Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics
Abstract
In recent years, calls to nurture and teach creativity from an early age in schools has intensified. Creativity is something regular in the teaching of arts subjects but is not a common feature in teaching science, technology, engineering and mathematics subjects. However, what really matters, is how the subject is being taught. This research aimed to foster creativity through the teaching of mathematics via problem solving that challenges the solving of problems in a creative manner, which is defined as creative problem solving. This quasi-experimental study investigates changes in students learning of mathematics via creative problem solving. Altogether, 172 Form 1 students forming treatment and comparison groups from four schools in Gombak District area, Malaysia were involved. A mixed qualitative and quantitative data were collected to investigate the effect of the 3 cycles of creative problem solving lessons implemented. Instruments used were Torrance Test of Creative Thinking, a mathematics problem solving test and creativity checklist. This paper will only present the quantitative data obtained. Results show statistically significant increases in scores for most categories of creativity and problem solving tests. This research brought together teachers and researchers in trialling creative problem solving to teach mathematics, to achieve the enhancement of students’ creative thinking and problem solving skills. This coincided with the introduction of Kurikulum Standard Sekolah Menengah with new emphasis to strengthen the quality of science, technology, engineering and mathematics education in general, where higher-order thinking reforms are emphasized.
Article in English.
Kūrybiškumo stiprinimas ir problemų sprendimo gebėjimai, kūrybiškai sprendžiant matematikos mokymo problemas
Santrauka
Pastaraisiais metais suaktyvėjo raginimai ugdyti kūrybiškumą ir jo mokyti nuo pat mažumės. Kūrybiškumas yra įprastas mokant meninių dalykų, tačiau nėra pastebimas bruožas mokant mokslinių, technologinių, inžinerinių ir matematinių disciplinų. Tačiau iš tiesų svarbu tai, kaip mokoma tam tikro dalyko. Šio tyrimo tikslas – skatinti kūrybiškumą matematikos mokymo pavyzdžiu, kai kūrybiškai sprendžiamos problemos, ir tai atitinkamai apibrėžiama. Šiame kvazieksperimentiniame tyrime nagrinėjami pokyčiai, susiję su tuo, kaip moksleiviai mokosi matematikos, kūrybiškai spręsdami problemas. Iš viso tyrime dalyvavo 172 pirmosios formos moksleiviai, priklausantys stebėjimo ir lyginimo grupėms iš keturių mokyklų, esančių Gombako rajono teritorijoje (Malaizija). Buvo surinkti mišrūs kokybiniai ir kiekybiniai duomenys, siekiant ištirti realizuotus tris ciklus pamokų, skirtų kūrybiniams problemų sprendimams. Buvo naudojamasi šiomis priemonėmis: Torrance’o kūrybinio mąstymo testu, matematinių problemų sprendimo testu ir kūrybiškumo rezultatų vertinimo kontroliniu sąrašu. Straipsnyje pristatomi tik kiekybiniai duomenys. Rezultatai atskleidžia statistiškai reikšmingą padidėjimą vertinant kūrybiškumą daugelyje kategorijų ir pasitelkiant problemų sprendimo testus. Šiame tyrime dalyvavo mokytojai ir tyrėjai, atlikti kūrybinio problemų sprendimo bandymai mokant matematikos ir stengiantis ugdyti moksleivių kūrybinį mąstymą bei problemų sprendimo gebėjimus. Tai atitinka Kurikulum Standard Sekolah Menengah įvadinę dalį, iš naujo pabrėžiant mokslinį, technologinį, inžinerinį ir matematinį ugdymą apskritai, šiose srityse akcentuojant aukštesnio lygio pertvarkytą mąstyseną.
Reikšminiai žodžiai: kūrybiškumo testas, kūrybiškumas matematikoje, gebėjimo spręsti problemas ugdymas, matematikos mokymasis sprendžiant problemas, pamokos tyrimas, Kurikulum Standard Sekolah Menengah naujas planas.
Keyword : creativity test, creativity in mathematics, enhancing problem solving ability, learning mathematics via problem solving, lesson study, new Kurikulum Standard Sekolah Menengah syllabus
How to Cite
Khalid, M., Saad, S., Abdul Hamid, S. R., Ridhuan Abdullah, M. ., Ibrahim, H., & Shahrill, M. (2020). Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics. Creativity Studies, 13(2), 270-291. https://doi.org/10.3846/cs.2020.11027
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Fard, A. E., Bahador, A., Moghadam, M. N., Rajabi, H., & Moradi, A. N. (2014). The possible impact of problem-solving method of instruction on exceptional students’ creativity. Journal of Education and Training Studies, 2(3), 60–68. https://doi.org/10.11114/jets.v2i3.342
Greeno, J. G. (2017). Forms of understanding in mathematical problem solving. Taylor & Francis. https://doi.org/10.4324/9781315188522-5
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Levenson, E. (2013). Tasks that may occasion mathematical creativity: Teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269–291. https://doi.org/10.1007/s10857-012-9229-9
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19.
Lim, Ch. S. (2010). Assessment in Malaysian school mathematics: Issues and concerns. http://www.criced.tsukuba.ac.jp/math/apec/apec2009/doc/pdf_20-21/LimChapSam-paper.pdf
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–262. https://doi.org/10.4219/jeg-2006-264
Mellou, E. (1996). Can creativity be nurtured in young children? Early Child Development and Care, 119(1), 119–130. https://doi.org/10.1080/0300443961190109
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OECD. (2014d). PISA 2012 technical report. http://www.oecd.org/pisa/pisaproducts/PISA-2012-technical-report-final.pdf
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Plucker, J. A., Beghetto, R. A., & Dow, G. T. (2004). Why isn’t creativity more important to educational psychologists? Potentials, pitfalls, and future directions in creativity research. Educational Psychologist, 39(2), 83–96. https://doi.org/10.1207/s15326985ep3902_1
Polya, G. (2004). How to solve it: A new aspect of mathematical method. Series: Princeton Science Library. Princeton University Press.
Posamentier, A. S., Smith, B. S., & Stepelman, J. (2009). Teaching secondary mathematics: Teaching and enrichments units. Merrill Prentice Hall.
Retalis, S., Katsamani, M., Georgiakakis, P., Lazakidou, G., Petropoulou, O., & Kargidis, Th. (2010). Designing collaborative learning sessions that promote creative problem solving using design patterns. In L. Dirckinck-Holmfeld, V. Hodgson, Ch. Jones, M. de Laat, D. McConnell, & Th. Ryberg (Eds.), Proceedings of the 7th International Conference on Networked Learning (pp. 490–498), 3–4 May, 2010. Aalborg, Denmark.
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Robinson, K., & Aronica, L. (2015). Creative schools: The grassroots revolution that’s transforming education. Penguin Books.
Runco, M. A., & Johnson, D. J. (2002). Parents’ and teachers’ implicit theories of children’s creativity: A cross-cultural perspective. Creativity Research Journal, 14(3–4), 427–438. https://doi.org/10.1207/S15326934CRJ1434_12
Saleh, S., & Aziz, A. (2012). Teaching practices among secondary school teachers in Malaysia. https://pdfs.semanticscholar.org/37a7/b40e50d9ab5eaf66e8abfcdebee4761ac9b9.pdf?_ga=2.20604029.454579747.1580658915-199233841.1528889777
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM: Mathematics Education, 29(3), 75–80. https://doi.org/10.1007/s11858-997-0003-x
Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36. https://doi.org/10.4219/jsge-2005-389
Sternberg, R. J. (2006). The nature of creativity. Creativity Research Journal, 18(1), 87–98. https://doi.org/10.1207/s15326934crj1801_10
Sternberg, R. J. (2012). The assessment of creativity: An investment-based approach. Creativity Research Journal, 24(1), 3–12. https://doi.org/10.1080/10400419.2012.652925
Teo, L. K. C., & Waugh, R. F. (2010). A Rasch measure of fostering creativity. Creativity Research Journal, 22(2), 206–218. https://doi.org/10.1080/10400419.2010.481534
Torrance, E. P. (1971). Are the Torrance tests of creative thinking biased against or in favor of “Disadvantaged” groups? Gifted Child Quarterly, 15(2), 75–80. https://doi.org/10.1177/001698627101500201
Trawick-Smith, J. (2014). Early childhood development: A multicultural perspective. Pearson Education Limited.
Ayob, A., Hussain, A., Marzuki Mustafa, M., & Fauzi Aminuddin Shazi Shaarani, M. (2011). Nurturing creativity and innovative thinking through experiential learning. Procedia: Social and Behavioral Sciences, 18, 247–254. https://doi.org/10.1016/j.sbspro.2011.05.035
Brunkalla, K. (2009). How to increase mathematical creativity – An experiment. The Mathematics Enthusiast, 6(1), 257–266.
Chamberlin, S. A., & Moon, S. M. (2005). Model eliciting activities as a tool to develop and identify creatively gifted mathematicians. The Journal of Secondary Gifted Education, 17(1), 37–47. https://doi.org/10.4219/jsge-2005-393
Costa, A. L. (Ed.). (2001). Developing minds: A resource book for teaching thinking. Alexandria: Association for Supervision and Curriculum Development.
Ellwood, S., Pallier, G., Snyder, A., & Gallette, J. (2009). The incubation effect: Hatching a solution? Creativity Research Journal, 21(1), 6–14. https://doi.org/10.1080/10400410802633368
Fard, A. E., Bahador, A., Moghadam, M. N., Rajabi, H., & Moradi, A. N. (2014). The possible impact of problem-solving method of instruction on exceptional students’ creativity. Journal of Education and Training Studies, 2(3), 60–68. https://doi.org/10.11114/jets.v2i3.342
Greeno, J. G. (2017). Forms of understanding in mathematical problem solving. Taylor & Francis. https://doi.org/10.4324/9781315188522-5
Griethuijsen, van R. A. L. F., Eijck, van M. W., Haste, H., Brok, den P. J., Skinner, N. C., Mansour, N., Savran Gencer, A., & BouJaoude, S. (2014). Global patterns in students’ views of science and interest in science. Research in Science Education, 45(4), 581–603. https://doi.org/10.1007/s11165-014-9438-6
Guilford, J. P. (1967). Creativity: Yesterday, today and tomorrow. The Journal of Creative Behavior, 1(1), 3–14. https://doi.org/10.1002/j.2162-6057.1967.tb00002.x
Haylock, D. W. (1987). A framework for assessing mathematical creativity in schoolchildren. Educational Studies in Mathematics, 18(1), 59–74. https://doi.org/10.1007/BF00367914
Hu, R., Xiaohui, S., & Shieh, Ch. J. (2017). A study on the application of creative problem solving teaching to statistics teaching. EURASIA: Journal of Mathematics, Science and Technology Education, 13(7), 3139–3149. https://doi.org/10.12973/eurasia.2017.00708a
Isoda, M. (2010). Lesson study: Problem solving approaches in mathematics education as a Japanese experience. Procedia: Social and Behavioral Sciences, 8, 17–27. https://doi.org/10.1016/j.sbspro.2010.12.003
James, M. A. (2015). Managing the classroom for creativity. Creative Education, 6, 1032–1043. https://doi.org/10.4236/ce.2015.610102
Kaplan, D. E. (2019). Creativity in education: Teaching for creativity development. Psychology, 10, 140–147. https://doi.org/10.4236/psych.2019.102012
Kaufman, J. C., & Sternberg, R. J. (Eds.). (2006). The international handbook of creativity. Cambridge University Press. https://doi.org/10.1017/CBO9780511818240
Khalid, M. (2017). Fostering problem solving and performance assessment among Malaysian mathematics teachers. Sains Humanika, 9(1–2), 51–55. https://doi.org/10.11113/sh.v9n1-2.1098
Kim, K. H. (2006). Can we trust creativity tests? A review of the Torrance Tests of Creative Thinking (TTCT). Creativity Research Journal, 18(1), 3–14. https://doi.org/10.1207/s15326934crj1801_2
Kopka, J. (2010). How to solve mathematical problems. Catholic University in Ružomberok. Ružomberok, Slovakia [unpublished source].
Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modelling. In Jr. F. K. Lester (Ed.), Second handbook for research on mathematics teaching and learning (pp. 763–802). Information Age Publishing.
Lester, F. K. Jr., Masingila, J. O., Mau, S. T., Lambdin, D. V., Santon, dos V. M., & Raymond, A. M. (1994). Learning how to teach via problem solving. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics (pp. 152–166). National Council of Teachers of Mathematics.
Levenson, E. (2013). Tasks that may occasion mathematical creativity: Teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269–291. https://doi.org/10.1007/s10857-012-9229-9
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19.
Lim, Ch. S. (2010). Assessment in Malaysian school mathematics: Issues and concerns. http://www.criced.tsukuba.ac.jp/math/apec/apec2009/doc/pdf_20-21/LimChapSam-paper.pdf
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–262. https://doi.org/10.4219/jeg-2006-264
Mellou, E. (1996). Can creativity be nurtured in young children? Early Child Development and Care, 119(1), 119–130. https://doi.org/10.1080/0300443961190109
Ministry of Education, Malaysia. (2013). Malaysia educational blueprint: Annual report 2013. https://www.padu.edu.my/wp-content/uploads/2018/01/PADU-AR-2013-ENG.pdf
National Council of Teachers of Mathematics. (2000). Executive summary: Principles and standards for school mathematics. https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf
Novak, J. D. (2010). Learning, creating and using knowledge: Concept maps as facilitative tools in schools and corporations. Routledge. https://doi.org/10.4324/9780203862001
OECD. (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. https://www.oecd-ilibrary.org/docserver/9789264190511-en.pdf?expires=1580654526&id=id&accname=guest&checksum=074EB03FD4D7FB122A322C1AB81A10BD
OECD. (2014a). Education at a Glance 2014: Highlights. https://www.oecd-ilibrary.org/docserver/eag_highlights-2014-en.pdf?expires=1580644839&id=id&accname=guest&checksum=4F347DD90BB5080FB66B3D588B605058
OECD. (2014b). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. https://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf
OECD. (2014c). PISA 2012 results: Creative problem solving. Students’ skills in tackling real-life problems. Vol. V. https://www.oecd-ilibrary.org/docserver/9789264208070-en.pdf?expires=1580659048&id=id&accname=guest&checksum=43503BB658FB2794E8280D794380E28E
OECD. (2014d). PISA 2012 technical report. http://www.oecd.org/pisa/pisaproducts/PISA-2012-technical-report-final.pdf
Park, M. (2013). Korean primary school teachers’ conceptions of foundations and creativity in mathematics. Korean Society of Mathematical Education (Series A: The Mathematical Education), 52(3), 399–422. https://doi.org/10.7468/mathedu.2013.52.3.399
Plucker, J. A., Beghetto, R. A., & Dow, G. T. (2004). Why isn’t creativity more important to educational psychologists? Potentials, pitfalls, and future directions in creativity research. Educational Psychologist, 39(2), 83–96. https://doi.org/10.1207/s15326985ep3902_1
Polya, G. (2004). How to solve it: A new aspect of mathematical method. Series: Princeton Science Library. Princeton University Press.
Posamentier, A. S., Smith, B. S., & Stepelman, J. (2009). Teaching secondary mathematics: Teaching and enrichments units. Merrill Prentice Hall.
Retalis, S., Katsamani, M., Georgiakakis, P., Lazakidou, G., Petropoulou, O., & Kargidis, Th. (2010). Designing collaborative learning sessions that promote creative problem solving using design patterns. In L. Dirckinck-Holmfeld, V. Hodgson, Ch. Jones, M. de Laat, D. McConnell, & Th. Ryberg (Eds.), Proceedings of the 7th International Conference on Networked Learning (pp. 490–498), 3–4 May, 2010. Aalborg, Denmark.
Robinson, K. (2006). Do schools kill creativity? TED: Ideas worth Spreading. https://www.ted.com/talks/sir_ken_robinson_do_schools_kill_creativity
Robinson, K., & Aronica, L. (2015). Creative schools: The grassroots revolution that’s transforming education. Penguin Books.
Runco, M. A., & Johnson, D. J. (2002). Parents’ and teachers’ implicit theories of children’s creativity: A cross-cultural perspective. Creativity Research Journal, 14(3–4), 427–438. https://doi.org/10.1207/S15326934CRJ1434_12
Saleh, S., & Aziz, A. (2012). Teaching practices among secondary school teachers in Malaysia. https://pdfs.semanticscholar.org/37a7/b40e50d9ab5eaf66e8abfcdebee4761ac9b9.pdf?_ga=2.20604029.454579747.1580658915-199233841.1528889777
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM: Mathematics Education, 29(3), 75–80. https://doi.org/10.1007/s11858-997-0003-x
Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36. https://doi.org/10.4219/jsge-2005-389
Sternberg, R. J. (2006). The nature of creativity. Creativity Research Journal, 18(1), 87–98. https://doi.org/10.1207/s15326934crj1801_10
Sternberg, R. J. (2012). The assessment of creativity: An investment-based approach. Creativity Research Journal, 24(1), 3–12. https://doi.org/10.1080/10400419.2012.652925
Teo, L. K. C., & Waugh, R. F. (2010). A Rasch measure of fostering creativity. Creativity Research Journal, 22(2), 206–218. https://doi.org/10.1080/10400419.2010.481534
Torrance, E. P. (1971). Are the Torrance tests of creative thinking biased against or in favor of “Disadvantaged” groups? Gifted Child Quarterly, 15(2), 75–80. https://doi.org/10.1177/001698627101500201
Trawick-Smith, J. (2014). Early childhood development: A multicultural perspective. Pearson Education Limited.