Abstract
Problem posing is a form of creative activity that can operate within tasks involving semi-structured rich situations, using real-life artefacts and human interactions. Several researchers have linked problem-posing skills with creativity, citing flexibility, fluency, and originality as creativity categories. However, the nature of this relationship still remains unclear. For this reason, the exploratory study presented here sought to begin to investigate the relationship between problem-posing activities (supported by problem-solving activities) and creativity. The study is part of an ongoing research project based on teaching experiments consisting of a series of classroom activities in upper elementary school, using suitable artefacts and interactive teaching methods, in order to create a substantially modified teaching/learning environment. In addition, the study provides a method for analyzing the products of problem posing that teachers could use in the classroom to identify and assess both the activity of problem posing itself and students’ creativity in mathematics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bonotto, C. (2005). How informal out-of-school mathematics can help students make sense of formal in-school mathematics: The case of multiplying by decimal numbers. Mathematical Thinking and Learning, 7(4), 313–344.
Bonotto, C. (2009). Working towards teaching realistic mathematical modelling and problem posing in Italian classrooms. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 297–313). Rotterdam, The Netherlands: Sense Publishers.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55. doi:10.1007/s10649-012-9441-7.
Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale, NJ: Erlbaum.
Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401–421.
Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9, 919–948.
Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt für Didaktik der Mathematik, 37(3), 149–158.
Dunker, K. (1945). On problem-solving. Psychological Monographs, 58(5), 270.
Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching and learning. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 987–1033). Dordrecht, The Netherlands: Kluwer.
English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.
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, The Netherlands: Sense Publishers.
Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht, The Netherlands: Kluwer.
Getzels, J. W. (1979). Problem finding: A theoretical note. Cognitive Science, 3, 167–172.
Guilford, J. P. (1950). Creativity. The American Psychologist, 5(9), 444–454.
Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.
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, NJ: Erlbaum.
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they? In M. Avotina, D. Bonka, H. Meissner, L. Sheffield, & E. Velikova (Eds.), Proceedings of the 6th International Conference Creativity in Mathematics Education and the Education of Gifted Students (pp. 120–125). Riga, Latvia: University of Latvia.
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161.
Leung, S. S. (1996). Problem posing as assessment: Reflections and reconstructions. The Mathematics Educator, 1(2), 159–171.
Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt für Didaktik der Mathematik, 97(3), 81–85.
Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24.
Mathematics Curriculum Development Group of Basic Education of Education Department. (2002). The interpretation of mathematics curriculum (trial version). Beijing, China: Beijing Normal University.
Mednick, S. A. (1962). The associative basis of the creative process. Psychological Review, 69, 220–232.
Ministry of Education of Italy. (2007). Indicazioni per il curriculo. Roma, Italy: Ministero della Pubblica Istruzione.
Ministry of Education of Peoples’ Republic of China (NCSM). (2001). Chinese national curriculum standards on mathematics. Beijing, China: Beijing Normal University.
Nadjafikhah, M., Yaftian, N., & Bakhashalizadeh, S. (2012). Mathematical creativity: Some definitions and characteristics. Social and Behavioural Sciences, 31, 285–291.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Palm, T. (2006). Word problems as simulations of real-world situations. A proposed framework. For the Learning of Mathematics, 26(1), 42–47.
Poincaré, H. (1908). L’invention mathématique. Bulletin de l’Institut Général Psychologique, 3(8), 175–187.
Schoenfeld, A. H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311–343). Hillsdale, NJ: Erlbaum.
Silver, E. A. (1994). On mathematical problem posing. 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. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80.
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.
Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135.
Siswono, T. Y. E. (2010). Leveling students’ creative thinking in solving and posing mathematical problem. Indonesian Mathematical Society Journal on Mathematics Education, 1(1), 20–41.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36.
Sriraman, B. (2009). The characteristics of mathematical creativity. Zentralblatt für Didaktik der Mathematik, 41(1–2), 13–27.
Stanic, G. M. A., & Kilpatrick, J. (1988). Historical perspectives on problem solving in the mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), Research agenda for mathematics education: The teaching and assessing of mathematical problem solving (Vol. 3, pp. 1–22). Hillsdale, NJ: Erlbaum.
Starko, A. J. (2010). Creativity in the classroom. Schools of curious delight. New York, NY: Routledge.
Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Melbourne, Australia: Mathematics Education Research Group of Australasia.
Torrance, E. P. (1966). Torrance tests of creative thinking. Princeton, NJ: Personnel Press.
UMI-CIIM. (2001). Matematica 2001. Materiali per il XXVII Convegno Nazionale sull’Insegnamento della matematica. Ischia, Italy: UMI.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.
Yuan, X., & Sriraman, B. (2010). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). Rotterdam, The Netherlands: Sense Publishers.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bonotto, C., Santo, L.D. (2015). On the Relationship Between Problem Posing, Problem Solving, and Creativity in the Primary School. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6258-3_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6257-6
Online ISBN: 978-1-4614-6258-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)