Analysis of a test for measuring mathematical creativity
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The aim of this paper is to examine the construct of mathematical creativity in secondary education, as well as its measurement through problem posing and problem solving. The study consisted of a sample of 62 high school students aged 12-14 years, all of them gifted and talented, and was conducted during a series of enrichment workshops. The measurement instrument used was the Mathematical Creative Problem Solving Ability Test (MCPSAT), which consists of four problem-solving tasks to assess the classic dimensions of creativity (fluency, flexibility and originality). To assess originality, a creativity quotient was obtained. The results revealed that the most effective to measure mathematical creativity are Tasks 1 (‘The Sixteen Points’) and Task 4 (‘Water Prism’). In addition, the test displayed an adequate internal structure, indicating a greater correlation between intra-task dimensions than between creative dimensions or abilities.
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AYAS, M. Bahadir; & SAK, Ugur. (2014). Objective measure of scientific creativity: Psychometric validity of the Creative Scientific Ability Test. Thinking Skills and Creativity, 13, 195-205. https://doi.org/10.1016/j.tsc.2014.06.001
BAER, John (1998). The case for domain specificity of creativity. Creativity Research Journal, 11(2), 173-177. https://doi.org/10.1207/s15326934crj1102_7
BAER, John (2015). The Importance of Domain-Specific Expertise in Creativity. Roeper Review, 37(3), 165-178. https://doi.org/10.1080/02783193.2015.1047480
BALKA, Don Stephen (1974). The development of an instrument to measure creative ability in mathematics (Publication No. 7515965) [Doctoral dissertation, University of Missouri]. ProQuest: https://www.proquest.com/openview/801a9fb46281ef1927e08d047c1cd2d8/1
BEATY, Roger E.; & SILVIA, Paul J. (2012). Why Do Ideas Get More Creative Across Time? An Executive Interpretation of the Serial Order Effect in Divergent Thinking Tasks. Psychology of Aesthetics, Creativity, and the Arts, 6(4), 309–319 https://doi.org/10.1037/a0029171
BERMEJO, Rosario; RUIZ, María José; FERRÁNDIZ, Carmen; SOTO, Gloria; SAINZ, Marta (2014). Pensamiento científico-creativo y rendimiento académico. Revista de estudios e investigación en psicología y educación, 1(1), 64-72. https://doi.org/10.17979/reipe.2014.1.1.24
BRAVO-VICK, Milagros; PADRÓ-COLLAZO, Pascua; BORRERO, Michelle (2019). Mathematics and science attitude inventory: validation for use in a Spanish-speaking context. Revista de estudios e investigación en psicología y educación, 6(2),167-178. https://doi.org/10.17979/reipe.2019.6.2.5687
CASTELLÓ, Antoni y BATLLE, Concepció (1998). Aspectos teóricos e instrumentales en la identificación del alumnado superdotado y talentoso. Propuesta de un protocolo. FAISCA, 6, 26-66. https://revistas.ucm.es/index.php/FAIS/article/view/FAIS9898110026A
CRAFT, Anna (2002). Creativity and Early Years Education: A Lifewide Foundation. Continuum.
DE VINK, Isabelle C; WILLEMSEN, Robin H; LAZONDER, Ard. W.; & KROESBERGEN, Evelyn H. (2021). Creativity in mathematics performance: The role of divergent and convergent thinking. British Journal of Educational Psychology, 1-18. https://doi.org/10.1111/bjep.12459
ESPARZA, Fernando Javier (2016). Propuesta de un programa para favorecer el pensamiento científico [Tesis de Licenciatura, Universidad de Murcia]. Repositorio Institucional de la Universidad de Murcia https://digitum.um.es/digitum/handle/10201/29897
FERRANDO, Mercedes; FERRÁNDIZ, Carmen; BERMEJO, Rosario; SÁNCHEZ, Cristina; PARRA, Joaquín y PRIETO, María Dolores (2007). Estructura interna y baremación del Test de Pensamiento Creativo de Torrance. Psicothema, 19(3), 489–496. https://www.psicothema.com/pii?pii=3390
GARDNER, Howard (1983). Frames of mind: The theory of multiple intelligences. Basic Books.
GUILFORD, Joy Paul (1959). Traits of creativity. In Harold H. Anderson (Ed.), Creativity and its Cultivation (pp. 167-188). Harper.
HAYLOCK, Derek William (1984). Aspects of mathematical creativity in children aged 11-12 [Doctoral dissertation, University of London]. King’s College London Research Portal. https://kclpure.kcl.ac.uk/portal/en/theses/aspects-of-mathematical-creativity-in-children-aged-11--12(ae59b6a1-8c6a-408c-932f-d7909b5d465f).html
HU, Weiping; & ADEY, Philip (2002). Scientific creativity test for secondary school students. International Journal of Science Education, 24(4), 389-403. https://doi.org/10.1080/09500690110098912
HWANG, Po-Sheng; PENG, Shu-Ling; CHEN, Hsueh-Chih; TSENG, Li-Cheng; & HSU, Li-Ching (2017). The relative influences of domain knowledge and domain-general divergent thinking on scientific creativity and mathematical creativity. Thinking Skills and Creativity, 25, 1-9. https://doi.org/10.1016/j.tsc.2017.06.001
IBM Corp. (2016). IBM SPSS Statistics for Windows, Version 24.0. Armonk, NY: IBM Corp.
KATTOU, Maria; KONTOYIANNI, Katerina; PITTA-PANTAZI, Demetra; & CHRISTOU, Constantinos (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45, 167–181. https://doi.org/10.1007/s11858-012-0467-1
KRUTETSKII, Vadim Andreyevich (1976). The psychology of Mathematical Abilities in Schoolchildren. University of Chicago Press.
LEE, Kang-Sup; HWANG, Dongjou; & SEO, Jong-Jin (2003). A Development of the Test for Mathematical Creative Problem Solving Ability. Research in Mathematical Education, 7(3), 163-189. https://www.koreascience.or.kr/article/JAKO200311921974337.page
LEIKIN, Roza (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 Publisher.
LOE, Ley Orgánica de 2/2006, de 3 de mayo, de la Educación. Boletín Oficial del Estado, núm. 106, de 4 de mayo de 2006, pp. 1 a 112. https://www.boe.es/eli/es/lo/2006/05/03/2
LOMCE, Ley Orgánica 8/2013, de 9 de diciembre, de Mejora de la Calidad Educativa. Boletín Oficial del Estado, núm. 295, de 10 de diciembre de 2013. https://www.boe.es/eli/es/lo/2013/12/09/8
LOMLOE, Ley Orgánica 3/2020, de 29 de diciembre, por la que se modifica la Ley Orgánica 2/2006, de 3 de mayo, de Educación. Boletín Oficial del Estado, núm. 340, de 30 de diciembre de 2020. https://www.boe.es/eli/es/lo/2020/12/29/3
LÓPEZ-GONZÁLEZ, Emelina; PÉREZ-CARBONELL, Amparo y RAMOS-SANTANA, Genoveva (2011). Modelos complementarios al Análisis Factorial en la construcción de escalas ordinales: un ejemplo aplicado a la medida del Clima Social Aula. Revista de Educación, 354, 369-397. https://doi.org/10.4438/1988-592X-RE-2011-354-004
LUCAS, Bill; CLAXTON, Guy; & SPENCER, Ellen (2013). Progression in Student Creativity in School: First steps towards new forms of formative assessments. OECD education Working Papers, 2, 81-121. https://doi.org/10.1787/5k4dp59msdwk-en
MANN, Eric Louis (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students (Publication No. 3205573) [Doctoral dissertation, University of Connecticut]. ProQuest: https://www.proquest.com/openview/b15acb3042c52bc857983c90e4817e1d/1?pq-origsite=gscholar&cbl=18750&diss=y
MOHAMED, Ahmed (2006). Investigating the scientific creativity of fifth-grade students [Doctoral dissertation, University of Arizona]. UA Campus Repository. https://repository.arizona.edu/handle/10150/194100
Real Decreto 126/2014, de 28 de febrero, por el cual se establece el currículo básico de la Educación Primaria. Boletín Oficial del Estado, núm. 52, de 1 de marzo de 2014, pp. 1-58. https://www.boe.es/eli/es/rd/2014/02/28/126
Real Decreto 1105/2014, de 26 de diciembre, por el cual se establece el currículo básico de la Educación Secundaria Obligatoria y el Bachillerato. Boletín Oficial del Estado, núm. 3, de 3 de enero de 2014, pp. 1-35. https://www.boe.es/eli/es/rd/2014/09/26/817
RUIZ, María José; BERMEJO, Rosario; PRIETO, María Dolores; FERRÁNDIZ, Carmen y ALMEIDA, Lenandro S. (2013). Evaluación del Pensamiento Científico-Creativo: Adaptación y validación de una prueba en población española. Revista Galego-Portuguesa de Psicoloxía e Educación, 21(1), 175-194. http://hdl.handle.net/2183/12613
SAK, Ugur; & AYAS, M. Bahadir (2013). Creative Scientific Ability Test (C-SAT): A new measure of scientific creativity. Psychological Test and Assessment Modelling, 55(3), 316-329. ProQuest: https://www.proquest.com/docview/1468914888?pq-origsite=gscholar&fromopenview=true
SAK, Ugur; & MAKER, June (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
SALAZAR, María; ZAPATERA, Alberto; BERMEJO, Rosario; y FERRANDO, Mercedes (febrero, 2016). Estudio de un test para evaluar el talento matemático-creativo. [Comunicación]. I Congreso Internacional: Nuevas Perspectivas en el estudio de la Superdotación y el Talento, Murcia-España.
SCHOVERS, Eveline; KROESBERGEN, Evelyn; & KATTOU, Maria (2020). Mathematical Creativity: A Combination of Domain-general Creative and Domain-specific Mathematical Skills. Journal of Creative Behaviour, 54, 242-252. https://doi.org/10.1002/jocb.361
SECKEL, María José; BREDA, Adriana; SÁNCHEZ, Alicia y FONT, Vicenç (2019). Criterios asumidos por profesores cuando argumentan sobre la creatividad matemática. Educaçao e Pesquisa, 45, 1-18. https://doi.org/10.1590/S1678-4634201945211926
SEO, Jong Jin; & HWANG, Dong-Jou (2004). Difference between Gifted and regular Students in Mathematical Creativity and Mathematical Self-Efficacy. Journal of the Korea Society of Mathematical Education Series D: Reseach in Mathematical Education, 8(3), 183-202. https://www.koreascience.or.kr/article/JAKO200411922954310.page
SEQUERA, Elba Cristina (2007). Creatividad y desarrollo profesional docente en matemáticas para la educación primaria [Tesis doctoral, Universidad de Barcelona]. Dipòsit Digital de la Universitat de Barcelona. http://hdl.handle.net/2445/41432
SILVER, Edward A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 3, 75-80. https://doi.org/10.1007/s11858-997-0003-x
SNYDER, Allan; MITCHELL, John; BOSSOMAIER, Terry; & PALLIER, Gerry. (2004). The creativity quotient: an objective scoring of ideational fluency. Creativity Research Journal, 16(4), 415-419. https://doi.org/10.1080/10400410409534552
SOTO, Gloria (2012). Diferentes Perspectivas de Evaluar El Pensamiento Creativo [Tesis Doctoral, Universidad de Murcia]. Repositorio Institucional de la Universidad de Murcia. https://digitum.um.es/digitum/handle/10201/29897
SRIRAMAN, Bharath (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19-34. https://doi.org/10.1007/s11858-008-0114-z
SRIRAMAN, Bharath (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education 17(1), 20–36. https://doi.org/10.4219/jsge-2005-389
SRIRAMAN, Bharath (2008). Are mathematical giftedness and mathematical creativity synonyms? A theoretical analysis of constructs. En B. Sriraman (Ed.), Creativity, Giftedness, and Talent Development in Mathematics (pp. 85-112). The Montana Mathematics Enthusiast.
STERNBERG, Robert J. (1996). What is mathematical thinking? In R. J. Sternberg; & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 303-318). Lawrence Erlbaum Associates.
STOYANOVA, Elena (1997). Extending and exploring students' problem solving via problem posing [Doctoral dissertation, Edith Cowan University]. Research Online Institutional Repository. https://ro.ecu.edu.au/theses/885
TAN, Ai-Girl; & SRIRAMAN, Barath (2017). Convergence in creativity development for mathematical capacity. In R. Leikin; & B. Sriraman (Eds.), Creativity and Giftedness (pp. 117–133). Springer. https://doi.org/10.1007/978-3-319-38840-3_8
TORRANCE, Paul (1966). Torrance Tests of Creative Thinking. Personnel Press.
USISKIN, Zalman (2000). The development into the mathematically talented. Journal of Secondary Gifted Education, 11, 152–162. https://doi.org/10.4219/jsge-2000-623
VALVERDE, Francisco Javier (2015). Creatividad y Aptitudes en alumnos de Educación Secundaria en los dominios figurativo y musical [Tesis Doctoral, Universidad de Murcia]. Repositorio Institucional de la Universidad de Murcia. https://digitum.um.es/digitum/handle/10201/46799
YUAN, Xianwei; & SRIRAMAN, Bharath (2011). An exploratory study of relationships between students’ creativity and mathematical problem-posing abilities. In B. Sriraman; & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5-28). Sense Publishers. https://doi.org/10.1007/978-94-6091-439-3