Utilización de una tarea de toma de decisiones: justificación matemática de los estudiantes en la resolución colaborativa de problemas

Autores/as

DOI:

https://doi.org/10.35763/aiem26.5341

Palabras clave:

Colaboración, Derivación, Justificación, Resolución de problemas, Tarea de toma de decisiones

Resumen

Muchos estudios informaron la importancia de la justificación matemática en la resolución colaborativa de problemas (CPS). Sin embargo, no todas las tareas podrían estimular la justificación matemática en CPS. Este estudio explora el potencial de una tarea de toma de decisiones para facilitar la justificación matemática en CPS de un tema derivado. Dos grupos de alumnos de 12º grado en Bandung, Indonesia, resuelven una tarea. Los trabajos grupales fueron observados, grabados y recopilados los trabajos escritos. Los hallazgos mostraron que la tarea animó a los grupos a centrarse en justificar afirmaciones matemáticas. Ambos grupos resolvieron con éxito la tarea, aunque se observaron diferentes justificaciones matemáticas. Discutimos los posibles roles de la dificultad de la tarea y la habilidad matemática de los grupos en la promoción de justificaciones matemáticas. Se recomendó para estudios posteriores comprobar la eficacia de la tarea en una muestra más grande.

Descargas

Los datos de descargas todavía no están disponibles.

Citas

Bieda, K. N., Conner, A. M., Kosko, K. W., & Staples, M. (Eds). (2022). Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof. Springer International Publishing. https://doi.org/10.1007/978-3-030-80008-6

Brodie, K. (2010a). Pressing dilemmas: Meaning-making and justification in math-ematics teaching. Journal of Curriculum Studies, 42(1), 27-50. https://doi.org/10.1080/00220270903149873

Brodie, K. (Ed.) (2010b). Teaching Mathematical Reasoning in Secondary School Class-rooms. Springer US. https://doi.org/10.1007/978-0-387-09742-8

Carpenter, T. P., Levi, L., Berman, P. W., & Pligge, M. (2005). Developing algebraic reasoning in the elementary school. In T. A. Romberg, T. P. Carpenter & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 81-98). Routledge.

Chiu, M. M. (2008). Flowing toward correct contributions during group problem solving: A statistical discourse analysis. Journal of the Learning Sciences, 17(3), 415-463. https://doi.org/10.1080/10508400802224830

Chiu, M. M., & Khoo, L. (2003). Rudeness and Status Effects During Group Problem Solving: Do They Bias Evaluations and Reduce the Likelihood of Correct Solu-tions? Journal of Educational Psychology, 95(3), 506-523. https://doi.org/10.1037/0022-0663.95.3.506

Chua, B. L. (2016). Examining Mathematics Teachers justification And Assessment of Students justifications. Proceedings of the 40th Conference of the Internation-al, August.

Chua, B. L. (2017). A Framework for Classifying Mathematical Justification Tasks. CERME 10, 115-122. https://hal.archives-ouvertes.fr/hal-01873071

Cirillo, M., Kosko, K. W., Newton, J., & Staples, M. (2016). White Paper 2016: Concep-tions and Consequences of What We Call Argumentation, Justification, and Proof. April. https://doi.org/10.13140/RG.2.1.5132.0727

Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23(1), 99-122. https://doi.org/10.1007/BF00302315

de Villiers, M. (1990). The role and function of proof in Mathematics. Pythagoras, 24(August), 17-23.

Díez-Palomar, J., Chan, M. C. E., Clarke, D., & Padrós, M. (2021). How does dialogi-cal talk promote student learning during small group work? An exploratory study. Learning, Culture and Social Interaction, 30, 100540. https://doi.org/10.1016/j.lcsi.2021.100540

Dillenbourg, P. (1999). What do you mean by collaborative learning?. In P. Dillen-bourg (Ed.), Collaborative learning: Cognitive and computational approaches (Vol. 1, pp. 1-19). https://telearn.archives-ouvertes.fr/hal-00190240

Ellis, A. B., Staples, M., & Bieda, K. N. (2022). Justification Across the Grade Bands (pp. 287-297). https://doi.org/10.1007/978-3-030-80008-6_23

Hamidy, A., & Suryaningtyas, S. (2016). Kemampuan Justifikasi Matematis Siswa SMP Pada Materi Segitiga. Prosiding Seminar Nasional Pendidikan Matematika, 978-989.

Heid, M. K., Hollebrands, K. F., & Iseri, L. W. (2002). Reasoning and Justification , with Examples from Technological Environments. The Mathematics Teacher, 95(3), 210-216.

Jaffe, A. (1997). Proof and the Evolution of Mathematics. Synthese, 111(2), 133-146. http://www.jstor.org/stable/20117623

Jermann, P. (2004). Computer Support for Interaction Regulation in Collaborative Problem-Solving. Proceedings of Computer Support for Collaborative Learning, CSCL 2002, 340, 601-602. https://telearn.hal.science/hal-00197373

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn Mathematics. National Academy Press.

Küchemann, D., & Hoyles, C. (2006). Influences on students’ mathematical reason-ing and patterns in its development: Insights from a Longitudinal study with particular reference to geometry. International Journal of Science and Mathe-matics Education, 4(4), 581-608. https://doi.org/10.1007/s10763-006-9039-6

Lai, E. R. (2011). Collaboration: A Literature Review. Pearson’s Research Reports.

McClain, K., & Cobb, P. (2001). An Analysis of Development of Sociomathematical Norms in One First-Grade Classroom. Journal for Research in Mathematics Edu-cation, 32(3), 236-266. https://doi.org/10.2307/749827

Mueller, M. F. (2009). The co-construction of arguments by middle-school stu-dents. Journal of Mathematical Behavior, 28(2-3), 138-149. https://doi.org/10.1016/j.jmathb.2009.06.003

NCTM. (2000). Principles and Standards for School Mathematics. Author.

Partanen, A. M., & Kaasila, R. (2015). Sociomathematical Norms Negotiated in the Discussions of Two Small Groups Investigating Calculus. International Journal of Science and Mathematics Education, 13(4), 927-946. https://doi.org/10.1007/s10763-014-9521-5

Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM - Mathematics Education, 53(4), 737-752. https://doi.org/10.1007/s11858-021-01244-3

Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15(1), 3-31. https://doi.org/10.1016/S0732-3123(96)90036-X

Sowder, L., & Harel, G. (1998). Types of Students’ Justifications. The Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/mt.91.8.0670

Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathemat-ics classrooms. Journal of Mathematical Behavior, 31(4), 447-462. https://doi.org/10.1016/j.jmathb.2012.07.001

Staples, M., & Conner, A. (2022). Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education. In K. N. Bieda, A. Conner, K. W. Kosko, & M. Staples (Eds.), Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof (pp. 1-10). Springer. https://doi.org/10.1007/978-3-030-80008-6_1

Stylianou, D. A., & Blanton, M. L. (2002). Sociocultural factors in undergraduate mathematics: the role of explanation and justification. Proceedings of the Sec-ond Annual Conference on the Teaching of Mathematics.

Tatsis, K. (2007). Investigating the influence of social and sociomathematical norms in collaborative problem solving. Cerme 5, 5(November), 1321-1330.

Tatsis, K., & Koleza, E. (2008). Social and socio-mathematical norms in collabora-tive problem-solving. European Journal of Teacher Education, 31(1), 89-100. https://doi.org/10.1080/02619760701845057

Taylor, J.., & McDonald, C. (2007). Writing in groups as a tool for non-routine prob-lem solving in first year university mathematics. International Journal of Mathematical Education in Science and Technology, 38(5), 639–655. https://doi.org/10.1080/00207390701359396

Thanheiser, E., & Sugimoto, A. (2022). Justification in the Context of Elementary Grades: Justification to Develop and Provide Access to Mathematical Reason-ing. In K. N. Bieda, A. Conner, K. W. Kosko, & M. Staples (Eds.), Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof (pp. 35-48). Springer. https://doi.org/10.1007/978-3-030-80008-6_4

Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2016). Mapping Var-iation in Children’s Mathematical Reasoning: The Case of ‘What Else Be-longs?’ International Journal of Science and Mathematics Education, 15(5), 873-894. https://doi.org/10.1007/s10763-016-9725-y

Walton, D. (2001). Abductive, presumptive and plausible arguments. Informal Logic, 21(2), 141-169. https://doi.org/10.22329/il.v21i2.2241

Whitacre, I., Azuz, B., Lamb, L. L. C., Bishop, J. P., Schappelle, B. P., & Philipp, R. A. (2017). Integer comparisons across the grades: Students’ justifications and ways of reasoning. Journal of Mathematical Behavior, 45, 47-62. https://doi.org/10.1016/j.jmathb.2016.11.001

Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics. Journal of the Korea Society of Mathemati-cal Education Series D: Research in Mathematical Education, 8(1), 1-18.

Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and auton-omy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.2307/749877

Descargas

Publicado

2024-10-31

Cómo citar

Fatmanissa, N. ., Yuli Eko Siswono, T., Lukito , A. ., & Ismail. (2024). Utilización de una tarea de toma de decisiones: justificación matemática de los estudiantes en la resolución colaborativa de problemas. Avances De Investigación En Educación Matemática, (26), 85–103. https://doi.org/10.35763/aiem26.5341

Número

Sección

Artículos