Mathematical Creativity in Solving Non-Routine Problems

Main Article Content

Erminda C. Fortes
Rose R. Andrade

Keywords

flexibility, fluency, mathematical creativity, and originality

Abstract

The study used the descriptive design to explore the students' mathematical creativity in terms of fluency, flexibility and originality in solving six non-routine problems. Thirty (30) participants chosen using stratified sampling from 123 Grade 10 students, were asked to solve six nonroutine problems. In each of the three sessions, two problems were answered by them, after which they were asked to write a journal about their experiences in solving a problem and then they were interviewed. Solutions of the participants which succeeded by an interview that were interpreted using validated rubrics described their mathematical creativity in terms of fluency, flexibility and originality. Results show that students may be described as “moderately creative” in all three components fluency, flexibility, originality. Likewise, the over-all level of mathematical creativity in solving nonroutine problems is moderately creative. Consequently, the researchers derived pedagogical implications to improve the mathematical creativity of students.

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References

Borja, M. (2011). Mathematical Creativity on Students' Solutions to Open-Ended Problems. Unpublished Master's Thesis. Philippine Normal University.

Celebioglu, B., Yazgan, Y., & Ezentas, R. (2010) Usage of non-routine problem solving strategies at first grade level. Uludag University Social Science Institute. Retrieved from http://www.sciencedirect.com/science/article/pii/S1877042810004891

Clark, A. (2009). Problem Solving in Singapore Math. Retrieved from http://www.scribd.com/doc/36990278/.

Cruz, I. (2010). Mini Critique: The K+12 debate. The Philippine Star. Retrieved from http://www.philstar.com/education-and-home/620399/k12-debate.

Dendane, A. (2009). Skills needed for mathematical problem solving. A Paper presented at the 10th Annual Research Conference-United Arab Emirates University. Retrieved from http://www.analyzemath.com/math_problems/paper_1.html

Herrera, K. (2013). Enhanced Learning Approach and Grade 7 Performance in Mathematics:Exploring Outcomes-Based Numeracy Skills. Unpublished Thesis. Laguna State Polytechnic University, San Pablo City Campus.

Kattou, M., Kontoyianni, K., Pitta-Pantazzi, D., & Christou, C (2011). How does mathematical creativity differentiate mathematical ability. Retrieved on September 5, 2015 from http://www.cerme7.univ.rzeszow.pl/WG/7/Kattou_et_alCERME7_WG7.pdf

K-12 Mathematics Education Curriculum Guide Mathematics (2012). Department of Education.

Kontorovich, I., Koichu, B., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they?. Proceedings of the 6th International Conference Creativity in Mathematics Education and the Education of Gifted Students (pp. 120-125). Latvia: Latvia University. Retrieved from https://
www.researchgate.net/publication/269466270_Indicators_of_creativity_in_mathematical_problem_posing_How_indicative_are_they

Kostos, K., & Shin, E. (2010). Using math journals to enhance second graders' communication of mathematical thinking. Early Childhood Education Journal, 38(3). Retrieved from http://ezproxy.tcnj.edu:2089/10.1007/s10643-010-0390-4.

Krulik, S., & Rudnick, J.A. (1996).The New Sourcebook for Teaching Reasoning and Problem Solving in Junior and Senior High Schools. Boston, MA: Allyn and Bacon.

Kumar, L. (n.d). Fostering Mathematical Creativity. The National Council of Educational Research and Training (NCERT). Retrieved from http://www.ncert.nic.in/pdf_files/Lalit%20Kumar.pdf.

Kwon, O.N., Park, J.S., & Park, J. H. (2006). Cultivating Divergent Thinking in Mathematics Through an Open-Ended Approach. Education Research Institute. Vol. 7. No.1. 51-61. Retrieved from http://www.eric.ed.gov./PDFS/EJ752327.pdf.

Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Retrieved from https://www.researchgate.net/publication/259772377_Exploring_mathematical_creativity.

Lev, M., & Leikin, R. (2013). The connection between mathematical
creativity and high ability in a mathematics University of Haifa. Retrieved from http://www.scholar.googleusercontent.com/.

Mabilangan, R. A. (2011). Problem Solving Strategies of High School Students on Non-routine Problems: An Exploratory Study. Unpublished Thesis. Philippine Normal University.

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.

Oregon Department of Education. (1991). Oregon Mathematics Problem Solving Rubric.

Piggott, J. (2011). Cultivating Creativity. Retrieved from https://nrich.maths.org/5784.

Siniguian, M. (n.d.) Students Difficulty in Solving Mathematical Problems. Retrieved from https://www.academia.edu/9066326/Students_Difficulty_in_Solving_Mathematical_Problems.

Sternberg, R. J. (1997) Successful Intelligence: how practical and creative intelligence determine success in life. NY: Penguin/Putnam.

Sternberg, R. J., & Lubart, T. I. (2000). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 93–115). NY: Cambridge University Press.

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

Vistro-Yu, C. (2012). PHL Science and Math should start in kinder, experts say. Retrieved from http://www.gmanetwork.com/news/story/252416/scitech/science/phlscience-and-math-education-should-start-in-kinder-experts-
say.

Yazgan, Y. (2015). Sixth graders and non-routine problems: Which strategies are decisive for success?. Academic Journals. Educational Research and Reviews. Vol. 10(13), pp.1807-1816. Retrieved from http://www.academicjournals.org/ERR.

Yimer, A. & Ellerton, N.F. (2009). Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model. Thesis, University Of Wisconsin-Green Bay and Illinois State University. Retrieved from http://www.merga.net.