Investigating of the mathematical creativity of tenth grade students using open ended problem posing in structured situations

Subject Areas : Other

Majid Yousefi ¹ , Ebrahim Reyhani ² , Mohammad Hassan Behzadi ³

1 - Islamic Azad University Science and Research Branch
2 - Faculty member of Shahid Rajaee Teacher Training University, Mathematics Department
3 - Associate Professor, Department of Statistics, Islamic Azad University, Science and Research Branch, Tehran, Iran

Received: 2022-05-27 Accepted : 2023-04-24 Published : 2023-02-20

Keywords: Mathematical creativity, problem-solving, Tenth Grade Students, Open-Ended Problem,

Abstract :

The purpose of this study was to investigate the mathematical creativity of tenth grade students using open ended problem posing in structured situations. The research method is descriptive of survey type. The participants in this study were 158 tenth grade gifted students in three cities in the south-east of Tehran province in the academic year 1399-1400. To collect the data, a researcher-made test was used, consisting of two open ended problem posing in structured situations (Stoyanova and Elrton). The validity of the test was confirmed by mathematics educators and experienced mathematics teachers. By using the criterion of Cronbach's alpha, this approximate reliability coefficient (0.71 and 0.82) was obtained. The result showed the math creativity score of the 10th grade students was 0.2082. The results indicated that tenth grade students have a low level of mathematical creativity. In fact, there was no sufficient situations for these students to encounter activities and tasks that enhance mathematical creativity, including problem-solving and ended problem posing in the classroom.

References:

اسکندری، مجتبی. (1392). بررسی تأثیر پرورش مهارت‌های طرح مسئله‌ ریاضی بر توانایی حل مسئله دانش‌آموزان سوم راهنمایی. پایان‌نامه کارشناسی ارشد آموزش ریاضی. دانشگاه تربیت دبیر شهید رجایی، دانشکده علوم پایه، تهران.

اسکندری، مجتبی و ریحانی، ابراهیم. (1393). بررسی فرایند طرح مسئله در آموزش ریاضی. دو فصلنامه نظریه و عمل در برنامه درسی، 2(3)، بهار و تابستان 1393، 140ـ117.

باقرزاده گل مکانی، ز.، و بنی جمالی، ش.، و سیف، ع. (1394). مقایسه روند تحول خلاقیت دانش آموزان دختر و پسر دوره متوسطه در مناطق بالا و پایین. ابتکار و خلاقیت در علوم انسانی،5(3)، 58-33.

بروجردی، مینا؛ اسدزاده، حسن؛ حجازی، مسعود؛ انتصار فومنی، غلام‌حسین. (1399). تأثیر موسیقی و نقاشی در افزایش خلاقیت و کاهش پرخاشگری کودکان پیش‌دبستانی شهر همدان. نشریه علمی ابتکار و خلاقیت در علوم انسانی، 10 (1)، 26-1.

ریحانی، ابراهیم و حق‌جو، سعید. (1399). حل مسئله ریاضی، از نظریه تا عمل (چاپ اول). تهران: انتشارات دانشگاه تربیت دبیر شهید رجایی.

سعیدی، الهه؛ پیرخائفی، علیرضا. (1399). مقایسه خلاقیت و حافظه دانش‌آموزان دارا و بدون ناتوانی یادگیری ریاضی. فصلنامه پژوهش در یادگیری آموزشگاهی و مجازی، 7 (4)، 30-21.

      سلیمیان، فاطمه؛ ریحانی، ابراهیم و بهرامی سامانی، احسان.(1398). بررسی تأثیر رویکرد آموزشی مبتنی بر مسئله باز-پاسخ بر توانایی حل‌مسئله دانش‌آموزان پایه هفتم. پژوهش‌های آموزش و یادگیری، 16(2)،پاییز و زمستان.

سیدان، سیدابوالقاسم و شبانی، ناهید.(1399). مقایسه خلاقیت دانش آموزان دختر و پسر متوسطه اول،ششمین کنفرانس بین المللی روانشناسی، علوم تربیتی و سبک زندگی

 شکوهی امیرآبادی، لیلا؛ دلاور، علی؛ عباسی سروک، لطف‌اله؛ کوشکی، شیرین. (1397). تحلیل محتوای سند تحول بنیادین آموزش و پرورش براساس خلاقیت و شادکامی. ابتکار و خلاقیت در علوم انسانی، 8 (3)، 192-165.

رضازاده بهادران، حمیدرضا؛ اسکندری، مهتاب. (1397). بررسی محتوای کتاب ریاضی یک پایه دهم دوره متوسطه براساس الگوی خلاقیت گیلفورد. فصلنامه علمی پژوهشی ابتکار و خلاقیت در علوم انسانی، 8 (1)، 164-143.

عابدی، جمال. (1372). خلاقیت و شیوه‌ای نو در اندازه‌گیری آن، پژوهشهای روان شناختی. 2(1-2) 54-46.

فلاح نسیمی، محمد. (1395). بررسی میزان توانایی طرح مسئله معلمان ابتدایی. پایان‌نامه کارشناسی ارشد آموزش ریاضی. دانشگاه تربیت دبیر شهید رجایی، دانشکده علوم پایه، تهران.

فلاح نسیمی، محمد؛ ریحانی، ابراهیم؛ اسلام‌پور، محمدجواد. (1400). جست و جوی عناصر اصلی خلاقیت در عملکرد معلمان دوره ابتدایی در فرایند طرح مسئله. مجله پژوهش در آموزش ریاضی، 2(1)،62-41.

نجفی، هادی. (1393). بررسی تفکر واگرای دانش‌آموزان پایه هفتم در حل مسائل بازپاسخ. پایان‌نامه کارشناسی ارشد آموزش ریاضی. دانشگاه تربیت دبیر شهید رجایی، دانشکده علوم پایه، تهران.

یافتیان، نرگس. (1397). شناسایی مدلی برای فعالیت‌های خلاقانه دانشجویان ریاضی: یک تحقیق کیفی. مجله علمی پژوهشی «پژوهش‌های برنامه درسی»، 8(2)، پیاپی 16، پاییز و زمستان 1397، 198-172.

Abu-Elwan. R. (2002). Effectiveness of Problem Posing Strategies on Prospective Mathematics Teachers’ Problem-Solving Performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69.

Amado, N., Carreira, S., & Jones, K. (Eds.). (2018). Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect. Springer.

Arikan, E. E. (2017). Is There a Relationship between Creativity and Mathematical Creativity? Journal of Education and Learning, 6(4), 239.

Becker, J. P., & Shimada, S. (1997). The open-ended approach: A New proposal for teaching Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Bicer, A., Lee, y., Perihan, C., Capraro, M., & Capraro, R. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics.

     https: // doi.org / 10.1007 / S16049-020-09995-8

Bonotto, C., & Dal Santo, L. (2015). On the Relationship Between Problem Posing, Problem Solving, and Creativity in the Primary School. In F.M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing. From research to effective Practice

     (pp. 103-123). Springer.

Briggs, M., & Davis, S. (2008). Creative Teaching Mathematics in the Early Years and Primary Classrooms. New York: Madison Ave.

Cai, W., Khapova, S., Bossink, B., Lysova, E., & yuan, J. (2020). Optimizing employee creativity in the digital era: Uncovering the interactional effects of abilities, motivations, and opportunities. International Journal of environmental research and public health, 17 (3), 10-38.

Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as tool to develop and identify creativity gifted mathematicians. Journal of Secondary Gifted Edcuation, 17(1), 37-47.

Christou, C., Mosoulides, N., Pitta-Pantazi, D., & Sriraman, B. (2005). An Empirical Taxonomy of Problem Posing Processes. ZDM, 37(3), 1-10.

Cifarelli, V., & Cai, J. (2005). The evolution of mathematical explorations in open-ended Problem-solving situations. In paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Roanoke, VA: Virginia Tech University Center.

Contveras, J. (2007). Unraveling the Mystery of the Origin of Mathematical Problem: Using a Problem-Posing Framework with Prospective Mathematics Teachers. The Mathematics Educator, 17(2), 15-23.

Crespo, S., & Harper, F. K. (2019). Learning to Pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research. Advance Online Publication.

Damayanti, H. T., & Sumardi, S. (2018). Mathematical Creative Thinking Ability of Junior High School Student in Solving Open-Ended Problem. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 36-45.

English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics,34(3), 183-217.

Guilford, J. P. (1959). Traits of Creativity. In H. H. Anderson (Ed.), Creativity and its Cultivation New York: Harper & Brothers Publishers, 142-161.

Glaveanu, V.P. (2018). Educating which creativity? Thinking Skills and Creativity, 27, 25-32.

Guilford, J.P. (1967). The nature of human intelligence. New York: MCGraw-Hill.

Hashimoto, Y. (1997). The methods of fostering creativity through mathematical problem solving. ZDM, 29(3), 86-87.

Haylock, D. W. (1987): A framework for assessing mathematical creativity in school children. In: Educational Studies in Mathematics. 18(1), 59-74.

Hetzroni, O., Agada, H., & Leikin, M. (2019). Creativity in autism: an examination of general a mathematical creative thinking among children with autism spectrum disorder and children with typical development. Journal of autism and development disorders, 49 (9), 3833-3844.

Jensen, L. R. (1973). The Relationships Among Mathematical Creativity, Numerical Aptitude, and Mathematical Achievement. Journal of Creative Behavior, 25(2), 154-161.

Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2012). Connecting Mathematical Creativity to Mathematical ability, ZDM, 45(2), 167-181.

Kattou, M., Christou, C., & Pitta-Pantazi, D. (2015). Mathematical creativity or general creativity? In Ninth Congress of the European Society for Research in Mathematical Education (pp. 1016-1023). Prague, Czech Rpublie.

Kilpatick, J. (1987). Problem formulating: Where do good problems Come frome? In: A.H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education

     (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum.

Koichu, B., & Kontorovich, I. (2013). Dissecting Success Stories on Mathematical Problem Posing: a case of the Billiard Task. Educational Studies in Mathematics,83, 71-86.

Kontrovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behavior, 31(1), 149-161.

Kwon, O. N., Park, J. H., & Park, J. S. (2006). Cultivating divergent thinking in mathmatics through an open-ended approach. Asia Pacific Education Review, 7(1), 51-61.

Laycock, M. (1970). Creative Mathematics at Nueva. Arithmetic Teacher, 17, 325-328.

Leikin, R., & Sriraman, B. (Eds). (2016). Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp.1-3). Springer.

Leikin, R., & Elgrably, H. (2019). Problem through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research.

Leikin, R., & Elgrably, H., (2022). Strategy creativity and outcome creativity when solving open tasks: focusing on problem posing through investigations. ZSM-Mathematics Education 54, 35-49.

Leung, S. K. S. (1997). On the role of creative thinking in problem posing. ZDM, 29(3), 81-85.

Liljedahl, P, & Sriraman, B. (2006). Musings on mathematical creativity. For The Learning of Mathematics, 26(1),20-23.

Lubart, T., & Guignard, J. H. (2004). The generatlity-specificity of creativity: A multivariate approach, In R. J. Sternberg, E. L. Grigornko, & J. L. Singer (Eds.), Creativity: From potential to realization (pp. 43-56). Washington, D.C: American Psychological Association.

Lurai, S. R., Sriraman, B., & Kaufman, J.C. (2017). Enhancing equity in the classroom by teaching for mathematical creativity. ZDM, 49, 1033-1039. https:// doi.org / 10.1007/ s11858-017-0892-2.

Mann, E. L. (2005). Mathematical Creativity and School Mathematics: Indicators of Mathematical Creativity in Middle School Students.

Mann, E. L. (2006). Creativity: The essence of Mathematics. Journal for the Education of the Gifted, 30(2), 236-260.

Murni. (2013). Open ended approach in learning to improve students thinking skill in Banda Aceh. International Journal of Independent Research and Studies, 2(2), 95-101.

NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA: The National Council of Teacher of Mathematics, Inc.

OECD. (2019). Framework for the assessment of creative thinking in PISA 2021. Accessed Nov 2020. https: // www. oecd.org/pisa/publications/PISA-2021-ceative-thinking-framework.pdf

Otgonbaatar, K. (2020). Examining Mathematical Creativity Among Mongolian Ninth-Grade Students Using Problem-Posing Approach. Journal of Education and Practice, 11 (27), 69-75.

Pehkonen, E. (1997). Use of Open-Ended Problem in Mathematics Classroom. Finland: University (Finland). Dept. of teacher Education.

Pehkonen, E. (1999). Open-Ended Problems: A method for an educational change. In International Symposium on Elementary Maths Teaching (SEMT99). Prague: Charles University.

Pehkonen, E. (2007). Problem Solving in mathematics education in Finland. WG2, Topic, 8,9.

Poincaré, H. (1948). Scince and method. New York: Dover.

Poincaré, H. (1956): Mathematical Creation. In: J. R. Newman (ed.): The world of mathematics, V4, New York: Simon and Schuster, pp. 2041-2050.

Sanchez, A., Font, V., & Breda, A. (2021). Significance of creativity and its development in mathematics classes for preservice teachers who are not trained to develop students' creativity. Mathematics Education Research Journal. https:// doi.org / 1007 / S13394-021-00367-w.

Sharma, Y. (2014). The Effects of Strategy Mathematics Anxiety on Mathematical Creativity of School Students. Mathematics Education, 9(1), 25-37.

Silver, E. A. (1994). On Mathematical Problem Posing. For the Learning of Mathematics, 14(1), 19-28

Sliver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing, Zentralblatt Fur Didaktik der Mathematic, 29 (3), 75-80.

Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Edcuation, 17, 20-36.

Sriraman, B.&Lee, K. (2011). The Elements of Creativity and Giftedness (Vol.1). Sense Publishers.

Sriraman, B., Haavold, P., & Lee, K. (2013). Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. ZDM, 1-11.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. P. Clarkson (Ed.), Technology in Mathematics Education

       (pp.518-525). Melbourn: Mathematics Education Research Group of Australasia.

Suherman. (2013). Kiat Pendidikan Mathematika di Indonesia: Konstatasi Keadaan Masa Kini Menuju Harapan Masa Depan. Jakarta: Direktorat Jenderal Pendidikan Tinggi, Departemen Pendidikan Nasional.

Sullivan, M. (2011). Precalculus. Ninth edition, Pearson Education.

Tjoe, H. (2019). Looking Back to Solve Differently: Familiarity, Fluency, and Flexibility. In Mathematical Problem Solving (PP. 3-20). Springer, Cham.

Torrance, E. P. (1966). Torrance Test of creative Thinking: Norms technical manual, Princeton, NJ: Personnel Press.

Torrance, E. P. (1974). Norms technical manual: Torrance Tests of Creative Thinking. Lexington, Mass: Ginn and Co.

Torrance, E. P. (1988). The nature of creativity as manifest in its testing, In R.J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (PP. 43-75). New York: Cambridge University Press.

Treffinger, D., Young, G., Selby, E., & Shepardson, C. (2002). Assessing Creativity: A guide for educators. Storrs, CT: The National Research Center on the Gifted and Talented.

Vistro‌‌ – ‌yu, C.P. (2009). Using innovation techniques to generate new problems. In Mathematical Problem Solving: Yearbook 2009, association of mathematics educators, PP. 185-207.

Wardani, S. B., Sumarmo, U., & Nishitoni, I. (2011). Mathematical Creativity and Disposition: Experiment with grade-10 students using silver inquiry approach.

Wechsler, S. M., Saiz, C., Rivas, S. F., Vendromini, M. C., & Franco, A. (2018). Creative and Critical Thinking: Independent or Overlapping Components. Thinking Skills and Creativity, 27(1), 114-122.

Wendy, B. Sanchez. (2013). Open-ended Questions and process Standards.                   National Concil of Teachers of Mathematics, 107 (3), 206-211.

Wessles, H. M. (2014). Levels of mathematical creativity in model-eliciting activities. Journal of Mathematical Modelling and Application, 1(9), 22-40.

Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities: comparing chines and u.s. students. In B. Sriraman, K. Lee (Eds.), The Elements of Creativity and Giftedness (pp. 5-28). Rotterdom, Netherlands: Sense Publisher.