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## Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems

#### Nurul AİNİ [1] , Dwi JUNIATI [2] , Tatag Yuli Eko SİSWONO [3]

Combinatorial reasoning was a basic competence that every student must have for solving mathematical problems, as it highly related to providing argumentation or strategy in solving mathematical problems. It was the process of creating complex constructs out of a set of given elements that satisfy the conditions explicitly given or inferred from the situation. Considering this issue, this study aimed to explore the combinatorial reasoning of high school students with cognitive-reflective and -impulsive styles in solving problems. More specifically, It correlated combinatorial reasoning with tempo cognitive style, since it applied time-based problem solving in which the speed of responding and the frequency of either correct or wrong answer might affect students’ mental action in solving problems. This study was a qualitative research. It used High school students in eleventh grade as the research subject through matching familiar figure test. The researchers distributed a task containing several problems that had similar concept for each and then organized an interview to explore the students’ combinatorial reasoning in solving the given problems. Cognitive-reflective subject decided to use two strategies –formula and filling slot- for the sake of her affirmation, while cognitive-impulsive subject decided to only use one strategy –formula. The cognitive-reflective subject tended to be more accurate and careful in solving the problems. Otherwise, the cognitive-impulsive ones tended to be careless and less accurate, given that the subject decided to do spontaneous mental action. The result of this study found some similarities and differences on the combinatorial reasoning of both reflective and impulsive students. The similarities referred to their ways in explaining the notation in the formula they used and generalizing their strategies. The differences referred to the process of investigating various factors, considering any probabilities that might reveal, and evaluation.
combinatorial Reasoning, Impulsive cognitive style, Mathematics education, Reflective cognitive style, Recursive
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Primary Language en Education and Educational Research September 2020 Thinking Skills Orcid: 0000-0003-2515-0788Author: Nurul AİNİ (Primary Author)Institution: Surabaya State UniversityCountry: Indonesia Orcid: 0000-0002-5352-3708Author: Dwi JUNIATI Institution: Surabaya State UniversityCountry: Indonesia Orcid: 0000-0002-7108-8279Author: Tatag Yuli Eko SİSWONO Institution: Surabaya State UniversityCountry: Indonesia SMA Misyikat Al-Anwar - We expressed our gratitude to the principal of SMA Misyikat Al-Anwar who had allowed us to do this research in that school. Publication Date : September 15, 2020
 Bibtex @research article { jegys768023, 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 = {1113 - 1124}, doi = {10.17478/jegys.768023}, title = {Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems}, key = {cite}, author = {Ai̇ni̇, Nurul and Junıatı, Dwi and Si̇swono, Tatag} } APA Ai̇ni̇, N , Junıatı, D , Si̇swono, T . (2020). Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems . Journal for the Education of Gifted Young Scientists , 8 (3) , 1113-1124 . DOI: 10.17478/jegys.768023 MLA Ai̇ni̇, N , Junıatı, D , Si̇swono, T . "Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems" . Journal for the Education of Gifted Young Scientists 8 (2020 ): 1113-1124 Chicago Ai̇ni̇, N , Junıatı, D , Si̇swono, T . "Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems". Journal for the Education of Gifted Young Scientists 8 (2020 ): 1113-1124 RIS TY - JOUR T1 - Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems AU - Nurul Ai̇ni̇ , Dwi Junıatı , Tatag Si̇swono Y1 - 2020 PY - 2020 N1 - doi: 10.17478/jegys.768023 DO - 10.17478/jegys.768023 T2 - Journal for the Education of Gifted Young Scientists JF - Journal JO - JOR SP - 1113 EP - 1124 VL - 8 IS - 3 SN - -2149-360X M3 - doi: 10.17478/jegys.768023 UR - https://doi.org/10.17478/jegys.768023 Y2 - 2020 ER - EndNote %0 Journal for the Education of Gifted Young Scientists Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems %A Nurul Ai̇ni̇ , Dwi Junıatı , Tatag Si̇swono %T Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems %D 2020 %J Journal for the Education of Gifted Young Scientists %P -2149-360X %V 8 %N 3 %R doi: 10.17478/jegys.768023 %U 10.17478/jegys.768023 ISNAD Ai̇ni̇, Nurul , Junıatı, Dwi , Si̇swono, Tatag . "Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems". Journal for the Education of Gifted Young Scientists 8 / 3 (September 2020): 1113-1124 . https://doi.org/10.17478/jegys.768023 AMA Ai̇ni̇ N , Junıatı D , Si̇swono T . Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. JEGYS. 2020; 8(3): 1113-1124. Vancouver Ai̇ni̇ N , Junıatı D , Si̇swono T . Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. Journal for the Education of Gifted Young Scientists. 2020; 8(3): 1113-1124.

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