STUDENTS’ THINKING PROCESS IN INVESTIGATING MATHEMATICAL STATEMENT
DOI:
https://doi.org/10.24127/ajpm.v11i1.4115Keywords:
Investigating, Mathematical Statement, ThinkingAbstract
The statement is a declaratif sentence that can be true or false. It can’t do both at the same time so it needs an investigation through proving process. This research aims to explore the students’ thinking process in investigating the truth value of matematical statement. This research is conducted to seventeen students of mathematical education whom are taking the Abstract Algebra Course. The subject selecting in this reasearch is based on the students’ ability in doing the investigating by using formal proof. The data collecting uses the written test and the interview. Meanwhile, the data analysis is conducted through three steps: data reduction, data interpretation, and taking a conclusion. Based on the result of the research, it is found that students do the thinking process in investigating the matematical statements’ truth value through four steps. The first step, students understand the statements by reading them and classifying them to be a number of objects. The second one, students determine the proof startegies based on the definition or axiom. The third one, students do the algebraic operation by using symbol manipulation. The last one, students provide justification as the form of their belief of the proof results.References
Aberdein, A. (2019). Evidence, proofs, and derivations. ZDM mathematics education, 51(4), 1–17.
Aristidou, B. M. (2020). Is Mathematical logic really necessary in teaching mathematical proofs ?. Athens Journal of Education, 7(1), 99-122.
Astawa, W. P., Ketut Budayasa, I., & Juniati, D. (2018). The process of student cognition in constructing mathematical conjecture. Journal on Mathematics Education, 9(1), 15–25 https://doi.org/10.22342/jme.9.1.4278.15-26
As’ari, A. R., Kurniati, D., & Subanji. (2019). Teachers expectation of students’ thinking processes in written works: A survey of teachers’ readiness in making thinking visible. Journal on Mathematics Education, 10(3), 409–424. https://doi.org/10.22342/jme.10.3.7978.409-424
Bleiler, S. K., Thompson, D. R., & KrajÄevski, M. (2014). Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17(2), 105–127. https://doi.org/10.1007/s10857-013-9248-1
Chua, B. L. (2016). Examining Mathematics Teachers' Justification and Assessment of Students' Justification. Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 155−162).
Chua, B. L. (2018). A framework for classifying mathematical justification tasks. To cite this version : HAL Id : hal-01873071.
Engeler, E. (2018). A forgotten theory of proofs? ArXiv, 15(3), 1–6. https://doi.org/10.23638/LMCS-15
Faizah, S., Nusantara, T., Sudirman, S., & Rahardi, R. (2020). Exploring students ’ thinking process i n mathematical proof of abstract algebra based on M ason ’ s framework. Journal for the Education of Gifted Young Scientist, 8(June), 871–884. https://doi.org/10.17478/jegys.689809
Imamoglu, Y., & Togrol, A. Y. (2015). Proof Construction and Evaluation Practices of Prospective Mathematics Educators. 3(2), 130–144.
Kidron, I., & Tall, D. (2015). The roles of visualization and symbolism in the potential and actual infinity of the limit process. Educational Studies in Mathematics, 88(2), 183–199. https://doi.org/10.1007/s10649-014-9567-x
Khusna, A. H. (2020). Analytical Thinking Process Of Student In Proving Mathematical Argument. 9(01), 1–4
Lopez, J. E., & Tancinco, N. P. (2016). Students Analytical Thinking Skills and Teachers ’ Instructional Practices in Algebra in Selected State Universities and Colleges. International Journal of Engineering Sciences & Research Technology, 3(6), 681–697. www.ijesrt.com
Metaxas, N., Potari, D., & Zachariades, T. (2016). Analysis of a teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes. Educational Studies in Mathematics, 93(3), 383–397. https://doi.org/10.1007/s10649-016-9701-z
Mukuka, A., & Shumba, O. (2016). Zambian University Student Teachers’ Conceptions of Algebraic Proofs. Journal of Education and Practic, 7(32), 157–171. https://files.eric.ed.gov/fulltext/EJ1122465
Netti, S., Nusantara, T., Subanji, S., Abadyo, A., & Anwar, L. (2016). The Failure to Construct Proof Based on Assimilation and Accommodation Framework from Piaget. International Education Studies, 9(12), 12. https://doi.org/10.5539/ies.v9n12p12
Ogan-Bekiroglu, F., & Eskin, H. (2012). Examination of the relationship between engagement in scientific argumentation and conceptual knowledge. International Journal of Science and Mathematics Education, 10(6), 1415–1443. https://doi.org/10.1007/s10763-012-9346-z
Öztürk, M., & Kaplan, A. (2019). Cognitive analysis of constructing algebraic proof processes: A mixed method research. Egitim ve Bilim, 44(197), 25–64. https://doi.org/10.15390/EB.2018.7504
Ramirez-Ucles, R. & Ruiz-hidalgo, J. F. (2022). Reasoning , Representing , and Generalizing in Geometric Proof Problems among 8th Grade Talented Students. Mathematics, 10(789), 1-21
Sutini, S., Aaidati, I. F., & Kusaeri, K. (2020). Identifying the structure of students’ argumentation in covariational reasoning of constructing graphs. Beta: Jurnal Tadris Matematika, 13(1), 61–80. https://doi.org/10.20414/betajtm.v13i1.374
Tall, D., & Witzke, I. (2020). Making Sense of Mathematical Thinking over the Long Term: The Framework of Three Worlds of Mathematics and New Developments. MINTUS: Beiträge Zur Mathematischen, Naturwissenschaftlichen Und Technischen Bildung, April.
Tall, D. (2013). The Development Of Mathematical Thinking : Problem-Solving And Proof.
Thaneerananon, T., Triampo, W., & Nokkaew, A. (2016). Development of a Test to Evaluate Students’ Analytical Thinking Based on Fact versus Opinion Differentiation. International Journal of Instruction, 9(2), 123–138. https://doi.org/10.12973/iji.2016.929
Umah, U., As’ari, A. R., & Sulandra, I. M. (2016). Struktur Argumentasi Penalaran Kovariasional Siswa Kelas VIIIB Mtsn 1 Kediri. JMPM: Jurnal Matematika Dan Pendidikan Matematika, 1(1), 1. https://doi.org/10.26594/jmpm.v1i1.498
Wardhani, W., Subanji, S., & Dwiyana, D. (2016). Proses Berpikir Siswa Berdasarkan Kerangka Kerja Mason. Jurnal Pendidikan - Teori, Penelitian, Dan Pengembangan, 1(3), 297–313. https://doi.org/10.17977/jp.v1i3.6152
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