PROMOTING MATHEMATICAL JUSTIFICATION THROUGH REALISTIC MATHEMATICS EDUCATION CLASSROOM
Abstract
The importance of mathematical justification in all classrooms is emphasized by reform movements in mathematics education. However, previous studies reveal that encouraging justification in mathematics classes is troblesome for mathematics teachers at all school levels. This present study is aimed to find out how justification help students to develop their mathematical understandings. To answer this question, we first determined the role of justification in teaching and learning process and how good students in justifying their answers. Design research was chosen as an appropriate mean to achive that goal. The study was conducted in a state university in Yogyakarta involving four students from fifty-one students as our focus group and one of researchers as a lecturer. Justification was the focus on this study and to promote it we chose RME as an approach that served as a learning environment. In this study, all data collected from classroom observation, group observation, students’ works, video recordings, field notes during teaching experiment, and students’ final writen test. Students’ works then analyzed using a justification rubric and describe thoroughly by considering other data collected during teaching learning process. The study revealed that there were some roles of justification in RME classroom, namely encouraged conceptual understanding, supported mathematical skill, promoted long lasting skill, and influenced social relationship. In this study, most students in our focus group have already made a good justification which was assessed by the points in the CLEAR rubric. Students wrote their solutions equipped by signs or simbols, made labels, used a complete sentence to answer the question, and elaborated procedures throroughly
Downloads
References
Ayalon, M., & Hershkowitz, R. (2017). Mathematics teachers ’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, November, 0–1. https://doi.org/10.1016/j.jmathb.2017.11.010
Bell, A. W., & 1976. (1976). A Study of Pupils ’ Proof-Explanations in Mathematical Situations. Educational Studies in Mathematics, 7(1), 23–40.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608–645. https://doi.org/10.1177/016146810811000302
Cioe, M., King, S., Ostien, D., Pansa, N., & Staples, M. (2015). Moving Students to “the Why.” Mathematics Teaching in The Middle School, 20(8), 484–491.
Conner, A., Kosko, K. W., Staples, M., Cirillo, M., Bieda, K., & Newton, J. (2017). 2017 PME-NA Working Group : Conceptions and Consequences of What We Call Argumentation, Justification, and Proof. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Issue October, pp. 1464–1473). Hoosier Association of Mathematics Teacher Educator.
De Villiers, M. (2002). Developing Understanding for Different Roles of Proof in Dynamic Geometry. ProfMat, October. http://mzone.mweb.co.za/residents/profmd/profmat.pdf
Francisco, J. M. (2022). Supporting argumentation in mathematics classrooms: The role of teachers’ mathematical knowledge. Lumat, 10(2), 147–170. https://doi.org/10.31129/LUMAT.10.2.1701
Freudenthal, H., & Reidel, D. (1983). Didactical Phenomenology o f Mathematical Structures,.
Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. van den Akker (Ed.), Educational Design Research (Issue May 2014, pp. 45–85). Routledge.
Hähkiöniemi, M., Hiltunen, J., Jokiranta, K., Kilpelä, J., Lehesvuori, S., & Nieminen, P. (2022). Students’ dialogic and justifying moves during dialogic argumentation in mathematics and physics. Learning, Culture and Social Interaction, 33(February). https://doi.org/10.1016/j.lcsi.2022.100608
Heuvel-Panhuizen, M. Van den. (2020). Mathematics in Teams—Developing Thinking Skills in Mathematics Education (M. Van den Heuvel-Panhuizen (ed.)). Springer. https://doi.org/10.1007/978-3-030-33824-4_2
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics. Educational Researcher, 25(4), 12. https://doi.org/10.2307/1176776
Hunter, J., & Anthony, G. (2008). The Development of Students ’ Use of Justification Strategies. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, 265–272.
Hunter, J. M. (2007). Developing Early Algebraic Understanding in an Inquiry Classroom A thesis presented in partial fulfilment of the Master of Education. Massey University.
James, C., Casas, A., & Grant, D. (2016). Using Scaffolding to Scale-up Justififcations. Mathematics Teaching in the Middle School, 22(5), 294–301. https://doi.org/10.5951/mathteacmiddscho.23.1.0004
James, C., Philiben, L., & Knievel, M. (2016). Doing the Math: Supporting Student Justifications. 21(7), 416–423.
Kazemi, E. (1998). Research into Practice: Discourse That Promotes Conceptual Understanding. Teaching Children Mathematics, 4(7), 410–414. https://doi.org/10.5951/tcm.4.7.0410
Kazemi, E., Ghousseini, H., Cordero, E., Sam, S., Elzena, P., Alison, M., & Resnick, F. (2021). Supporting teacher learning about argumentation through adaptive , school ‑ based professional development. ZDM – Mathematics Education, 53(2), 435–448. https://doi.org/10.1007/s11858-021-01242-5
Lannin, J., Baker, D., & Townsend, B. (2006). Why , Why Should I Justify ? Mathematics Teaching in The Middle School, 11(9), 438–443.
Larbi, E., & Mavis, O. (2016). The Use of Manipulatives in Mathematics Instruction | LD OnLine. Journal of Education and Practice, 7(36), 53–61. http://www.ldonline.org/spearswerling/The_Use_of_Manipulatives_in_Mathematics_Instruction
Liang, C. B. (2020). Justification in Mathematics. Office of Education Research (OER), NIE.
Mata-pereira, J., & Ponte, J. (2017). Enhancing students ’ mathematical reasoning in the classroom : teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96, 169–186. https://doi.org/10.1007/s10649-017-9773-4
McCrone, S. S. (2005). The Development of Mathematical Discussions: An Investigation in a Fifth-Grade Classroom. Mathematical Thinking and Learning, 7(2), 111–133. https://doi.org/10.1207/s15327833mtl0702_2
Melhuish, K., Fasteen, J., Thanheiser, E., & Fredericks, J. (2015). Teacher Noticing of Justification: Attending to The Complexity of Mathematical Content and Practice. In H. Bartell, T. G., Bieda, K. N., Putnam, R. T., Bradfield, K., & Dominguez (Ed.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 748–755). East Lansing.
NCTM. (1991). Professional standards for teaching mathematics: related to dis. In Nctm (Vol. 2).
NCTM. (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics, Inc.
Rizkianto, I. (2013). Norma Sosiomatematik Dalam Kelas Matematika. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika, November, 978–979.
Sarumaha, Y. A. (2016). Perubahan Pembelajaran yang Berpusat pada Guru ke Berpusat pada Siswa. Intersections, 1(1), 1–10.
Sarumaha, Y. A. (2018). Justifikasi dalam Pembelajaran Matematika. Prosiding Seminar Nasional Etnomatnesia, ISBN: 978-602-6258-07-6, 286–295.
Sarumaha, Y. A., Putri, R. I. I., & Hartono, Y. (2018). Percentage Bar: A Model for Helping Fifth Grade Students Understand Percentages. Mosharafa, 7(2), 155–166.
Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms. Journal of Mathematical Behavior, 31(4), 447–462. https://doi.org/10.1016/j.jmathb.2012.07.001
Van Den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute CD-Rom for ICME9, 2(March 1999), 1–32. http://www.staff.science.uu.nl/~heuve108/download/VandenHeuvel-Panhuizen_papers-about-RME/RME-topics/other-rme-topics/vdHeuvel-2000_rme-guided-tour.pdf
Van Den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 521–525). Springer Dordrecht Heidelberg. https://doi.org/https://doi.org/10.1007/978-94-007-4978-8.
Van Zanten, M., & Van Den Heuvel-Panhuizen, M. (2021). Mathematics curriculum reform and its implementation in textbooks: Early addition and subtraction in realistic mathematics education. Mathematics, 9(7). https://doi.org/10.3390/math9070752
Widjaja, W. (2014). Year 3 / 4 Children ’ s Forms of Justification. In A. P. J Anderson, M Cavanagh (Ed.), Mathematics Education Research Group of Australasia. Annual Conference 37th (pp. 694–697). Mathematics Education Research Group of Australasia.
Wood, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222–255
Copyright (c) 2022 Yenny Anggreini Sarumaha, Ilham Rizkianto
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Jurnal Pendidikan Matematika (Jupitek) Posting Your Article Policy.
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with Jurnal Pendidikan Matematika (Jupitek) agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-NC-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- 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 acknowledgment of its initial publication in this journal.
- 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.
.png)
