Abstract

The aim of this study is to investigate the trends in research related to problem posing in mathematics education. The study focuses on the articles on problem posing in the Web of Science database between 1990 and 2021. The term co-occurrence map, which was created depending on the data in the text with the bibliometric analysis of the articles on problem posing that met the specified criteria, revealed a four-cluster structure according to the degree of relations between the terms. These clusters are called effect (the effect of problem posing on various variables), creativity (the relationship between problem posing and creativity), construct (understandings of how it is thought in the problem posing process and the nature of problem posing) and intervention (opportunities provided by changing existing teaching by including problem posing). This study provides evidence on trends in problem posing related studies. Knowing the research trends on this issue will help researchers obtain information about the areas where more research is needed and plan their future work in that direction.

Keywords

References

• Abramovich, S. (2014). Revisiting mathematical problem solving and posing in the digital era: toward pedagogically sound uses of modern technology. International Journal of Mathematical Education in Science and Technology, 45(7), 1034-1052. https://doi.org/10.1080/0020739X.2014.902134
• Abramovich, S., & Cho, E. K. (2008). On mathematical problem posing by elementary pre-teachers: The case of spreadsheets. Spreadsheets in Education, 3(1), 1-19.
• Aytekin-Uskun, K., Çil, O., & Kuzu, O. (2021). The effect of realistic mathematics education on fourth graders’ problem posing/problem-solving skills and academic achievement. Journal of Qualitative Research in Education, 28, 22-50. https://doi.org/10.14689/enad.28.2
• Ayvaz, Ü., & Durmuş, S. (2021). Fostering mathematical creativity with problem posing activities: An action research with gifted students. Thinking Skills and Creativity, 40, 100846. https://doi.org/10.1016/j.tsc.2021.100846
• Bicer, A., Lee, Y., Perihan, C., Capraro, M., & Capraro, R. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105, pages 457–485. https://doi.org/10.1007/s10649-020-09995-8
• Cai, J., & Brook, M. (2006). Looking back in problem solving. Mathematics Teaching, 196, 42-45.
• Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. https://doi.org/10.1016/j.ijer.2019.01.001
• Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: conceptualization and initial findings of a problem‑posing project. ZDM–Mathematics Education, 53(6), 1403-1416. https://doi.org/10.1007/s11858-021-01252-3
• Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics, 105, 287–301. https://doi.org/10.1007/s10649-020-10008-x
• Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L., & Song, N. (2020).. Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research, 102, 101404. https://doi.org/10.1016/j.ijer.2019.02.004
• 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). Springer.
• Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Gfarber, T. (2013). Mathematical problem posing as a measure of curricular effect on students' learning. Educational Studies in Mathematics, 83(1), 57-69. https://doi.org/10.1007/s10649-012-9429-3
• Cankoy, O. (2014). Interlocked problem posing and children's problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 12, 219-238. https://doi.org/10.1007/s10763-013-9433-9
• Chang, N. (2007). Responsibilities of a teacher in a harmonic cycle of problem solving and problem posing. Early Childhood Education Journal, 34(4), 265-271 https://doi.org/10.1007/s10643-006-0117-8
• Chen, L., Van Dooren, W., & Verschaffel, L. (2013). The relationship between students’ problem posing and problem solving abilities and beliefs: A small-scale study with Chinese elementary school children. Frontiers of Education in China, 8(1), 147–161. https://doi.org/10. 3868/110-002-013-0010-5
• Chen, L., Van Dooren, W., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving abilities, beliefs, and attitudes: A design experiment. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 309– 329). Springer.
• 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. https://doi.org/10.1007/s11858-005-0004-6
• Crespo, S. (2003). Learning to pose mathematical problems: exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52(3), 243–270. https://doi.org/10.1023/A:1024364304664
• Dede, E. & Özdemir, E. (2022). Mapping and performance evaluation of mathematics education research in Turkey: A bibliometric analysis from 2005 to 2021. Journal of Pedagogical Research, 6(4), 1-19. https://doi.org/10.33902/JPR.202216829
• Dogan-Coskun, S. (2019). The analysis of the problems posed by pre-service elementary teachers for the addition of fractions. International Journal of Instruction, 12(1), 1517-1532.
• Donthu, N., Kumar, S., Mukherjee, D., Pandey, N., & Lim, W. M. (2021). How to conduct a bibliometric analysis: An overview and guidelines. Journal of Business Research, 133, 285-296. https://doi.org/10.1016/j.jbusres.2021.04.070
• Elgrably, H., & Leikin, R. (2021). Creativity as a function of problem-solving expertise: Posing new problems through investigations. ZDM–Mathematics Education, 53(4), 891-904. https://doi.org/10.1007/s11858-021-01228-3
• Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.
• 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/s10649-012-9449-z
• English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.
• 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. (2020). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research, 102, 101451. https://doi.org/10.1016/j.ijer.2019.06.014
• Ertane-Baş, Ö., & Özturan-Sağirli, M. (2021). A content analysis related to the problem themed articles on mathematics education in Turkey. Cukurova University Faculty of Education Journal, 50(2), 778-832. https://doi.org/10.14812/cuefd.821846
• Gökçe, S., & Güner, P. (2021). Forty Years of Mathematics Education: 1980-2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514-539. https://doi.org/10.46328/ijemst.1361
• Gökçe, S., & Güner, P. (2022). Dynamics of GeoGebra ecosystem in mathematics education. Education and Information Technologies, 27, 5301-5323. https://doi.org/10.1007/s10639-021-10836-1
• Guo, M., Leung, F. K. S., & Hu, X. (2020). Affective determinants of mathematical problem posing: The case of Chinese Miao students. Educational Studies in Mathematics, 105, 367–387. https://doi.org/10.1007/s10649-020-09972-1
• Guo, Y., Yan, J., & Men, T. (2021). Chinese junior high school students’ mathematical problem-posing performance. ZDM–Mathematics Education, 53(4), 905-917. https://doi.org/10.1007/s11858-021-01240-7
• Güner, P., & Gökçe, S. (2021). Monitoring the nomological network of number sense studies. International Journal of Mathematical Education in Science and Technology, 52(4), 580-608. https://doi.org/10.1080/0020739X.2021.1895343
• Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems? ZDM–Mathematics Education, 53(4), 919-935. https://doi.org/10.1007/s11858-021-01224-7
• Isik, C., & Kar, T. (2012). The analysis of the problems posed by the pre-service teachers about equations. Australian Journal of Teacher Education, 37(9), 93-113.
• Kılıç, Ç. (2013a). Determining the performances of pre-service primary school teachers in problem posing situations. Educational Sciences: Theory and Practice, 13(2), 1207–1211.
• Kılıç, Ç. (2013b). 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. http://dx.doi.org/10.1007/s40299-013-0073-1
• Kılıç, Ç. (2015). Analyzing pre-service primary teachers’ fraction knowledge structures through problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1603–1619. http://dx.doi.org/10.12973/eurasia.2015.1425a
• Kılıç, Ç. (2017). A new problem-posing approach based on problem-solving strategy: Analyzing pre-service primary school teachers’ performance. Educational Sciences: Theory & Practice, 17(3), 771-789. http://dx.doi.org/10.12738/estp.2017.3.0017
• Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Lawrence Erlbaum Associates.
• Koichu, B. (2010). On the relationships between (relatively) advanced mathematical knowledge and (relatively) advanced problem-solving behaviours. International Journal of Mathematical Education in Science and Technology, 41(2), 257-275. https://doi.org/10.1080/00207390903399653
• 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/s10649-012-9431-9
• Koichu, B., Harel, G., & Manaster, A. (2013). Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions. Instructional Science, 41(4), 681-698. https://doi.org/10.1007/s11251-012-9254-1
• 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. https://doi.org/10.1007/s10763-013-9467-z
• Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., … Capraro, R. M. (2019). The effects of problem-posing intervention on elementary students’ problem-solving. Educational Studies, 45, 708–725. https://doi.org/10.1080/03055698.2018.1509785
• Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259–274. http://dx.doi.org/10.1007/s10649-008-9154-0
• Land, T. J. (2017). Teacher attention to number choice in problem posing. The Journal of Mathematical Behavior, 45(1), 35–46. https://doi.org/10.1016/j.jmathb.2016.12.001
• Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23(4), 341-361. https://doi.org/10.1007/s10857-018-09425-w
• Leavy, A., & Hourigan, M. (2021). Balancing competing demands: Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative. Journal of Mathematics Teacher Education, 25, 293-320. https://doi.org/10.1007/s10857-021-09490-8
• Lee, S. Y. (2021). Research status of mathematical problem posing in mathematics education journals. International Journal of Science and Mathematics Education, 19(8), 1677-1693. https://doi.org/10.1007/s10763-020-10128-z
• Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. https://doi.org/10.1016/j.ijer.2019.04.002
• Li, X., Song, N., Hwang, S., & Cai, J. (2020). Learning to teach mathematics through problem posing: Teachers’ beliefs and performance on problem posing. Educational Studies in Mathematics, 105(3), 325-347. https://doi.org/10.1007/s10649-020-09981-0
• Liljedahl, P., & Cai, J. (2021). Empirical research on problem solving and problem posing: a look at the state of the art. ZDM-Mathematics Education, 53, 723–735. https://doi.org/10.1007/s11858-021-01291-w
• Mallart, A., Font, V., & Diez, J. (2018). Case study on mathematics pre-service teachers’ difficulties in problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1465-1481. https://doi.org/10.29333/ejmste/83682
• Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24(3-4), 385-401. https://doi.org/10.1016/j.jmathb.2005.09.011
• Martinez-Luaces, V., Fernández-Plaza, J. A., Rico, L., & Ruiz-Hidalgo, J. F. (2021). Inverse reformulations of a modelling problem proposed by prospective teachers in Spain. International journal of mathematical education in science and technology, 52(4), 491-505. https://doi.org/10.1080/0020739X.2019.1683773
• National Council of Teachers of Mathematics [NCTM]. (1989). Principles and standards for school mathematics. Author.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Author.
• Nuha, M. A., Waluya, S. B., & Junaedi, I. (2018). Mathematical creative process wallas model in students problem posing with lesson study approach. International Journal of Instruction, 11(2), 527-538. https://doi.org/10.12973/iji.2018.11236a
• Olson, J. C., & Knott, L. (2013). When a problem is more than a teacher’s question. Educational Studies in Mathematics, 83(1), 27–36. https://doi.org/10.1007/s10649-012-9444-4
• Osana, H., & Pelczer, I. (2015). A review on problem posing in teacher education. In F. Singer, N. Ellerton, & J. Cai (Eds.), Problem posing in mathematics: From research to effective practice (pp. 469-492). Springer.
• Özdemir, A. S., & Şahal, M. (2018). The effect of teaching integers through the problem posing approach on students’ academic achievement and mathematics attitudes. Eurasian Journal of Educational Research, 18(78), 117-138. http://dx.doi.org/10.14689/ejer.2018.78.6
• Palmér, H., & van Bommel, J. (2020). Young students posing problem-solving tasks: what does posing a similar task imply to students?. ZDM-Mathematics Education, 52(4), 743-752. https://doi.org/10.1007/s11858-020-01129-x
• Parhizgar, Z., Dehbashi, A., Liljedahl, P., & Alamolhodaei, H. (2021). Exploring students’ misconceptions of the function concept through problem-posing tasks and their views thereon. International Journal of Mathematical Education in Science and Technology, 1-25. https://doi.org/10.1080/0020739X.2021.1937732
• Pólya, G. (1945). How to solve it. Princeton University Press.
• Ponte, J. P. P., & Henriques, A. (2013). Problem posing based on investigation activities by university students. Educational Studies in Mathematics, 83(1), 145–156. https://doi.org/10.1007/s 10649-012-9443-5
• Rosli, R., Capraro, M., Goldsby, D., Gonzalez Gonzalez, E., Onwuegbuzie, A., & Capraro, R. (2015). Middle grade preservice teachers’ mathematical problem solving and problem posing. In F. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 333- 354). Springer
• Samková, L., & Tichá, M. (2016). On the way to develop open approach to mathematics in future primary school teachers. Journal on Efficiency and Responsibility in Education and Science, 9(2), 37-44. https://doi.org/10.7160/eriesj.2016.090202.
• Samková, L., & Tichá, M. (2017). On the way to observe how future primary school teachers reason about fractions. Journal on Efficiency and Responsibility in Education and Science, 10(4), 93-100. http://doi.org/10.7160/eriesj.2016.090202
• Schindler, M., & Bakker, A. (2020). Affective field during collaborative problem posing and problem solving: A case study. Educational Studies in Mathematics, 105(3), 303-324. https://doi.org/10.1007/s10649-020-09973-0
• Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). Macmillan.
• Silber, S., & Cai, J. (2021). Exploring underprepared undergraduate students’ mathematical problem posing. ZDM–Mathematics Education, 53(4), 877-889. https://doi.org/10.1007/s11858-021-01272-z
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
• Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83, 157–162. https://doi.org/10. 1007/s10649-013-9477-3
• Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539. https://doi.org/10.2307/749846
• Silver, E., Mamona-Downs, J., Leung, S., & Kenney, P. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27(3), 293–309. https://doi.org/10.2307/749366
• 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. https://doi.org/10.1007/s10649-012-9422-x
• Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1-7. https://doi.org/10.1007/s10649-013-9478-2
• Singer, F. M., Voica, C., & Pelczer, I. (2017). Cognitive styles in posing geometry problems: Implications for assessment of mathematical creativity. ZDM- Mathematics Education, 49(1), 37-52. http://dx.doi.org/10.1007/s11858-016-0820-x
• Song, P., & Wang, X. (2020). A bibliometric analysis of worldwide educational artificial intelligence research development in recent twenty years. Asia Pacific Education Review, 21(3), 473–486. https://doi.org/10.1007/s12564-020-09640-2
• 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). Mathematics Education Research Group of Australasia.
• Suarsana, I., Lestari, I. A. P. D., & Mertasari, N. M. S. (2019). The effect of online problem posing on students' problem-solving ability in mathematics. International Journal of Instruction, 12(1), 809-820. http://dx.doi.org/10.29333/iji.2019.12152a
• Tichá, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in preservice teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 1941–1950). Institut National de Recherche Pédagogique.
• Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83, 133–143. https://doi.org/10.1007/s10649-012-9455-1
• Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. http://dx.doi.org/10.1016/j.tate.2008.08.003
• Van Eck, N. J., & Waltman, L. (2020). Manuscript for VOSviewer version 1.6.15. Universiteit Leiden
• 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. https://doi.org/10.1007/s10649-012-9419-5
• 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. https://doi.org/10.1007/s11858-013-0492-8
• Weber, K., & Leikin, R. (2016). Problem solving and problem posing. In A. Gutierez, G. Leder, & P. Boero (Eds.), 2nd Handbook on the psychology of mathematics education (pp. 353–382). Sense Publishers.
• Xia, X., Lu, C., Wang, B., & Song, Y. (2007). Experimental research on mathematics teaching of “Situated creation and problem-based instruction” in Chinese primary and secondary schools. Frontiers of Education in China, 2(3), 366–377. https://doi.org/10.1007/s11516-007-0030-y
• Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101-118. https://link.springer.com/article/10.1007/s10649-017-9760-9
• Xu, B., Cai, J., Liu, Q., & Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j. ijer.2019.04.005
• Yao, Y., Hwang, S. & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM-Mathematics Education, 53, 937–949. https://doi.org/10.1007/s11858-021-01277-8
• Yığ, K. G. (2022). Research trends in mathematics education: A quantitative content analysis of major journals 2017-2021. Journal of Pedagogical Research, 6(3), 137-153. https://doi.org/10.33902/JPR.202215529
• Zhang, H., & Cai, J. (2021). Teaching mathematics through problem posing: Insights from an analysis of teaching cases. ZDM-Mathematics Education, 53(4), 961-973. https://doi.org/10.1007/s11858-021-01260-3
• Zupic, I., & Čater, T. (2015). Bibliometric methods in management and organization. Organizational Research Methods, 18(3), 429-472. https://doi.org/10.1177%2F1094428114562629

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.