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

Year 2020, Volume: 8 Issue: 3, 1113 - 1124, 15.09.2020
https://doi.org/10.17478/jegys.768023

Abstract

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.

Supporting Institution

SMA Misyikat Al-Anwar

Project Number

-

Thanks

We expressed our gratitude to the principal of SMA Misyikat Al-Anwar who had allowed us to do this research in that school.

References

  • Aini, N., Dwi, J.,&Tatag, Y, E, S. (2019).Profile of Students’ Strategy in Senior High School with Cognitive Reflective and Impulsive Style in Solving the Combinatorial Questions. Journal of Physics: Conference Series. 1417 (2019) 012058 Doi:10.1088/1742-6596/1417/1/012058
  • Ainswort, S.(2006).Deft: A Conceptual Framework For Considering Learning With Multiple Representations.Elsevier.,16,183-198.
  • Creswell, W.J.(2010). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. California: Saga Publication.
  • Csapo, B. &Adey, P., (2012). Developing And Assessing Scientific Reasoning. In B. Csapó& G. Szabó (Eds.). Framework For Diagnostic Assessment Of Science, Pp. 17-53.
  • English, L. D. (1993). Children's strategies in solving two- and three-dimensionalcombinatorial problems. Journal for Research in Mathematics Education, 24(3),255-273
  • Ersari, E. (2015). A Synthesis Of The Combinatorial Reasoning And Proportional Reasoning Studies In Terms Of Piaget’s Description Of Development Stages.Turki: B.A., AbantIzzetBaysal University
  • Firdaus, A. M., Juniati, D., & Wijayanti, P. (2019a). Generalization Pattern’s Strategy of Junior High School students based on Gender. Journal of Physics: Conference Series, 1417(1). https://doi.org/10.1088/1742-6596/1417/1/012045
  • Kemendikbud.(2014). Kurikulum 2013 SekolahMenengah Atas/Madrasah Aliyah, Jakarta: Kemendikbud
  • Lahey, B. B., Schneider, S. A., Landrum, R. E., & Landrum, T. (1995). Psychology: An introduction. Brown & Benchmark Publishers.
  • Lockwood, E. (2011). Student Approaches to Combinatorial Enumeration The Role of Set-Oriented Thinking. Journal Educ Stud Math DOI 10.1007/s10649-011-9320-7. Springer Science+Business Media B.V
  • Lockwood, E. (2013). A model of students’ combinatorial thinking.The Journal Of Mathematical Behavior. 32 (2013) 251– 265
  • Lockwood, E. (2015). Attending to precision: a need for characterizing and promoting careful mathematical work..America: Oregon State University
  • Lockwood, E. (2018). Students’ Combinatorial Reasoning: Counting Processes and Sets of Outcomes. DOCEAMUS. DOI: http://dx.doi.org/10.1090/noti1705
  • Miles, H., & Huberman, A. M. S. (2014). Qualitative data analysis: A Methods Sourcebook.
  • Moleong, L. J. (2012). Metode Penelitian Kualitatif (Edisi Revisi). PT. Remaja Rosdakarya.
  • Muhtarom, Juniati, D., & Siswono, T. Y. E. (2019). Examining prospective teachers’ belief and pedagogical content knowledge towards teaching practice in mathematics class: A case study. Journal on Mathematics Education, 10(2), 185–202. https://doi.org/10.22342/jme.10.2.7326.185-202
  • NCTM. (2000). Principles and Standards for School Mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
  • Palengka, I., Juniati, D & Abadi. (2019). Creative Mathematical Reasoning of Prospective Teachers in Solving Problems Reviewed Based on Working Memory Capacity. Journal of Physics: Conference Series 1417 (2019) 012055 Doi:10.1088/1742-6596/1417/1/012055
  • Rezaie, M & Gooya, Z. (2011). Teachers for the Knowledge Society “ What Do I Mean By Combinatorial Thinking?”. Procedia Social andBehavioral Sciences, 11 (2011) 122–126
  • Rosdiana., Budayasa, I.K., & Lukito, A. (2019). Preservice Primary School Teachers’ Mathematical Reasoning Skills from Gender Perspectives: A Case Study. Journal for the Education of Gifted Young Scientists, 7(4), 1107-1122. DOI:http://dx.doi.org/10.17478/jegys.620234
  • Rosidah, Budayasa, I.K & Juniati, D (2018). An Analysis of Statistical Reasoning Process of High School Students in Solving the Statistical Problem. Journal of Physics: Conf. Series 1028 (2018) 012125 Doi :10.1088/1742-6596/1028/1/012125
  • Rozencwajg, P. and Corroyer, Denis. (2005). Cognitive Processes in the Reflective–Impulsive Cognitive Style. The Journal of Genetic Psychology 166(4): 451–463.
  • Shin, J. & Steffe, L.P. (2009). Seventh graders’ use of additive and multiplicativereasoning for enumerative combinatorial problems. Proceedings of the 3st AnnualMeeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (hlm. 170-177). Atlanta: GeorgiaState University.
  • Sukriyani, A, Juniati, D & Siswono, T.Y.E. (2017). Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style. AIP Conference Proceedings 1868, 050009 (2017); Doi: 10.1063/1.4995136
  • Sumaji, Sa’dijah, C., Susiswo., & Sisworo (2020). Mathematical Communication Process of Junior High School Students in SolvingProblems based on Apos Theory. Journal for the Education of Gifted YoungScientists, 8(1), 197-221. DOI: http://dx.doi.org/10.17478/jegys.652055
  • Warli. (2011). Differences In Creativity Qualities Between Reflective And Impulsive Students In Solving Mathematics Problems. Proceedings of “The 6th SEAM-UGM Conference 2011” Mathematics Education, pp 569-670.
  • William, McGalliard. (2012). Constructing Sample Space with Combinatorial Reasoning: A Mixed Methods Study. Greensboro: TheUniversity of North Carolina.
Year 2020, Volume: 8 Issue: 3, 1113 - 1124, 15.09.2020
https://doi.org/10.17478/jegys.768023

Abstract

Project Number

-

References

  • Aini, N., Dwi, J.,&Tatag, Y, E, S. (2019).Profile of Students’ Strategy in Senior High School with Cognitive Reflective and Impulsive Style in Solving the Combinatorial Questions. Journal of Physics: Conference Series. 1417 (2019) 012058 Doi:10.1088/1742-6596/1417/1/012058
  • Ainswort, S.(2006).Deft: A Conceptual Framework For Considering Learning With Multiple Representations.Elsevier.,16,183-198.
  • Creswell, W.J.(2010). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. California: Saga Publication.
  • Csapo, B. &Adey, P., (2012). Developing And Assessing Scientific Reasoning. In B. Csapó& G. Szabó (Eds.). Framework For Diagnostic Assessment Of Science, Pp. 17-53.
  • English, L. D. (1993). Children's strategies in solving two- and three-dimensionalcombinatorial problems. Journal for Research in Mathematics Education, 24(3),255-273
  • Ersari, E. (2015). A Synthesis Of The Combinatorial Reasoning And Proportional Reasoning Studies In Terms Of Piaget’s Description Of Development Stages.Turki: B.A., AbantIzzetBaysal University
  • Firdaus, A. M., Juniati, D., & Wijayanti, P. (2019a). Generalization Pattern’s Strategy of Junior High School students based on Gender. Journal of Physics: Conference Series, 1417(1). https://doi.org/10.1088/1742-6596/1417/1/012045
  • Kemendikbud.(2014). Kurikulum 2013 SekolahMenengah Atas/Madrasah Aliyah, Jakarta: Kemendikbud
  • Lahey, B. B., Schneider, S. A., Landrum, R. E., & Landrum, T. (1995). Psychology: An introduction. Brown & Benchmark Publishers.
  • Lockwood, E. (2011). Student Approaches to Combinatorial Enumeration The Role of Set-Oriented Thinking. Journal Educ Stud Math DOI 10.1007/s10649-011-9320-7. Springer Science+Business Media B.V
  • Lockwood, E. (2013). A model of students’ combinatorial thinking.The Journal Of Mathematical Behavior. 32 (2013) 251– 265
  • Lockwood, E. (2015). Attending to precision: a need for characterizing and promoting careful mathematical work..America: Oregon State University
  • Lockwood, E. (2018). Students’ Combinatorial Reasoning: Counting Processes and Sets of Outcomes. DOCEAMUS. DOI: http://dx.doi.org/10.1090/noti1705
  • Miles, H., & Huberman, A. M. S. (2014). Qualitative data analysis: A Methods Sourcebook.
  • Moleong, L. J. (2012). Metode Penelitian Kualitatif (Edisi Revisi). PT. Remaja Rosdakarya.
  • Muhtarom, Juniati, D., & Siswono, T. Y. E. (2019). Examining prospective teachers’ belief and pedagogical content knowledge towards teaching practice in mathematics class: A case study. Journal on Mathematics Education, 10(2), 185–202. https://doi.org/10.22342/jme.10.2.7326.185-202
  • NCTM. (2000). Principles and Standards for School Mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
  • Palengka, I., Juniati, D & Abadi. (2019). Creative Mathematical Reasoning of Prospective Teachers in Solving Problems Reviewed Based on Working Memory Capacity. Journal of Physics: Conference Series 1417 (2019) 012055 Doi:10.1088/1742-6596/1417/1/012055
  • Rezaie, M & Gooya, Z. (2011). Teachers for the Knowledge Society “ What Do I Mean By Combinatorial Thinking?”. Procedia Social andBehavioral Sciences, 11 (2011) 122–126
  • Rosdiana., Budayasa, I.K., & Lukito, A. (2019). Preservice Primary School Teachers’ Mathematical Reasoning Skills from Gender Perspectives: A Case Study. Journal for the Education of Gifted Young Scientists, 7(4), 1107-1122. DOI:http://dx.doi.org/10.17478/jegys.620234
  • Rosidah, Budayasa, I.K & Juniati, D (2018). An Analysis of Statistical Reasoning Process of High School Students in Solving the Statistical Problem. Journal of Physics: Conf. Series 1028 (2018) 012125 Doi :10.1088/1742-6596/1028/1/012125
  • Rozencwajg, P. and Corroyer, Denis. (2005). Cognitive Processes in the Reflective–Impulsive Cognitive Style. The Journal of Genetic Psychology 166(4): 451–463.
  • Shin, J. & Steffe, L.P. (2009). Seventh graders’ use of additive and multiplicativereasoning for enumerative combinatorial problems. Proceedings of the 3st AnnualMeeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (hlm. 170-177). Atlanta: GeorgiaState University.
  • Sukriyani, A, Juniati, D & Siswono, T.Y.E. (2017). Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style. AIP Conference Proceedings 1868, 050009 (2017); Doi: 10.1063/1.4995136
  • Sumaji, Sa’dijah, C., Susiswo., & Sisworo (2020). Mathematical Communication Process of Junior High School Students in SolvingProblems based on Apos Theory. Journal for the Education of Gifted YoungScientists, 8(1), 197-221. DOI: http://dx.doi.org/10.17478/jegys.652055
  • Warli. (2011). Differences In Creativity Qualities Between Reflective And Impulsive Students In Solving Mathematics Problems. Proceedings of “The 6th SEAM-UGM Conference 2011” Mathematics Education, pp 569-670.
  • William, McGalliard. (2012). Constructing Sample Space with Combinatorial Reasoning: A Mixed Methods Study. Greensboro: TheUniversity of North Carolina.
There are 27 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Thinking Skills
Authors

Nurul Aini 0000-0003-2515-0788

Dwi Junıatı 0000-0002-5352-3708

Tatag Siswono This is me 0000-0002-7108-8279

Project Number -
Publication Date September 15, 2020
Published in Issue Year 2020 Volume: 8 Issue: 3

Cite

APA Aini, N., Junıatı, D., & Siswono, 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. https://doi.org/10.17478/jegys.768023
AMA Aini N, Junıatı D, Siswono T. Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. JEGYS. September 2020;8(3):1113-1124. doi:10.17478/jegys.768023
Chicago Aini, Nurul, Dwi Junıatı, and Tatag Siswono. “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, no. 3 (September 2020): 1113-24. https://doi.org/10.17478/jegys.768023.
EndNote Aini N, Junıatı D, Siswono T (September 1, 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.
IEEE N. Aini, D. Junıatı, and T. Siswono, “Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems”, JEGYS, vol. 8, no. 3, pp. 1113–1124, 2020, doi: 10.17478/jegys.768023.
ISNAD Aini, Nurul et al. “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.
JAMA Aini N, Junıatı D, Siswono T. Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. JEGYS. 2020;8:1113–1124.
MLA Aini, Nurul et al. “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, vol. 8, no. 3, 2020, pp. 1113-24, doi:10.17478/jegys.768023.
Vancouver Aini N, Junıatı D, Siswono T. Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems. JEGYS. 2020;8(3):1113-24.