CONVERGENT AND DIVERGENT THINKING IN PROBLEM SOLVING (CASE STUDY ON JUNIOR HIGH SCHOOL STUDENTS)

Hairus Saleh

Abstract


This research involves 38 JUNIOR students with math skills vary, 12 students with high math ability, 18 students with the capabilities of the math medium, and 8 students with a mathematical ability is low. The entire students are asked to work on the problem-solving tests individually, with its main focus are as follows: (1) students were asked to write down what was known to be reserved; (2) write back what is asked the question; (3) write the problem resolution plan; (4) to resolve the issue in accordance with the plans that have been written; (5) try the other possible alternative in resolving problems; (6) rechecking problem resolution. The findings show that students answer math problems solving has diversity which is categorized into four categories: no changes mean, a variability of blind, orthodoxy, and creativity. Students in the creative categories are students who can solve problems by integrating CT and DT by using two models: the CDM and DCM. Students in this category can have opportunities to create and explore the variability.

Full Text:

PDF

References


Akgul, S., & Kahvecil, N. G. (2016). A Study on the Development of a Mathematics Creativity Scale. Eurasian Journal of Educational Research, 62(62), 57–76. Retrieved from http://dx.doi.org/10.14689/ejer.2016.62.5

Beghetto, R. A., Kaufman, J. C., & Baer, J. (2014). Teaching for creativity in the common core classroom. Teachers College Press.

Beghetto, R.A., & Sriraman, B. (2017). Creative contradictions in education: Cross disciplinary paradoxes and perspectives. Switzerland: Springer International Publishing.

Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer, Berlin.

Cattell, R.B., & Butcher, H.J. (1968). The prediction of achievement and creativity. HJ. Oxford: Bobbs-Merrill.

Cropley, A. (2006). In praise of convergent thinking. Creativity research journal, 18(3), 391–404.

Fatah, A., Suryadi, D., Sabandar, J., & Turmudi, T. (2016). Open-Ended Approach: an Effort in Cultivating Students’ Mathematical Creative Thinking Ability and Self-Esteem in Mathematics. Journal on Mathematics Education, 7(1), 9–18. https://doi.org/10.22342/jme.7.1.2813.9-18

Foster, C. (2015). The Convergent–Divergent model: an opportunity for teacher–learner development through principled task design. Educational Designer, 2(8), 1–25.

Gregory, E., Hardiman, M., Yarmolinskaya, J., Rinne, L., & Limb, C. (2013). Building Creative Thinking in the Classroom: From Research to Practice. International Journal Educational Research, 62, 43–50. Retrieved from http://olms.cte.jhu.edu/olms2/data/ck/sites/237/files/Gregory et al.pdf

Hargrove, R. A. (2013). Assessing the long-term impact of a metacognitive approach to creative skill development. International Journal of Technology and Design Education, 23(3), 489–517. https://doi.org/10.1007/s10798-011-9200-6

Haylock, D. W. (1987). A Framework for Assessing Mathematical Creativity in Schoolchilren. Educational Studies in Mathematics, 18(1), 59–74. https://doi.org/10.1007/BF00367914

Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.

İnce, H., Çenberci, S., & Yavuz, A. (2018). The Relationship between the Attitudes of Mathematics Teacher Candidates towards Scientific Research and Their Thinking Styles. Universal Journal of Educational Research, 6(7), 1467–1476. https://doi.org/10.13189/ujer.2018.060707

Korthagen, F.A., & Kessels, J.P. (1999). Linking theory and practice: Changing the pedagogy of teacher education. Educational Researcher, 28(4), 4–17.

Lee, K. S., Hwang, D., & Seo, J. J. (2003). A Development of the Test for Mathematical Creative Problem Solving Ability. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 7(3), 163–189.

Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Creativity in Mathematics and the Education of Gifted Students, 9, 129–145.

Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM - International Journal on Mathematics Education, 45(2), 183–197. https://doi.org/10.1007/s11858-012-0460-8

Lin, C. (2017). Threshold Effects of Creative Problem-Solving Attributes on Creativity in the Math Abilities of Taiwanese Upper Elementary Students. Education Research International, 2017, 1–9. Retrieved from https://doi.org/10.1155/2017/4571383

Mastuti, A. G., Nusantara, T., Purwanto, As’ari, A., Subanji, Abadyo, & Susiswo. (2016). Interpretation Awareness of Creativity Mathematics Teacher High School. International Education Studies, 9(9), 32–41. https://doi.org/10.5539/ies.v9n9p32

Newton, D. P. (2013). Moods, emotions and creative thinking: A framework for teaching. Thinking Skills and Creativity, 8(1), 34–44. https://doi.org/10.1016/j.tsc.2012.05.006

Runesson, U. (2005). Beyond discourse and interaction. Variation: a critical aspect for teaching and learning mathematics. Cambridge journal of education, 35(1), 69–87.

Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: implementation of realistic mathematics education. Thinking Skills and Creativity, 16, 1–13. https://doi.org/10.1016/j.tsc.2016.09.007

Sriraman, B., Yaftian, N., & Lee, K. (2011). Mathematical creativity and mathematics education. In B.

Sriraman & K. Lee (Eds.), The Elements of Creativity and Giftedness in Mathematics (pp. 119– 130). The Netherlands: Sense Publishers.

Sriwongchai, A., Jantharajit, N., & Chookhampaeng, S. (2015). Developing the Mathematics Learning Management Model for Improving Creative Thinking In Thailand. International Education Studies, 8(11), 77–87. https://doi.org/10.5539/ies.v8n11p77

Stein, M.K., Grover, B.W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

Švecová, V., Rumanová, L., & Pavlovičová, G. (2014). Support of Pupil’s Creative Thinking in Mathematical Education. Procedia - Social and Behavioral Sciences, 116, 1715–1719. https://doi.org/10.1016/j.sbspro.2014.01.461

Van Akker, J., & Nieveen, N. (2017). The role of teachers in design research in education. In S. Doff & R. Komoss (Eds.), Making change happen (pp. 75–86). Wiesbaden: Springer Fachmedien.

Warren, F., Mason-Apps, E., Hoskins, S., Azmi, Z., & Boyce, J. (2018). The role of implicit theories, age, and gender in the creative performance of children and adults. Thinking Skills and Creativity, 28(2010), 98–109. https://doi.org/10.1016/j.tsc.2018.03.010

Watson, A., & Ohtani, M. (Eds.). (2015). Task design in mathematics education: An ICMI study 22. Switzerland: Springer.

Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers’ professional development. For the Learning of Mathematics, 15(3), 15–20.

Zimmerman, B.J., & Dibenedetto, M.K. (2008). Mastery learning and assessment: Implications for students and teachers in an era of high-stakes testing. Psychology in the Schools, 45(3), 206–216.


Refbacks

  • There are currently no refbacks.


International Journal of Insight for Mathematics Teaching is licensed under
Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)