve it. Princeton University.
Ruthven, K. (2022). Ergonomic, epistemological and existential challenges of integrating digital tools into school mathematics. Asian Journal for Mathematics Education, I(I), 7–18. https://doi.org/10.1177/27527263221077314
Santos-Trigo, M. (2019). Mathematical problem solving and the use of digital technologies. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical Problem Solving. ICME 13 monographs (pp. 63–89). Springer Nature ISBN 978-3-030-10471-9, ISBN 978-3-030-10472-6. https://doi.org/10.1007/978-3-030-10472-6_4
Santos-Trigo, M. (2020a). Problem-solving in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 686–693). Springer.
Santos-Trigo, M. (2020b). Prospective and practicing teachers and the use of digital technologies in mathematical problem-solving approaches. In S. Llinares & O. Chapman (Eds.), International handbook of mathematics teacher education: volume 2, tools and processes in mathematics teacher education (pp. 163–195). Koninklijke Brill NV. https://doi.org/10.1163/9789004418967_007
Santos-Trigo, M. (2022). Intertwining cumulated and current mathematical problem-solving developments to frame and support teaching practices. In C. Fernández, S. Llinares, A. Gutiérrez & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 35–50). PME.
Santos-Trigo, M., Barrera-Mora, F., & Camacho-Machín, M. (2021). Teachers’ use of technology affordances to contextualize and dynamically enrich and extend mathematical problem-solving strategies. Mathematics, 9(8), 793. https://doi.org/10.3390/math9080793
Santos-Trigo, M., & Reyes-Martínez, I. (2019). High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies. International Journal of Mathematical Education in Science and Technology, 50(2), 182–201. https://doi.org/10.1080/0020739X.2018.1489075
Santos-Trigo, M., Reyes-Martínez, I., & Gómez-Arciga, A. (2022a). A conceptual framework to structure remote learning scenarios: A digital wall as a reflective tool for students to develop mathematics problem-solving competencies. International Journal of Learning Technology, 17(1), 27–52.
Santos-Trigo, M., Reyes-Martínez, I., & Gómez-Arciga, A. (2022b). The importance of tasks and the use of digital technologies affordances in mathematical problem-solving approaches. In L. Uden & D. Liberona (Eds.), Learning technology for educational challenges, CCIS 1595 (pp. 113–124). https://doi.org/10.1007/978-3-031-08890-2_9
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
Schoenfeld, A. H. (2015). How we think: A theory of human decision-making, with a focus on teaching. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 229–243). https://doi.org/10.1007/978-3-319-12688-3_16
Schoenfeld, A. H. (2020). Mathematical practices, in theory and practice. ZDM Mathematics Education, 52, 1163–1175. https://doi.org/10.1007/s11858-020-01162-w
Schoenfeld, A. H. (2022). Why are learning and teaching mathematics so difficult? In M. Danesi (Ed.), Handbook of cognitive mathematics (pp. 1–35). Springer. https://doi.org/10.1007/978-3-030-44982-7_10-1
Trouche, L. (2016). The development of mathematics practices in the Mesopotamian scribal schools. In J. Monaghan et al. (Eds.), Mathematics Education Library. Tools and mathematics (pp. 117–138). Springer. https://doi.org/10.1007/978-3-319-02396-0_5
Trouche, L., Rocha, K., Gueudet, G., & Pepin, B. (2020). Transition to digital resources as a critical process in teachers’ trajectories: The case of Anna’s documentation work. ZDM Mathematics Education, 52, 1243–1257. https://doi.org/10.1007/s11858-020-01164-8
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Santos-Trigo, M. (2023). Trends and Developments of Mathematical Problem-Solving Research to Update and Support the Use of Digital Technologies in Post-confinement Learning Spaces. In: Toh, T.L., Santos-Trigo, M., Chua, P.H., Abdullah, N.A., Zhang, D. (eds) Problem Posing and Problem Solving in Mathematics Education. Springer, Singapore. https://doi.org/10.1007/978-981-99-7205-0_2
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