Araştırma Makalesi
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Mathematical Creativity Test (MCT) development for middle school students

Yıl 2022, Cilt: 11 Sayı: 4, 242 - 268, 31.10.2022
https://doi.org/10.19128/turje.1037694

Öz

This study presents the development of a mathematical creativity test and exploration of its psychometric properties. The study was conducted in six public schools and a high ability center between 2015 and 2018. The sample of the study included 1129 middle school students. The Mathematical Creativity Test (MCT) consists of problem posing, making conjecture, and proof subtests. Each test has two items. The scores of the MCT are composed of fluency, flexibility, and creativity quotient. For construct validity, EFA yielded a 3-factor solution, namely, problem posing, making conjecture, and proof subtests. CFA confirmed the 3-factor solution, and all fit indices were found to be good. For criterion validity, one-way ANOVA for independent samples was conducted in different classes, and it showed that there was a significant difference, and Pearson's correlation coefficient was investigated between MCT scores and the report card grades of the mathematics lesson. There was a strong and positive correlation between the two variables. The internal consistency and the interrater reliability of the test scores were high.

Destekleyen Kurum

Anadolu University

Proje Numarası

1605E493

Kaynakça

  • Akbulut, Y. (2010). Sosyal bilimlerde SPSS uygulamaları [SPSS applications in social sciences]. Pasifik Ofset.
  • Akgül, S. (2014). Üstün yetenekli öğrencilerin matematik yaratıcılıklarını açıklamaya yönelik bir model geliştirilmesi [A model study to examine gifted and talented students’ mathematical creativity] [Unpublished doctoral dissertation]. İstanbul Üniversitesi.
  • Akgul. S., & Kahveci, N. G. (2016). A study on the development of a mathematics creativity scale. Eurasian Journal of Educational Research, 62, 57-76. http://dx.doi.org/10.14689/ejer.2016.62.5
  • Amabile, T. M. (1983). The social psychology of creativity: A componential conceptualization. Journal of Personality and Social Psychology, 45(2), 357-376. https://doi.org/10.1037/0022-3514.45.2.357
  • Anastasi, A., & Urbina, S. (1997). Psychological testing. Prentice-Hall.
  • Anderson, R., & Freebody, P. (1981). Vocabulary knowledge. In J. Guthrie (Ed.), Comprehension and teaching: Research review (pp. 71–117). International Reading Association.
  • Baer, J. (2012). Domain specificity and the limits of creativity theory. Journal of Creative Behavior, 46(1), 16-29. https://doi.org/10.1002/jocb.002
  • Bahar, A. K., & Maker, J. C. (2011). Exploring the relationship between mathematical creativity and mathematical achievement. Asia-Pacific Journal of Gifted and Talented Education, 3(1), 33-48.
  • Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics [Unpublished doctoral dissertation]. University of Missouri.
  • Bal-Sezerel, B. (2019). Ortaokul öğrencilerinin yaratıcılığını ölçmeye yönelik matematiksel üretkenlik testinin geliştirilmesi [Development of a mathematical creativity test for creativity of middle school students] [Unpublished doctoral dissertation]. Anadolu Üniversitesi.
  • Bicer, A., Chamberlin, S., & Perihan, C. (2020). A meta-analysis of the relationship between mathematics achievement and creativity. Journal of Creative Behaviour, 55(3), 569-590. https://doi.org/10.1002/jocb.474
  • Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105, 457-485. https://doi.org/10.1007/s10649-020-09995-8
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, E. A., Karadeniz, Ş. ve Demirel, F. (2017). Bilimsel araştırma yöntemleri [Scientific research methods] (23th ed.). Pegem Akademi.
  • Büyüköztürk, Ş. (2011). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences] (14th ed.). Pegem Akademi.
  • Cicchetti, D. V., & Sparrow, S. S. (1990). Assessment of adaptive behavior in young children. In J. J. Johnson, & J. Goldman (Eds.), Developmental assessment in clinical child psychology: A handbook (pp. 173–196). Pergamon Press.
  • Cohen, S. A., & Stover, G. (1981). Effects of teaching sixth-grade students to modify format variables of math word problems. Reading Research Quarterly, 16(2), 175-200. https://doi.org/10.2307/747554
  • Cohen, J. W. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
  • Cohen, R. J., & Swerdlik, M. (2002). Psychological testing and assessment: An introduction to test and measurement (5th ed.). McGraw-Hill.
  • Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2012). Sosyal bilimler için çok değişkenli istatistik: SPSS ve LISREL uygulamaları [Multivariate statistics for social sciences: SPSS and LISREL applications] (2nd ed.). Pegem Akademi.
  • DeVellis, R. F. (2012). Scale development: Theory and applications (3rd ed.). Sage Publications.
  • Dunn, J. A. (1975). Tests of creativity in mathematics. International Journal of Mathematical Education in Science and Technology,6(3), 327-332. https://doi.org/10.1080/0020739750060310
  • Dunteman, G. H. (1989). Principal component analysis: Quantitative applications in the social sciences series (Vol. 69). Sage Publications.
  • Einstein, A., & lnfeld, L. (1938). The evolution of physics. Simon & Schuster.
  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42-53). Kluwer.
  • Evans, E. W. (1964). Measuring the ability of students to respond in creative mathematical situations at the late elementary and early junior high school level [Unpublished Doctoral Dissertation]. University of Michigan.
  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). Sage Publication.
  • Fisher, R. (1990). “Teaching for thinking: Language and maths”and “teaching for thinking across the curriculum”, chapters in teaching children to think. Basil Blackwell.
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Ortaokul öğrencilerine yönelik Matematiksel Yaratıcılık Testi’nin (MYT) geliştirilmesi

Yıl 2022, Cilt: 11 Sayı: 4, 242 - 268, 31.10.2022
https://doi.org/10.19128/turje.1037694

Öz

Bu çalışmada matematik alanında yaratıcı olan öğrencileri tanılamak amacıyla matematiksel yaratıcılık ölçeği geliştirmek ve ölçeğin psikometrik özelliklerini ortaya koymak amaçlanmıştır. Araştırma 2015-2018 yılları arasında 5., 6., 7. ve 8. sınıf düzeyindeki 1129 öğrencinin devam ettiği MEB’e bağlı altı ortaokul ve özel yeteneklilere yönelik bir merkezde gerçekleştirilmiştir. Matematiksel Yaratıcılık Testi (MYT) üç alt ölçekten (problem oluşturma, varsayım oluşturma, kanıtlama) oluşmaktadır. Alt ölçekler ikişer maddeden meydana gelmektedir. Ölçekten akıcılık, esneklik ve yaratıcılık bölümü olmak üzere üç puan türü elde edilmektedir. Yapı geçerliğini sağlamak için açımlayıcı faktör analizi ve doğrulayıcı faktör analizi (AFA ve DFA) yapılmıştır. AFA üç faktörlü yapı önermiş, DFA ise kuramsal modeli doğrulamıştır. MYT’nin ölçüt geçerliğini ortaya koymak için yapılan bağımsız gruplar için tek yönlü ANOVA sınıflar arasında anlamlı farklılık olduğunu ve matematik dersi karne notları ile yapılan Pearson korelasyon analizi ise MYT ile korelasyonun yüksek olduğunu göstermiştir. MYT’nin iç tutarlık güvenirlik değerleri ve okuyucular arası güvenirlik değerleri de yüksek çıkmıştır.

Proje Numarası

1605E493

Kaynakça

  • Akbulut, Y. (2010). Sosyal bilimlerde SPSS uygulamaları [SPSS applications in social sciences]. Pasifik Ofset.
  • Akgül, S. (2014). Üstün yetenekli öğrencilerin matematik yaratıcılıklarını açıklamaya yönelik bir model geliştirilmesi [A model study to examine gifted and talented students’ mathematical creativity] [Unpublished doctoral dissertation]. İstanbul Üniversitesi.
  • Akgul. S., & Kahveci, N. G. (2016). A study on the development of a mathematics creativity scale. Eurasian Journal of Educational Research, 62, 57-76. http://dx.doi.org/10.14689/ejer.2016.62.5
  • Amabile, T. M. (1983). The social psychology of creativity: A componential conceptualization. Journal of Personality and Social Psychology, 45(2), 357-376. https://doi.org/10.1037/0022-3514.45.2.357
  • Anastasi, A., & Urbina, S. (1997). Psychological testing. Prentice-Hall.
  • Anderson, R., & Freebody, P. (1981). Vocabulary knowledge. In J. Guthrie (Ed.), Comprehension and teaching: Research review (pp. 71–117). International Reading Association.
  • Baer, J. (2012). Domain specificity and the limits of creativity theory. Journal of Creative Behavior, 46(1), 16-29. https://doi.org/10.1002/jocb.002
  • Bahar, A. K., & Maker, J. C. (2011). Exploring the relationship between mathematical creativity and mathematical achievement. Asia-Pacific Journal of Gifted and Talented Education, 3(1), 33-48.
  • Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics [Unpublished doctoral dissertation]. University of Missouri.
  • Bal-Sezerel, B. (2019). Ortaokul öğrencilerinin yaratıcılığını ölçmeye yönelik matematiksel üretkenlik testinin geliştirilmesi [Development of a mathematical creativity test for creativity of middle school students] [Unpublished doctoral dissertation]. Anadolu Üniversitesi.
  • Bicer, A., Chamberlin, S., & Perihan, C. (2020). A meta-analysis of the relationship between mathematics achievement and creativity. Journal of Creative Behaviour, 55(3), 569-590. https://doi.org/10.1002/jocb.474
  • Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105, 457-485. https://doi.org/10.1007/s10649-020-09995-8
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, E. A., Karadeniz, Ş. ve Demirel, F. (2017). Bilimsel araştırma yöntemleri [Scientific research methods] (23th ed.). Pegem Akademi.
  • Büyüköztürk, Ş. (2011). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences] (14th ed.). Pegem Akademi.
  • Cicchetti, D. V., & Sparrow, S. S. (1990). Assessment of adaptive behavior in young children. In J. J. Johnson, & J. Goldman (Eds.), Developmental assessment in clinical child psychology: A handbook (pp. 173–196). Pergamon Press.
  • Cohen, S. A., & Stover, G. (1981). Effects of teaching sixth-grade students to modify format variables of math word problems. Reading Research Quarterly, 16(2), 175-200. https://doi.org/10.2307/747554
  • Cohen, J. W. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
  • Cohen, R. J., & Swerdlik, M. (2002). Psychological testing and assessment: An introduction to test and measurement (5th ed.). McGraw-Hill.
  • Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2012). Sosyal bilimler için çok değişkenli istatistik: SPSS ve LISREL uygulamaları [Multivariate statistics for social sciences: SPSS and LISREL applications] (2nd ed.). Pegem Akademi.
  • DeVellis, R. F. (2012). Scale development: Theory and applications (3rd ed.). Sage Publications.
  • Dunn, J. A. (1975). Tests of creativity in mathematics. International Journal of Mathematical Education in Science and Technology,6(3), 327-332. https://doi.org/10.1080/0020739750060310
  • Dunteman, G. H. (1989). Principal component analysis: Quantitative applications in the social sciences series (Vol. 69). Sage Publications.
  • Einstein, A., & lnfeld, L. (1938). The evolution of physics. Simon & Schuster.
  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42-53). Kluwer.
  • Evans, E. W. (1964). Measuring the ability of students to respond in creative mathematical situations at the late elementary and early junior high school level [Unpublished Doctoral Dissertation]. University of Michigan.
  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). Sage Publication.
  • Fisher, R. (1990). “Teaching for thinking: Language and maths”and “teaching for thinking across the curriculum”, chapters in teaching children to think. Basil Blackwell.
  • Fornell, C. & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. American Marketing Association, 18(1). 39-50. https://doi.org/10.2307/3151312
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  • Jöreskog, K. G., & Sörbom, D. (1993). Lisrel 8: Structural equation modeling with the simples command language. Scientific Software International.
  • Karasar, N. (2016). Bilimsel araştırma yöntemi: Kavramlar ilkeler teknikler [Scientific research method: Concepts principles techniques] (30th ed.). Nobel.
  • Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45, 167-181. https://doi.org/10.1007/s11858-012-0467-1
  • Kaufman, J. C., & Baer, J. (2005). Creativity across domains: Faces of the muse. Lawrence Erlbaum.
  • Kaufman, J. C., Plucker, J. A., & Baer, J. (2008). Essentials of creativity assessment. John Wiley & Sons.
  • Kesici, A., & Aşılıoğlu, B. (2017). Developing stress scale for secondary school students: Reliability and validity study. Kastamonu Eğitim Dergisi, 25(6), 2413-2426.
  • Kim, H., Cho, S., & Ahn, C. (2003). Development of mathematical creative problem solving ability test for identification of the gifted in math. Gifted Education International, 18(2), 164-174. https://doi.org/10.1177/026142940301800206
  • Kline, R. B. (2010). Principles and practice of structural equation modeling. Guilford Publications.
  • Kozlowski, J. S., & Si, S. (2019). Mathematical creativity: A vehicle to foster equity. Thinking Skills and Creativity, 33, 1-8. https://doi.org/10.1016/j.tsc.2019.100579
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. The University of Chicago Press.
  • Küchemann, D., and Hoyles, C. (2009). From empirical to structural reasoning in mathematics. In D. A. Stykianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspectives (pp. 171-203). Taylor & Francis.
  • 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. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129-145). Sense Publishers.
  • Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM-The International Journal on Mathematics Education, 45(2), 183–197. https://doi.org/10.1007/s11858-012-0460-8
  • Leung, S. S. (1997). On the role of creative thinking in problem posing. ZDM Mathematics Education, 29(3), 81-85. https://doi.org/10.1007/s11858-997-0004-9
  • Livne, N. L., & Milgram, R. M. (2006). Academic versus creative abilities in mathematics: Two components of the same construct? Creativity Research Journal, 18(2), 199-212. https://doi.org/10.1207/s15326934crj1802_6
  • Long, C. T., DeTemple, D. W., & Millman, R. S. (2012). Mathematical reasoning for elementary teachers (6th ed.). Pearson.
  • Mann, E. L. (2009). The search for mathematical creativity: Identifying creative potential in middle school students. Creativity Research Journal, 21(4), 338-348. https://doi.org/10.1080/10400410903297402
  • Matlin, M. (1994). Cognition (3rd ed.). Hartcout Brace.
  • Ministry of National Education. (2020). Milli Eğitim Bakanlığı öğretim programlarını izleme ve değerlendirme sistemi [The system of monitoring and evaluation of the curriculum of the Ministry of National Education]. http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • National Council of Teachers Mathematics. (1990). Teaching & learning mathematics in the 190’s. The National Council of Teachers Mathematics Inc.
  • Nickerson, R. S. (2010). Mathematical reasoning. Psychology Press.
  • Pallant, J. (2005). SPSS survival manual (12nd ed.). Allen & Unwin.
  • Pelczer, I., & Rodriguez, F. G. (2011). Creativity assessment in school settings through problem posing tasks. The Montana Mathematics Enthusiast, 8(1), 383-398.
  • Pham, L. H. (2014). Validation of prediction relationship of creative problem-solving attributes with math creativity [Unpublished doctoral dissertation]. St. John’s University.
  • Programme for International Student Assessment. (2022). PISA 2022 creative thinking framework (draft). OECD. https:// www.oecd.org/pisa/innovation/creative-thinking/
  • Plucker, J. A., Beghetto, R. A., & Dow, G. (2004). Why isn’t creativity more important to educational psychologist? Potential, pittfalls, and future directions in creativity research. Educational Psychologists, 39(2), 83-96. https://doi.org/10.1207/s15326985ep3902_1
  • Poincarê, H. (1952). Science and method: Henri Poincarê. The Modern Library.
  • Pollak, M. (1987). Average run lengths of an optimal method of detecting a change in distribution. The Annals of Statistics, 15(2), 749-779. https://doi.org/10.1214/aos/1176350373
  • Polya, G. (1954). Induction and analogy in mathematics. Princeton University Press.
  • Prouse, H. L. (1967). Creativity in school mathematics. National Council of Teacher of Mathematics, 60(8), 876-879. https://doi.org/10.5951/MT.60.8.0876
  • Rips, L. J., & Asmuth, J. (2007). Mathematical induction and induction in mathematics. In A. Feeney, & E. Heit (Eds.), Inductive reasoning: experimental, developmental and computational approaches (pp. 248-268). Cambridge University Press.
  • 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.
  • Sak, U. (2014). Yaratıcılık gelişimi ve geliştirilmesi [Growth and development creativity]. Vize.
  • Sak, U., Ayvaz, Ü., Bal-Sezerel, B., & Özdemir, N. N. (2017). Creativity in the domain of mathematics. In J. Kaufman, V. Glăveanu, & J. Baer (Eds.) The Cambridge handbook of creativity across domains (pp. 276-298). Cambridge University Press.
  • Sak, U., & Maker, C. J. (2006). Developmental variation in children's creative mathematical thinking as a function of schooling, age, and knowledge. Creativity Research Journal, 18(3), 279-291. https://doi.org/10.1207/s15326934crj1803_5
  • Sanacore, J., & Palumbo, A. (2009). Understanding the fourth-grade slump: Our point of view. The Educational Forum, 73(1), 67-74. https://doi.org/10.1080/00131720802539648
  • Sarouphim, K. M. (1999). Discovering multiple intelligences through a performance-based assessment: consistency with independent ratings. Exceptional Children, 65(2), 151-161. https://doi.org/10.1177/001440299906500201
  • Sarouphim, K. M. (2001). DISCOVER: Concurrent validity, gender differences, and identification of minority students. Gifted Child Quarterly, 45(2), 130-138. https://doi.org/10.1177/001698620104500206
  • Seddon, G. M. (1983). The measurement and properties of divergent thinking ability as a single compound entity. Journal of Educational Mesaurement, 20(4), 393-402. https://doi.org/10.1111/j.1745-3984.1983.tb00216.x
  • Silver, E. A. (1994). On mathematical problem solving. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-The International Journal on Mathematical Education, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.2307/749846
  • Simonton, D. K. (1983). Formal education, eminence and dogmatism: The curvilinear relationship. The Journal of Creative Behavior, 17(3), 149-162. https://doi.org/10.1002/j.2162-6057.1983.tb00348.x
  • Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1-7. https://doi.org/10.1007/s10649-013-9478-2
  • Singh, B. (1987). The development of tests to measure mathematical creativity. International Journal of Mathematical Education in Science and Technology, 18(2), 181-186. https://doi.org/10.1080/0020739870180203
  • Snyder, A., Mitchell, J., Bossomaier, T., & Pallier, G. (2004) The creativity quotient: An objective scoring of ideational fluency. Creativity Research Journal, 16(4), 415-420. https://doi.org/10.1080/10400410409534552
  • Sternberg, R. J., & Lubart, T. I. (2009). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 3-15). Cambridge University Press.
  • Stoyanova, E. (1997). Extending and exploring student’s problem solving via problem posing: A study of years 8 and 9 students involved in mathematics challenge and enrichment stages of Euler enrichment for young Australians [Unpublished doctoral dissertation]. Edith Cowan University.
  • Tabachnick, B. G., & Fidel, L. S. (2007). Using multivariate statistics (5th ed.). Allyn & Bacon Inc.
  • Tanaka, J. S. (1987). How big is big enough? Sample size and goddness of fit in structural equation models with latent variables. Child Development, 58(1), 134-146. https://doi.org/10.2307/1130296
  • Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. American Psychological Association.
  • Tompkins, G. (1994). Teaching writing: Balancing process and product. Macmillan.
  • Trochim, W. M., & Donnelly, J. P. (2006). The research methods knowledge base (3rd ed.). Atomic Dog.
  • Vale, I., Pimentel, T., & Barbosa, A. (2018). The power of seeing in problem solving and creativity: an issue under discussion. In N. Amado, S. Carreira, & K. Jones (Eds.), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect (pp. 243-272). Springer.
  • Wolf, R. S. (1998). Proof, logic, and conjecture: The mathematician’s toolbox. W. H. Freeman.
  • Yıldırım, C. (2000). Matematiksel düşünme [Mathematical thinking] (3rd ed). Remzi.
Toplam 105 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Araştırma Makaleleri
Yazarlar

Bilge Bal Sezerel 0000-0001-7262-3563

Uğur Sak 0000-0001-6312-5239

Proje Numarası 1605E493
Yayımlanma Tarihi 31 Ekim 2022
Kabul Tarihi 26 Ekim 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 11 Sayı: 4

Kaynak Göster

APA Bal Sezerel, B., & Sak, U. (2022). Mathematical Creativity Test (MCT) development for middle school students. Turkish Journal of Education, 11(4), 242-268. https://doi.org/10.19128/turje.1037694

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