RESEARCH PAPER
Creativity of Pre-service Teachers in Problem Posing
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An-Najah National University, Nablus, West Bank, PALESTINE
 
2
Al-Qasemi Academic College of Education, Baqa El-Garbiah, ISRAEL
 
 
Online publication date: 2018-05-11
 
 
Publication date: 2018-05-11
 
 
EURASIA J. Math., Sci Tech. Ed 2018;14(7):2929-2945
 
KEYWORDS
ABSTRACT
Problem posing and technology are attracting the attention of mathematics educators because of their potential to affect positively many aspects of students’ learning. Little research has been done on the relationship between technology and mathematical creativity. The present study investigates this issue in the context of problem posing, in the presence and absence of a strategy for problem posing (the “what-if-not” strategy). Participants were pre-service mathematics teachers. The research was conducted during the academic year 2013-2014. Participants were randomly divided into four groups of 19 to 21 participants and who differed in their use of technology and of the what-if-not strategy. The participants who used technology used the Paper Pools applet. The data was collected from the participants’ posing problems on a specific mathematics situation; the Paper Pool situation. The data analysis was done using SPSS 18.0. The research findings indicate that the combination of technology and the what-if-not strategy has a positive and significant effect on the three components of participants’ creativity: fluency, flexibility and originality. Separately, both technology and the what-if-not strategy had a positive and significant effect on participants’ fluency and flexibility related to problem types, but not related to strategy types. The findings also indicate that the originality of participants who worked without technology but with the what-if-not strategy was significantly lower than that of participants who worked with technology, whether with or without the what-if-not strategy. Thus, results indicated that technology is more effective than the what-if-not strategy in encouraging originality in problem posing. We recommend the use of technology together with the what-if-not strategy to enhance pre-service teachers’ mathematical thinking, because this combination makes available for student’s learning multiple agencies required for his/her creative acts.
REFERENCES (83)
1.
Abramovich, S., & Cho, E. (2006). Technology as a Medium for Elementary Preteachers’ Problem-Posing Experience in Mathematics. Journal of Computers in Mathematics and Science Teaching, 25(4), 309-323.
 
2.
Abramovich, S., & Cho, E. (2015). Using digital technology for mathematical problem posing, in: F. M. Singer, N. Ellerton, & J. Cai (Eds), Mathematical problem posing: From research to effective practice (pp. 71-102), New York: Springer. https://doi.org/10.1007/978-1-....
 
3.
Abu-Elwan, R. (2011). How prospective teachers’ use of the Cabri II environment can have an effect on the posing of fractal problems In M. Joubert, A. Clark-Wilson, & M. McCabe (eds.), The 10th International Conference on Technology in Mathematics Teaching (pp. 56-61). Portsmouth, UK: University of Portsmouth.
 
4.
Akay, H., & Boz, N. (2009). Prospective teachers’ views about problem-posing activities. Procedia Social and Behavior Sciences, 1(1), 1192–1198. https://doi.org/10.1016/j.sbsp....
 
5.
Amabile, T. M. (1983). The social psychology of creativity. New York: Springer-Verlag. https://doi.org/10.1007/978-1-....
 
6.
Amabile, T. M. (1999). How to kill creativity. Harvard Business Review, 76(5), 76-87.
 
7.
Beal, C. R., & Cohen, P. R. (2012). Teach Ourselves: Technology to Support Problem Posing in the STEM Classroom. Creative Education, 3(4), 513-519. https://doi.org/10.4236/ce.201....
 
8.
Behzadi, M., & Manuchehri, M. (2013). Examining creativity of students through smart board in learning mathematics. Mathematics Education Trends and Research, 1, 1-7. Retrieved from http://www.ispacs.com/journals... https://doi.org/10.5899/2013/m....
 
9.
Bolden, D., Harries, A., & Newton, D. (2010). Pre-service primary teachers’ conceptions of creativity in mathematics. Educational Studies in Mathematics, 73 (2), 143-157. https://doi.org/10.1007/s10649....
 
10.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55. https://doi.org/10.1007/s10649....
 
11.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.
 
12.
Brown, S. I., & Walter, I. (1990). The art of problem posing (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
 
13.
Brown, S. I., & Walter, M. I. (1969). What if not? Mathematics Teaching, 46, 38-45.
 
14.
Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In S. I. Brown & M. I. Walter (Eds.), Problem posing: Reflections and application (pp. 16-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
 
15.
Buteau, C. (2008). Triggering university students’ mathematical creativity and intellectual independence by use of technology: une implémentation à brock university. Paper presented at the Deuxième Congrès Canada-France Université du Québec à Montréal, 2 au 5 Juin 2008.
 
16.
Christou, C. (2005). Problem solving and problem posing in a dynamic geometry environment. The Montana Mathematics Enthusiast, 2(2), 125–143.
 
17.
Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem Solving and Problem Posing in a Dynamic Geometry Environment. The Mathematics Enthusiast, 2(2). http://scholarworks.umt.edu/tm....
 
18.
Clements, D. H. (1995). Teaching creativity with computers. Educational Psychology Review, 7(2), 141–161. https://doi.org/10.1007/BF0221....
 
19.
Cohen, J. (1960) A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37-46. https://doi.org/10.1177/001316....
 
20.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.
 
21.
Dunham, P., & Dick, T. (1994). Research on graphing calculators. Mathematics Teacher, 87, 440–445.
 
22.
Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. https://doi.org/10.1007/s10649....
 
23.
English, L. D. (2009). The changing realities of classroom mathematical problem solving. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 351–362). Rotterdam: Sense Publishers.
 
24.
English, L. N. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-107. https://doi.org/10.2307/749719.
 
25.
Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht: Kluwer.
 
26.
Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. The Journal of Mathematical Behavior, 22(1), 73–89. https://doi.org/10.1016/S0732-....
 
27.
Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444-454. https://doi.org/10.1037/h00634....
 
28.
Guilford, J. P. (1975). Creativity: A quarter century of progress. In I. A.Taylor & J. W. Getzels (Eds.), Perspectives in creativity (pp. 37-59). Chicago: Aldine.
 
29.
Haylock, D. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59–74. https://doi.org/10.1007/BF0036....
 
30.
Hoyles, C. (2001). Steering between skills and creativity: A role for the computer? For the Learning of Mathematics, 21, 33-39.
 
31.
James, V., Lederman, G. R., & Vagt-Traore, B. (2010). Enhancing creativity in the classroom. In M. Orey (Ed.), Emerging perspectives on learning, teaching, and technology (pp. 104-114). Zurich, Switzerland: Jacobs Foundation.
 
32.
Kanematsu, H., & Barry, D.M. (2016). STEM and ICT education in intelligent environments. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-....
 
33.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM, 45(2), 167-181. https://doi.org/10.1007/s11858....
 
34.
Kilic, C. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686. https://doi.org/10.1007/s40299....
 
35.
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale: Lawrence Erlbaum Associates.
 
36.
Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the billiard task. Educational Studies in Mathematics, 83(1), 71–86. https://doi.org/10.1007/s10649....
 
37.
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they? In M. Avotiņa, D. Bonka, H. Meissner, L. Ramāna, L. Sheffield & E. Velikova (Eds.), Proceedings of the 6th International Conference Creativity in Mathematics Education and the Education of Gifted Students (pp. 120-125). Latvia: Latvia University.
 
38.
Lagrange, J.-B., & Artigue, M. (2009). Students’ activities about functions at upper secondary level: a grid for designing a digital environment and analysing uses. In M. Tzekaki, M. Kaldrimidou & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 465-472). Thessaloniki, Greece: PME.
 
39.
Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and Mathematics Education: A Multidimensional Study of the Evolution of Research and Innovation. In A. Bishop, M.A. Clements, C. Keitel-Kreidt, J. Kilpatrick, & F.K.-S. Leung (eds.), Second International handbook of research in mathematics education (pp.239-271). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94....
 
40.
Lai, E. R. (2011). Critical thinking: A literature review. http://www.pearsonassessments.....
 
41.
Lavy, I., & Bershadsky, I. (2003). Problem Posing via “What if not?” strategy in Solid Geometry - A Case Study. The Journal of Mathematical Behavior, 22(4) 369-387. https://doi.org/10.1016/j.jmat....
 
42.
Lavy, I., & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. The Journal of Mathematical Behavior, 29(1), 11-24. https://doi.org/10.1016/j.jmat....
 
43.
Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: what makes the difference? ZDM, 45(2), 183–197. https://doi.org/10.1007/s11858....
 
44.
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: the state of the art. ZDM, 45(2), 159–166. https://doi.org/10.1007/s11858....
 
45.
Leikin, R., Koichu, B., & Berman, A. (2009). Mathematical giftedness as a quality of problem-solving acts. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 115-128). Rotterdam: Sense Publishers.
 
46.
Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. https://doi.org/10.1007/s10649....
 
47.
Levenson, E. (2011). (Naïve) beliefs and affect associated with creative mathematical tasks: Three cases. In B. Rösken & M. Casper (Eds.), current state of research on mathematical beliefs XVII: Proceedings of the MAVI-17 Conference (pp. 140–149). Bochum, Germany: MAVI.
 
48.
Liekin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1&2), 167-188.
 
49.
Lombardi, M. M. (2007). Authentic learning for the 21st century: An overview. Educause Learning Initiative. https://net.educause.edu/ir/li....
 
50.
Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24, 385–401. https://doi.org/10.1016/j.jmat....
 
51.
Mann, E. (2005). Mathematical Creativity and School Mathematics: Indicators of Mathematical Creativity in Middle School Students (Unpublished doctoral dissertation). University of Connecticut, Connecticut, US.
 
52.
Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–260. https://doi.org/10.4219/jeg-20....
 
53.
Nadjafikhah, M., Yaftian, N., & Bakhshalizadeh, S. (2012). Mathematical creativity: some definitions and characteristics. Procedia-Social and Behavioral Sciences, 31, 285–291. https://doi.org/10.1016/j.sbsp....
 
54.
National Advisory Committee on Creative and Cultural Education (NACCCE) (1999). All our futures: Creativity, culture and education. London, UK: DFES.
 
55.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author.
 
56.
Palha, S., Schuitema, J., van Boxtel, C., & Peetsma, T. (2015). The effect of high versus low guidance structured tasks on mathematical creativity. In K. Krainer, & N. Vondrová (eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp.1039-1045). Prague, Czech Republic: ERME.
 
57.
Pásztor, A., Molnár, G., & Csapó, B. (2015). Technology-based assessment of creativity in educational context: the case of divergent thinking and its relation to mathematical achievement. Thinking Skills and Creativity, 18, 32-42. https://doi.org/10.1016/j.tsc.....
 
58.
Pea, R. D. (1987). Cognitive technologies in mathematics education. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89–122). Hilldale, NJ: Erlbaum.
 
59.
Sarrazy, B., & Novotna, J. (2013). Didactical contract and responsiveness to didactical contract: a theoretical framework for enquiry into students’ creativity in mathematics. ZDM, 45(2), 281–293. https://doi.org/10.1007/s11858....
 
60.
Scherer, R., & Tiemann, R. (2014). Evidence on the effects of task interactivity and grade level on thinking skills involved in complex problem solving. Thinking Skills and Creativity, 11, 48-64. https://doi.org/10.1016/j.tsc.....
 
61.
Shriki, A. (2013). A model for assessing the development of students’ creativity in the context of problem posing. Creative Education, 4(7), 430-439. https://doi.org/10.4236/ce.201....
 
62.
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14, 19-28.
 
63.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 3, 75-80. https://doi.org/10.1007/s11858....
 
64.
Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
 
65.
Silver, E. A., Mamona–Downs, J., Leung, S., & Kenny, P. A. (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27(3), 293–309. https://doi.org/10.2307/749366.
 
66.
Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261–284. https://doi.org/10.1207/s15327....
 
67.
Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: the murky and furtive world of mathematical inventiveness. ZDM, 45(2), 239–252. https://doi.org/10.1007/s11858....
 
68.
Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem posing research in mathematics education: new questions and directions. Education Studies in Mathematics, 83(1), 1-7. https://doi.org/10.1007/s10649....
 
69.
Sophocleous, P., & Pitta-Pantazi, D. (2011). Creativity in three-dimensional geometry: How an interactive 3D-geometry software environment enhance it? In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of Seventh Conference of the European Research in Mathematics Education (pp. 1143 - 1153). Rzeshów, Poland: ERME.
 
70.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Prufrock Journal, 17(1), 20-36. https://doi.org/10.4219/jsge-2....
 
71.
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, 45(2), 215-225. https://doi.org/10.1007/s11858....
 
72.
Sternberg, R. J., & Lubart, T. I. (1999). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 3-15). Cambridge: Cambridge University Press.
 
73.
Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: a contemporary perspective (pp. 164 - 185). Edith Cowan University: MASTEC.
 
74.
Subhi, T. (1999). The impact of logo on gifted children’s achievement and creativity. Journal of Computer Assisted Learning, 15(2), 98–108. https://doi.org/10.1046/j.1365....
 
75.
Tall, D. O. (1989). Concept images, generic organizers, computers & curriculum change. For the Learning of Mathematics, 9(3), 37–42.
 
76.
Tall, D. O. (2002). Using technology to support an embodied approach to learning concepts in mathematics. Paper presented at First Coloquio do Historia e Tecnologia no Ensino de Matematica at Universidade do Estado do Rio De Janiero, February 21-3, 2002.
 
77.
Torrance, E. P. (1966). The Torrance tests of creative thinking-norms-technical manual research edition-verbal tests, forms A and B-figural tests, forms A and B. Princeton, NJ: Personnel Press.
 
78.
Torrance, E. P. (1969). Creativity. What research says to the teacher. Washington, DC: National Education Association.
 
79.
Torrance, E. P. (1974). Torrance tests of creative thinking: Norms-technical manual. Bensenville, IL: Scholastic Testing Service.
 
80.
Voica, C., & Singer, F. M. (2013). Problem modification as a tool for detecting cognitive flexibility in school children. ZDM, 45(2), 267–279. https://doi.org/10.1007/s11858....
 
81.
Wood, R., & Ashfield, J. (2008). The use of the interactive whiteboard for creative teaching and learning in literacy and mathematics: a case study. British Journal of Educational Technology, 39(1), 84-96. https://doi.org/10.1111/j.1467....
 
82.
Yerushalmy, M. (2009). Educational technology and curricular design: Promoting mathematical creativity for all students. In R. Leikin, A. Berman & B. Koichu (Eds.), Mathematical creativity and the education of gifted students (pp. 101-113). Rotterdam, The Netherlands: Sense Publishers.
 
83.
Zales, C. R. (1997). Improving student achievement in mathematics through active learning. Center Valley, Pennsylvania: Allentown College of St. Francis de Sales.
 
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