Skip to main content

On the Relationship Between Problem Posing, Problem Solving, and Creativity in the Primary School

  • Chapter
Mathematical Problem Posing

Part of the book series: Research in Mathematics Education ((RME))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt fĂĽr Didaktik der Mathematik, 37(3), 149–158.

    Article  Google Scholar 

  • Dunker, K. (1945). On problem-solving. Psychological Monographs, 58(5), 270.

    Google Scholar 

  • 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.

    Google Scholar 

  • English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Getzels, J. W. (1979). Problem finding: A theoretical note. Cognitive Science, 3, 167–172.

    Article  Google Scholar 

  • Guilford, J. P. (1950). Creativity. The American Psychologist, 5(9), 444–454.

    Article  Google Scholar 

  • Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Leung, S. S. (1996). Problem posing as assessment: Reflections and reconstructions. The Mathematics Educator, 1(2), 159–171.

    Google Scholar 

  • Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt fĂĽr Didaktik der Mathematik, 97(3), 81–85.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Mathematics Curriculum Development Group of Basic Education of Education Department. (2002). The interpretation of mathematics curriculum (trial version). Beijing, China: Beijing Normal University.

    Google Scholar 

  • Mednick, S. A. (1962). The associative basis of the creative process. Psychological Review, 69, 220–232.

    Article  Google Scholar 

  • Ministry of Education of Italy. (2007). Indicazioni per il curriculo. Roma, Italy: Ministero della Pubblica Istruzione.

    Google Scholar 

  • Ministry of Education of Peoples’ Republic of China (NCSM). (2001). Chinese national curriculum standards on mathematics. Beijing, China: Beijing Normal University.

    Google Scholar 

  • Nadjafikhah, M., Yaftian, N., & Bakhashalizadeh, S. (2012). Mathematical creativity: Some definitions and characteristics. Social and Behavioural Sciences, 31, 285–291.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Palm, T. (2006). Word problems as simulations of real-world situations. A proposed framework. For the Learning of Mathematics, 26(1), 42–47.

    Google Scholar 

  • PoincarĂ©, H. (1908). L’invention mathĂ©matique. Bulletin de l’Institut GĂ©nĂ©ral Psychologique, 3(8), 175–187.

    Google Scholar 

  • 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.

    Google Scholar 

  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

    Google Scholar 

  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt fĂĽr Didaktik der Mathematik, 29(3), 75–80.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Sriraman, B. (2009). The characteristics of mathematical creativity. Zentralblatt fĂĽr Didaktik der Mathematik, 41(1–2), 13–27.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Starko, A. J. (2010). Creativity in the classroom. Schools of curious delight. New York, NY: Routledge.

    Google Scholar 

  • 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.

    Google Scholar 

  • Torrance, E. P. (1966). Torrance tests of creative thinking. Princeton, NJ: Personnel Press.

    Google Scholar 

  • UMI-CIIM. (2001). Matematica 2001. Materiali per il XXVII Convegno Nazionale sull’Insegnamento della matematica. Ischia, Italy: UMI.

    Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.

    Google Scholar 

  • 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cinzia Bonotto .

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics