Utilizing Decision-making Task: Students’ Mathematical Justification in Collaborative Problem Solving

Authors

DOI:

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

Keywords:

Collaboration, Derivative, Justification, Problem-solving, Decision-making task

Abstract

Many studies reported the importance of mathematical justification in collaborative problem-solving (CPS). However, not all tasks could stimulate mathematical justification in CPS. This study explores the potential of a decision-making task in facilitating mathematical justification in CPS of a derivative topic. Two groups of 12 graders in Bandung, Indonesia solved a task. The group works were observed, recorded, and the written works were collected. The findings showed that the task encouraged the groups to focus on justifying mathematical claims. Both groups successfully solved the task, yet different mathematical justifications were observed. We discussed the possible roles of the task difficulty and groups’ mathematics ability in promoting mathematical justifications. Checking the effectiveness of the task on a larger sample was recommended for further studies.

Downloads

Download data is not yet available.

References

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

Downloads

Published

2024-10-31

How to Cite

Fatmanissa, N. ., Yuli Eko Siswono, T., Lukito , A. ., & Ismail. (2024). Utilizing Decision-making Task: Students’ Mathematical Justification in Collaborative Problem Solving. Advances of Research in Mathematics Education, (26), 85–103. https://doi.org/10.35763/aiem26.5341

Issue

No. 26 (2024)

Section

Artículos

License

Copyright (c) 2024 Namirah Fatmanissa, Tatag Yuli Eko Siswono, Agung Lukito, Ismail

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The articles published in this journal are under a license Creative Commons: By 4.0 España from  number 21 (2022).

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and keep the acknowledgement of authorship.
  2. The texts published in this journal are – unless indicated otherwise – covered by the Creative Commons Attribution 4.0 international licence. You may copy, distribute, transmit and adapt the work, provided you attribute it (authorship, journal name, publisher) in the manner specified by the author(s) or licensor(s). The full text of the licence can be consulted here: http://creativecommons.org/licenses/by-nc/4.0.
  3. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  4. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).