KnE Social Sciences

ISSN: 2518-668X

The latest conference proceedings on humanities, arts and social sciences.

Analysis of Students' Combinatorial Thinking Model in Solving Combinatorics Problems

Published date: Apr 26 2024

Journal Title: KnE Social Sciences

Issue title: International Conference on Mathematics and Science Education (ICMScE 2022): Learning Models and Teaching Approaches

Pages: 1084–1095

DOI: 10.18502/kss.v9i13.16034

Authors:

Rita Desfitri - rdesfitri@bunghatta.ac.id - https://orcid.org/0000-0001-6450-8733

Abstract:

The purpose of this study was to analyze students’ combinatorial thinking in solving combinatorics problems. This study was organized into two related areas. The first focused on whether students applied combinatorial thinking in Lockwoods’ model, and the second emphasized on students’ ability in solving the given combinatorics problems. This research method used was a qualitative descriptive method. Participants of this study were students majoring mathematics education at Bung Hatta University who took combinatorics courses. Five combinatorics problems were given to the students and then analyzed. The result showed that based on Lockwoods’ model, the aspect of combinatorial thinking that was more widely applied in solving combinatorics problems was the counting process. However, most students who were able to solve problems quite well, and tended to solve problems with steps from formulating, followed by the process of counting to reach a set outcome. Whereas students who did the counting process stage without formulating problems into mathematics expressions, generally checked a set of outcomes by trial and errors. It can also be noted that in general, f/or any problem given, the percentage of students who faced difficulties when formulating problems into mathematical expressions or on the counting process was more that 50%, and the number of students who reached the correct set of outcomes was relatively low.

Keywords: student, combinatorial thinking model, solving combinatorics problems

References:

[1] NCTM. National council of teachers of mathematics. Principles and standards for school mathematics. Reston (VA): NCTM; 2000.

[2] Pittman LC, Herman GL. “Documenting students’ faulty schema and misconceptions about combinations and permutations,” In: 2015 IEEE Frontiers in Education Conference (FIE). pp. 1–9. IEEE (2015). https://doi.org/10.1109/FIE.2015.7344035.

[3] Godino JD, Batanero C, Font V. The onto-semiotic approach to research in mathematics education. ZDM Math Educ. 2007;39(1–2):127–35.

[4] Melušová J, Šunderlík J. “Pre-service teachers’ problem posing in combinatorics,” In: et al Ondrej Sedivy, Ed. The 12th Conference Proceeding. Faculty of Natural Science, Constantine of Philosopher, University of Nitra. pp. 115–122. University of Nitra (2014).

[5] Mashiach Eizenberg M, Zaslavsky O. Students’ verification strategies for combinatorial problems. Math Think Learn. 2004;6(1):15–36.

[6] Batanero C, Navarro-Pelayo V, Godino JD. Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educ Stud Math. 1997;32(2):181–99.

[7] Sriraman B, English LD. Combinatorial mathematics: research into practice. Math Teach. 2004;98(3):182–91.

[8] Rezaie M, Gooya Z. What do I mean by combinatorial thinking? Procedia Soc Behav Sci. 2011;11:122–6.

[9] Lockwood E. A model of students’ combinatorial thinking. J Math Behav. 2013;32(2):251–65.

[10] Lockwood E. “Students approaches to combinatorial enumeration: The role of setoriented htinking,” http://archives.pdx.edu/ds/psu/7054, (2011).

[11] Crespo S. Learning to pose mathematical problems: exploring changes in preservice teachers’ practices. Educ Stud Math. 2003;52(3):243–70.

[12] Desfitri R. Pre-service teachers’ challenges in presenting mathematical problems. J Phys Conf Ser. 2018;948(1):012035.

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