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## Level of combinatorial thinking in solving mathematical problems

#### Yulıa Maftuhah HİDAYATİ [1] , Abdul NGALİM [2] , Sutama SUTAMA [3] , Zainal ARİFİN [4] , Zaenal ABİDİN [5] , Eka RAHMAWATİ [6]

Combinatorial thinking is an important reasoning process in building one's knowledge and experience. The purpose of this study is to describe the characteristics of the level of combinatorial thinking in solving mathematical problems. The subjects of the study were 40 students of Elementary Teacher Education Department (PGSD): 20 students of the second semester and the others of the sixth semester. The reason for choosing subjects from these two levels is to meet all levels of combinatorial thinking. All research subjects were given test questions about combinatorial problems. From 40 subjects, five students were selected to be interviewed as they had fulfilled all five levels of combinatorial thinking. The data validity was conducted by triangulation through recording interview results and comparing it with data from students' written test results to ensure the validity and reliability of this research. The results show that there are five levels of combinatorial thinking in solving mathematical problems: investigating “some cases’, systematically checking cases, using the calculation order, systematically generating all cases, and changing the problem into another combinatorial problem. Level one is the identification of the possibility of students’ understanding the questions incorrectly, or vice versa, already can answer the questions with systematic procedures but the results are less precise. Level two is conducting systematic checking about students' understanding of the combination material. Besides, it also concerns about the ability to answer problems systematically using diagram trees. Level three is students are able to apply the calculation orders, which are addition and multiplication. Level four is systematically generating all cases about the ability to calculate possibilities without schematic, drawings, or diagrams. Level five is changing the problem into another combinatorial problem, it is the ability to calculate possibilities with complex problems Based on the research findings, it turns out there is another level of combinatorial thinking, which is using the calculation order and this is found between level two and level three. The researchers recommend further research to explore more on the application of calculation order.
Combinatorial thinking level, Mathematics education, Mathematical problems, Students of elementary teacher
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Primary Language en Education and Educational Research September 2020 Thinking Skills Orcid: 0000-0003-0842-0897Author: Yulıa Maftuhah HİDAYATİ (Primary Author)Institution: Universitas Muhammadiyah SurakartaCountry: Indonesia Orcid: 0000-0001-9196-3918Author: Abdul NGALİMInstitution: Universitas Muhammadiyah SurakartaCountry: Indonesia Orcid: 0000-0002-9006-8388Author: Sutama SUTAMAInstitution: Universitas Muhammadiyah SurakartaCountry: Indonesia Orcid: 0000-0002-0945-0943Author: Zainal ARİFİNInstitution: Universitas Muhammadiyah SurakartaCountry: Indonesia Orcid: 0000-0003-1102-430XAuthor: Zaenal ABİDİNInstitution: Universitas Muhammadiyah SurakartaCountry: Indonesia Orcid: 0000-0003-0484-2937Author: Eka RAHMAWATİInstitution: Universitas Muhammadiyah SurakartaCountry: Indonesia Universitas Muhammadiyah Surakarta Publication Date : September 15, 2020
 Bibtex @research article { jegys751038, journal = {Journal for the Education of Gifted Young Scientists}, issn = {}, eissn = {2149-360X}, address = {editorjegys@gmail.com}, publisher = {Genç Bilge Yayıncılık}, year = {2020}, volume = {8}, pages = {1231 - 1243}, doi = {10.17478/jegys.751038}, title = {Level of combinatorial thinking in solving mathematical problems}, key = {cite}, author = {Hidayati, Yulıa Maftuhah and Ngalim, Abdul and Sutama, Sutama and Arifin, Zainal and Abidin, Zaenal and Rahmawati, Eka} } APA Hidayati, Y , Ngalim, A , Sutama, S , Arifin, Z , Abidin, Z , Rahmawati, E . (2020). Level of combinatorial thinking in solving mathematical problems . Journal for the Education of Gifted Young Scientists , 8 (3) , 1231-1243 . DOI: 10.17478/jegys.751038 MLA Hidayati, Y , Ngalim, A , Sutama, S , Arifin, Z , Abidin, Z , Rahmawati, E . "Level of combinatorial thinking in solving mathematical problems" . Journal for the Education of Gifted Young Scientists 8 (2020 ): 1231-1243 Chicago Hidayati, Y , Ngalim, A , Sutama, S , Arifin, Z , Abidin, Z , Rahmawati, E . "Level of combinatorial thinking in solving mathematical problems". Journal for the Education of Gifted Young Scientists 8 (2020 ): 1231-1243 RIS TY - JOUR T1 - Level of combinatorial thinking in solving mathematical problems AU - Yulıa Maftuhah Hidayati , Abdul Ngalim , Sutama Sutama , Zainal Arifin , Zaenal Abidin , Eka Rahmawati Y1 - 2020 PY - 2020 N1 - doi: 10.17478/jegys.751038 DO - 10.17478/jegys.751038 T2 - Journal for the Education of Gifted Young Scientists JF - Journal JO - JOR SP - 1231 EP - 1243 VL - 8 IS - 3 SN - -2149-360X M3 - doi: 10.17478/jegys.751038 UR - https://doi.org/10.17478/jegys.751038 Y2 - 2020 ER - EndNote %0 Journal for the Education of Gifted Young Scientists Level of combinatorial thinking in solving mathematical problems %A Yulıa Maftuhah Hidayati , Abdul Ngalim , Sutama Sutama , Zainal Arifin , Zaenal Abidin , Eka Rahmawati %T Level of combinatorial thinking in solving mathematical problems %D 2020 %J Journal for the Education of Gifted Young Scientists %P -2149-360X %V 8 %N 3 %R doi: 10.17478/jegys.751038 %U 10.17478/jegys.751038 ISNAD Hidayati, Yulıa Maftuhah , Ngalim, Abdul , Sutama, Sutama , Arifin, Zainal , Abidin, Zaenal , Rahmawati, Eka . "Level of combinatorial thinking in solving mathematical problems". Journal for the Education of Gifted Young Scientists 8 / 3 (September 2020): 1231-1243 . https://doi.org/10.17478/jegys.751038 AMA Hidayati Y , Ngalim A , Sutama S , Arifin Z , Abidin Z , Rahmawati E . Level of combinatorial thinking in solving mathematical problems. JEGYS. 2020; 8(3): 1231-1243. Vancouver Hidayati Y , Ngalim A , Sutama S , Arifin Z , Abidin Z , Rahmawati E . Level of combinatorial thinking in solving mathematical problems. Journal for the Education of Gifted Young Scientists. 2020; 8(3): 1231-1243. IEEE Y. Hidayati , A. Ngalim , S. Sutama , Z. Arifin , Z. Abidin and E. Rahmawati , "Level of combinatorial thinking in solving mathematical problems", Journal for the Education of Gifted Young Scientists, vol. 8, no. 3, pp. 1231-1243, Sep. 2020, doi:10.17478/jegys.751038

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