Skip to main content

Advertisement

Log in

Research Status of Mathematical Problem Posing in Mathematics Education Journals

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

This study analyzed the research status of mathematical problem posing in thirteen major mathematics education journals from each journal’s earliest publication year the study could access to the year of 2018 or 2019, among which 49 years long was the longest and 14 years long was the shortest. After a systematic and comprehensive review of all the journal publications, a total of 62 articles on mathematical problem posing were analyzed in the study. It was found that empirical research constituted the majority of the studies; teachers were the largest research sample group; the research issue of teaching and teacher education was devoted to most frequently; most of the research issues preferred the qualitative research type, posing questions for a problem situation was the most popular type of problem posing task of empirical research articles; and each research sample group was presented each type of problem posing tasks in different frequencies. Implications for research were derived from the results of research types, research sample groups, research issues, and types of problem posing tasks. The current research status and future research perspectives of mathematical problem posing were accordingly proposed in the study.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55.

    Article  Google Scholar 

  • Brown, S. I., & Walter, M. I. (Eds.). (1993). Problem posing: reflections and applications. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Brown, S. L., & Walter, M. I. (1983). The art of problem posing. Philadelphia, PA: Franklin Institute Press.

    Google Scholar 

  • Cai, J., & Brook, M. (2006). Looking back in problem solving. Mathematics Teaching, 196, 42-45.

  • Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics: some answered and unanswered questions. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). New York, NY: Springer.

  • Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521–1540.

    Article  Google Scholar 

  • Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69.

    Article  Google Scholar 

  • Cañadas, M., Molina, M., & Río, A. (2018). Meanings given to algebraic symbolism in problem-posing. Educational Studies in Mathematics, 98, 19–37.

    Article  Google Scholar 

  • Cankoy, O. (2014). Interlocked problem posing and children’s problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 12(1), 219–238.

    Article  Google Scholar 

  • Cankoy, O., & Özder, H. (2017). Generalizability theory research on developing a scoring rubric to assess primary school students’ problem posing skills. Eurasia Journal of Mathematics Science and Technology Education, 13(6), 2423–2439.

    Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM Mathematics Education, 37(3), 149–158.

    Article  Google Scholar 

  • Crespo, S. (2003). Learning to pose mathematical problems: exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52(3), 243–270.

    Article  Google Scholar 

  • Creswell, J. W., & Creswell, J. D. (2018). Research design (5th ed.). Los Angeles, CA: Sage.

  • Dix, A. (2007). Theoretical analysis and theory creation. Cambridge, England: Cambridge University Press.

  • Einstein, A., & Insfeld, L. (1938). The evolution of physics. New York, NY: Simon and Schuster.

  • Ellerton, N. (1986). Children’s made-up mathematics problems—a new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271.

    Article  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 

  • Gall, M. D., Gall, J. P., & Borg, W. R. (2007). Educational research: An introduction (8th ed.). Boston, MA: Pearson.

  • Kar, T. (2015). Analysis of problems posed by sixth-grade middle school students for the addition of fractions in terms of semantic structures. International Journal of Mathematical Education in Science and Technology, 46(6), 879–894.

    Article  Google Scholar 

  • Kattou, M., & Christou, C. (2013). In A. M. Lindmeier & A. Heinze (Eds.), Investigating the effect of general creativity, mathematical knowledge and intelligence on mathematical creativity, Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, p. 239). Kiel.

  • Kilic, C. (2015). Analyzing pre-service primary teachers’ fraction knowledge structures through problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1603–1619.

    Article  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: Lawrence Erlbaum.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Komatsu, K., & Tsujiyama, Y. (2013). Principles of task design to foster proofs and refutations in mathematical learning: Proof problem with diagram. In C. Margolinas (Ed.), Task design in mathematics education. Proceedings of ICMI Study 22 (pp. 471–480). Oxford, England: ICMI.

  • Kontorovich, I., & Koichu, B. (2016). A case study of an expert problem poser for mathematics competitions. International Journal of Science and Mathematics Education, 14(1), 81–99.

    Article  Google Scholar 

  • Land, T. J. (2017). Teacher attention to number choice in problem posing. The Journal of Mathematical Behavior, 45(1), 35–46.

    Article  Google Scholar 

  • Leikin, R., & Grossman, D. (2013). Teachers modify geometry problems: from proof to investigation. Educational Studies in Mathematics, 82(3), 515–531.

    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 

  • Lowrie, T. (2002). Young children posing problems The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87–98.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM). (1991). Professional standards for school mathematics. Reston, VA: Author.

    Google Scholar 

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

    Google Scholar 

  • Olson, J. C., & Knott, L. (2013). When a problem is more than a teacher’s question. Educational Studies in Mathematics, 83(1), 27–36.

    Article  Google Scholar 

  • Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: a view from a small-scale intervention study. The Journal of Mathematical Behavior, 30(4), 333–352.

    Article  Google Scholar 

  • Ponte, J. P. P., & Henriques, A. (2013). Problem posing based on investigation activities by university students. Educational Studies in Mathematics, 83(1), 145–156.

    Article  Google Scholar 

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

    Google Scholar 

  • Silver, E. A. (2013). Problem-posing research in mathematics education: looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157–162.

    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 

  • Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26.

    Article  Google Scholar 

  • Smith, M. C., Locke, S. G., Boisse, S. J., Gallagher, P. A., Krengel, L. E., Kuczek, J. E., McFarland, J. E., Rapoo, B., & Wertheim, C. (1998). Productivity of educational psychologists in educational psychology journals, 1991-1996. Contemporary Educational Psychology, 23, 173–181.

    Article  Google Scholar 

  • Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

  • Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM: The International Journal on Mathematics Education, 41(1&2), 13–27.

    Article  Google Scholar 

  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Proceedings of the 19th annual conference of the Mathematics Education Research Group of Australasia (pp. 518–525). Melbourne, Australia: Mathematics Education Research Group of Australia.

  • Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143.

    Article  Google Scholar 

  • Tilly, C. (1984). Big structures, large processes, huge comparisons. New York, NY: Russell Sage.

  • Törner, G., & Arzarello, F. (2012). Grading mathematics education journals. European Mathematical Society Newsletter, 52–54.

  • Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students' mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117–132.

    Article  Google Scholar 

  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201–221.

    Article  Google Scholar 

  • Voica, C., & Singer, F. M. (2013). Problem modification as a tool for detecting cognitive flexibility in school children. ZDM Mathematics Education, 45(2), 267–279.

    Article  Google Scholar 

  • Williams, S., & Leatham, K. (2017). Journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 369–396.

    Article  Google Scholar 

  • Xie, J., & Masingila, J. O. (2016). Mathematical visualization supported by alternating problem posing and problem solving. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 921–925). Tucson, AZ: The University of Arizona.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shin-Yi Lee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, SY. Research Status of Mathematical Problem Posing in Mathematics Education Journals. Int J of Sci and Math Educ 19, 1677–1693 (2021). https://doi.org/10.1007/s10763-020-10128-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-020-10128-z

Keywords

Navigation