ON CREATIVITY THROUGH MATHEMATIZATION IN SOLVING NON-ROUTINE PROBLEMS

Sujinal Arifin, Zulkardi Zulkardi, Ratu Ilma Indra Putri, Yusuf Hartono

Abstract


This study aimed to describe and compare the students’ fluency, flexibility, and originality in solving non-routine problems in the Palembang context. They were depicted from the student’s fluency, flexibility, and originality of solving the horizontal and vertical mathematization forms. This qualitative study employed. The subjects of this study were 30 students of grade nine of junior high schools in Palembang. The instruments used were tests and interviews. The tests were employed to investigate the written horizontal and vertical mathematizations forms. Meanwhile, the interviews were to explore the students’ ideas with inadequately detailed answers. Then, the test and interview data were reduced and grouped based on the indicators of creativity. The reduced data were presented in a descriptive form for conclusions. The results of the data analysis showed that the high-ability students were the most fluent and flexible in solving the problems. Still, the provided solutions were less original and tended to use formal mathematics in the forms of formulas, symbols, and operations. Meanwhile, the moderate-ability students tended to start to solve problems by simplifying them, then presenting them in visual images. The answer sheets of the moderate-ability students revealed their fluency in understanding the problems and solutions, flexibility, and originality of thinking. This study obtained different results from the low-ability students who tended to have difficulties understanding the problems and made many errors in solving them.  Such a condition showed their inability to write the known data and relate the data to other facts they had already learned. As a result, their answers did not represent fluency, flexibility, and originality.

Keywords


Mathematization; Creativity; Problem-Solving; Non-routine

Full Text:

PDF

References


AlMutairi, A. N. M. (2015). The Effect of Using Brainstorming Strategy in Developing Creative Problem-Solving Skills among Male Students in Kuwait: A Field Study on Saud Al-Kharji School in Kuwait City. Journal of Education and Practice, 6(3), 136-145. https://files.eric.ed.gov/fulltext/EJ1083780.pdf

Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 42-47. https://flm-journal.org/Articles/4B432EC08630646B693621E55ECA5C.pdf

Barnard, & Herbst. (2018). Entrepreneurship, Innovation and Creativity: The Creative Process of Entrepreneurs and Innovator. http://dx.doi.org/10.2139/ssrn.3195912

Benedek, M., Könen, T., & Neubauer, A. C. (2012). Associative abilities underlying creativity. Psychology of Aesthetics, Creativity, and the Arts, 6(3), 273–281. https://doi.org/10.1037/a0027059

Cai, J & Ding, M. (2015). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Eduacation, 18(5), 5-29. http://dx.doi.org/10.1007/s10857-015-9325-8

Carson, J. (2007). A Problem with Problem Solving: Teaching Thinking without Teaching Knowledge. The Mathematics Educator, 17(2), 7-14. https://ojs01.galib.uga.edu/tme/article/view/1912

Celebioglu, B, Yazgan, Y & Ezentas, R. (2010). Usage of non-routine problem-solving strategies at first grade level. Procedia - Social and Behavioral Sciences, 2(2), 2968–2974. https://doi.org/10.1016/j.sbspro.2010.03.449

Chamberlin, S. A. (2010). Mathematical problems that optimize learning for academically advanced students in grades K-6. Journal of Advanced Academics, 22(1), 52–76. https://doi.org/10.1177/1932202X1002200103

Chong, M. S. F, Shahrill, M, Putri, R. I. I, & Zulkardi. (2018). Teaching Problem Solving Using Non-Routine Tasks. AIP Conference Proceedings, 1952(1), 020020. http://dx.doi.org/10.1063/1.5031982

Cropley, A., & Cropley, D. (2009). Fostering creativity: A diagnostic approach for education and organizations. Cresskill, NJ: Hampton Press.

Csapó, B. & Funke, J. (Eds.) (2017). The Nature of Problem Solving. Using research to inspire 21st century learning. Paris: OECD Publishing.

DeHaan, R. L. (2009) Teaching creativity and inventive problem solving in science. CBE Life Science Education, 8(3), 172–181. https://doi.org/10.1187/cbe.08-12-0081

Dendane, A. (2009) Skills Needed for Mathematical Problem Solving, [Online], Available: http://www.analyzemath.com/ math_problems/paper_7.html

Diyanni, R. (2016). Critical and Creative Thinking: A Brief Guide for Teachers. West Sussex: John Wiley & Sons, Inc. https://download.e-bookshelf.de/download/0003/6422/56/L-G-0003642256-0007213179.pdf

Fischer, A., Greiff, S., & Funke, J. (2012). The process of solving complex problems. Journal of Problem Solving, 4(1), 19-42. http://hdl.handle.net/10993/3184

Gilhooly, K. J. (2016). Incubation and Intuition in Creative Problem Solving. Frontiers in Psychology, 7, 1076. https://doi.org/10.3389/fpsyg.2016.01076

Hartono, Y. (2014). Problem Solving Strategy [in Bahasa]. Yogyakarta: Graha Ilmu.

Heffernan, K., & Teufel, S. (2018). Identifying Problems and Solutions in Scientific Text. Scientometrics, 116, 1367–1382. https://doi.org/10.1007/s11192-018-2718-6

?ncebacak, B. B., & Ersoy, E. (2016). Problem Solving Skills of Secondary School Students. China-USA Business Review, 15(6), 275-285. https://doi.org/10.17265/1537-1514/2016.06.002

Loc, N. P., & Hao, M. H. (2016). Teaching Mathematics Based On “Mathematization” of Theory of Realistic Mathematics Education: A Study of the Linear Fungtion Y=Ax+B. The International Journal of Engineering and Science (IJES), 5(6). 20-23. http://www.theijes.com/papers/v5-i6/D050602023.pdf

Mabilangan, R. A., Limjap, A. A., & Belecina, R. R. (2011). Problem solving strategies of high school students on non-routine problems: A case study. Alipato: A Journal of Basic Education, 5, 23-46. https://www.journals.upd.edu.ph/index.php/ali/article/download/2759/2580

Madzík, P. (2019) Capture and evaluation of innovative ideas in early stages of product development. TQM J, 31(6), 908–927. https://doi.org/10.1108/TQM-02-2019-0050

Malik, R. S. (2018). Educational Challenges In 21 St Century and Sustainable Development. Journal of Sustainable Development Education and Research, 2(1), 9-20. https://doi.org/10.17509/jsder.v2i1.12266

Maulana, F., & Yuniawati, N. T. (2018). Students’ Problem-Solving Ability in Non-routine Geometry Problem. International Journal of Information and Education Technology, 8(9), 661-667. http://www.ijiet.org/vol8/1118-SK012.pdf

Marchetti, G. (2018) Consciousness: a unique way of processing information. Cognitive Processing, 19, 435–464 (2018). https://doi.org/10.1007/s10339-018-0855-8

Menon, U. (2013). Mathematization – Vertical and Horizontal. Conference: epiSTEME 5 International Conference to Review Research on Science, Technology and Mathematics Education, Conference Proceedings., At Mumbai, India. http://episteme.hbcse.tifr.res.in/index.php/episteme5/5/paper/view/168/52

Miller, B., & Ranum, D. (2013) Problem solving with algorithms and data structures, 3rd edn. Franklin: Beedle & Associates.

Minarni, A., Napitupulu, E. E., & Husein, R. (2016). Mathematical understanding and representation ability of public junior high school in north sumatra. Journal on Mathematics Education, 7(1), 43-56. http://dx.doi.org/10.22342/jme.7.1.2816.43-56

Murdiyani, N. M. (2018). Developing non-routine problems for assessing students’ mathematical literacy. Journal of Physics: Conference Series, 983(1), 012115. https://doi.org/10.1088/1742-6596/983/1/012115

Novita, R., & Putra, M. (2016). Using task like PISA’s problem to support student’s creativity in mathematics. Journal on Mathematics Education, 7(1), 31-42. https://doi.org/10.22342/jme.7.1.2815.31-42

Nufus, H., Duskri, M., & Bahrun. (2018). Mathematical creative thinking and student self-confidence in the challenge-based learning approach. Journal of Research and Advances in Mathematics Education, 3(2), 57-68. https://doi.org/10.23917/jramathedu.v3i2.6367

Ozturk, T., & Guven, B. (2016). Evaluating Students’ Beliefs in Problem Solving Process: A Case Study. Eurasia Journal of Mathematics, Science & Technology Education, 12(2), 411–429. https://doi.org/10.12973/eurasia.2016.1208a

Pitta-Pantazi, D., & Christou, C. (2009). Cognitive Styles, Dynamic Geometry and Measurement Performance. Educational Studies in Mathematics, 70(1), 5-26. https://doi.org/10.1007/s10649-008-9139-z

Puccio, G. (2017). From the dawn of humanity to the 21st century: Creativity as an enduring survival skill. The Journal of Creative Behavior, 51(4), 330-334. https://doi.org/10.1002/jocb.203

Saragih, S., & Habeahan, W. L. (2014). The Improving of Problem-Solving Ability and Students’ Creativity Mathematical by Using Problem Based Learning in SMP Negeri 2 Siantar. Journal of Education and Practice, 5(35), 123-132. https://www.iiste.org/Journals/index.php/JEP/article/viewFile/17463/17722

Siswono, T. Y. E. (2010). Levelling students’ creative thinking in solving and posing mathematical problem. Journal on Mathematics Education, 1(1), 17–40. https://doi.org/10.22342/jme.1.1.794.17-40

Starko, A. J. (2013). Creativity in the classroom: Schools of curious delight. Mahwah, NJ: Lawrence Erlbaum.

Sudia, M., & Lambertus. (2017). Profile of High School Student Mathematical Reasoning to Solve the Problem Mathematical Viewed from Cognitive Style. International Journal of Education and Research, 5(6), 163-174. https://www.ijern.com/journal/2017/June-2017/14.pdf

Tambychik, T., & Meerah, T. S. M. (2010). Students’ Difficulties in Mathematics Problem-Solving: What do they Say? Procedia - Social and Behavioral Sciences, 8, 142–151. https://doi.org/10.1016/j.sbspro.2010.12.020

Tjoe, H. (2019). “Looking Back” to Solve Differently: Familiarity, Fluency, and Flexibility. In P. Liljedahl, & M. Santos-Trigo (Eds). Mathematical Problem Solving. ICME-13 Monographs (pp. 3-20). Cham: Springer. https://doi.org/10.1007/978-3-030-10472-6_1

Torrance, E. P. (1972). Predictive validity of the Torrance Tests of Creative Thinking. The Journal of Creative Behavior, 6(4), 236–252. https://doi.org/10.1002/j.2162-6057.1972.tb00936.x

Villareal, I. (2014). Heuristics in solving non-routine problems of selected students in a city science high school. Master’s Thesis. Manila: Philippine Normal University.

Yimer, A., & Ellerton, N. F. (2009). Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model. Identities, Cultures, and Learning Spaces, 575-582. http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=736B460ACDD8EADC7F5BE63B11DA5704?doi=10.1.1.554.9923&rep=rep1&type=pdf

Yazgan, Y. (2015). Sixth graders and non-routine problems: Which strategies are decisive for success? Educational Research and Reviews, 10(13), 1807-1816. https://doi.org/10.5897/ERR2015.2230




DOI: https://doi.org/10.22342/jme.12.2.13885.313-330

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id
p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.


View My Stats