Using Open-ended Problem-solving Tests to Identify Students’ Mathematical Creative Thinking Ability

Year 2021, Volume: 8 Issue: 3, 285 - 299, 01.08.2021

Sri Rahayuningsih Sirajuddin Sirajuddin Muhammad Ikram

https://doi.org/10.17275/per.21.66.8.3

Cited By: 6

Abstract

This study aimed to examine an open-ended problem-solving assessment tool that can be used to measure the profile of students’ mathematical creativity based on the type of mathematical creativity. The open-ended problem-solving assessment consists of open-ended problem-solving sheets and interview guidelines to measure the profile of students' mathematical creativity. One hundred and five students were asked to solve open-ended problems. From each group, one student was selected to be interviewed with the aim of obtaining a more detailed explanation of each of these types. The two types can be explained as follows. The “very creative” students were those who could perform cognitive flexibility and cognitive fluency in solving open-ended problems. The other type of students was creative students who were able to think flexibly (cognitive flexibility) when solving open-ended problems. Cognitive flexibility includes the ability to describe various solutions and provide more than one answer to a problem. Cognitive fluency includes the ability to interpret the answer smoothly and accurately without any constraints. It may also refer to the ability to correct a wrong answer even though there was a mistake during the operating process. The analysis results showed that the open-ended problem-solving assessment was an effective tool to measure students' mathematical creativity in terms of results (products) and processes. In terms of results (products), it was able to determine the type of students’ mathematical creative ability, namely very creative and creative, while in terms of processes, it was able to describe the differences in the cognitive profile of the two types. 

Keywords

Open-Ended Problem-Solving Tests (OEPST), mathematical creative thinking ability, cognitive flexibility, cognitive fluency

Thanks

STKIP YPUP Makassar and Makassar Muhammadiyah University

References

• Althuizen, N., Wierenga, B., & Rossiter, J. (2010). The validity of two brief measures of creative ability. Creativity Research Journal, 22(1), 53–61. https://doi.org/10.1080/10400410903579577
• Bart, W. M., Hokanson, B., & Can, I. (2017). An investigation of the factor structure of the torrance tests of creative thinking. Kuram ve Uygulamada Egitim Bilimleri, 17(2), 515–528. https://doi.org/10.12738/estp.2017.2.0051
• Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. In Educational Research (Vol. 4). https://doi.org/10.1017/CBO9781107415324.004
• Deak, G. O. (2003). The development of cognitive flexibilty and language abilities. Advances in Child Development and Behavior, 31, 271–327.
• Dietrich, A., & Kanso, R. (2010). A review of EEG, ERP, and neuroimaging studies of creativity and insight. Psychological Bulletin, 136(5), 822–848. https://doi.org/10.1037/a0019749
• Fisher, M. H., Eisenhardt, S., Schack, E. O., Yoder, M., Thomas, J., & Tassell, J. (2011). THE STAGES OF EARLY ARITHMETIC LEARNING : A CONTEXT FOR LEARNING TO PROFESSIONALLY NOTICE.
• Fraenkel. (2011). How to Design Research in Education and Evaluate (S. Kiefer (ed.); 8th ed.). McGraw-Hill. www.mhle.com
• Furr, N. R. (2009). Cognitive Flexibility: The Adaptive Reality of Concrete Organization Change. 1–212. https://doi.org/10.1002/j.2162-6057.2004.tb01240.x
• Gervás, P., & León, C. (2014). The need for multi-aspectual representation of narratives in modelling their creative process. OpenAccess Series in Informatics, 41, 61–76. https://doi.org/10.4230/OASIcs.CMN.2014.61
• Goncalo A. Jack;Katz H. Joshua;Vincent C. Lynne;Krause Verena;Yang Shiyu. (2020). Creativity Connects: How the Creative Process Fosters Social Connection and
• Combats Loneliness at Work. In FORTHCOMING, HANDBOOK OF RESEARCH ON CREATIVITY AND INNOVATION.
• Kaufman, J C, Plucker, J. a, & Baer, J. (2008). Essentials of creativity assessment. In Essentials of psychological assessment series. http://www.loc.gov/catdir/enhancements/fy0827/2008008343-d.html%5Cnhttp://www.loc.gov/catdir/enhancements/fy0827/2008008343-t.html
• Kaufman, James C., Kaufman, S. B., & Lichtenberger, E. O. (2011). Finding Creative Potential on Intelligence Tests via Divergent Production. Canadian Journal of School Psychology, 26(2), 83–106. https://doi.org/10.1177/0829573511406511
• Kim, K. H. (2006). Can We Trust Creativity Tests? A Review of the Torrance Tests of Creative Thinking (TTCT). Creativity Research Journal, 18(1), 3–14. https://doi.org/https://doi.org/10.1207/s15326934crj1801_2
• Ladd, G. W., & Troop-Gordon, W. (2003). 9 Ladd. Child Development, 74(5), 1344–1367. https://doi.org/10.1111/1467-8624.00611
• Levin, M. (2008). The potential for developing algebraic thinking from purposeful guessing and checking. Computer-Supported Collaborative Learning Conference, CSCL, PART 1, 469–476.
• Mosimege, M. D., & Engagement, C. (2016). The Role and Importance of language in Ethnomathematical Research and Implications for Mathematics teaching and learning. 13th International Congress on Mathematical Education Hamburg, July, 24–31. https://www.researchgate.net/publication/306358855%0AThe
• 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
• Orion, N., & Hofstein, A. (1994). Factors that influence learning during a scientific field trip in a natural environment. Journal of Research in Science Teaching, 31(10), 1097–1119. https://doi.org/10.1002/tea.3660311005
• Rahayuningsih, S., Nusantara, T., As, A., & Susanto, H. (2019). Cognitive Styles: Characterization of College Students’ Creative Mathematical Thinking. International Journal of Humanities, Social Sciences and Education, 6(3), 50–60. https://doi.org/10.20431/2349-0381.0603007
• Robert J. Stenberg & Karin Stenberg. (2012). Cognitive Psychology 6th. In Science. Wadsworth Cengge Learning. https://doi.org/10.1126/science.198.4319.816
• Runco, M. A., & Acar, S. (2012). Divergent Thinking as an Indicator of Creative Potential. Creativity Research Journal, 24(1), 66–75. https://doi.org/10.1080/10400419.2012.652929
• Silvia, P. J., Wigert, B., Reiter-Palmon, R., & Kaufman, J. C. (2012). Assessing creativity with self-report scales: A review and empirical evaluation. Psychology of Aesthetics, Creativity, and the Arts, 6(1), 19–34. https://doi.org/10.1037/a0024071
• Singer, F. M., & Voica, C. (2015). Is problem posing a tool for identifying and developing mathematical creativity? Mathematical Problem Posing: From Research to Effective Practice, December 2014, 141–174. https://doi.org/10.1007/978-1-4614-6258-3_7
• Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM - International Journal on Mathematics Education, 41(1–2), 13–27. https://doi.org/10.1007/s11858-008-0114-z