776
Views
2
CrossRef citations to date
0
Altmetric
Research Article

A Meta-Analysis on the Effects of Problem-Posing in Mathematics Education on Performance and Dispositions

ORCID Icon, &

References

  • Abu Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.), Proceedings of the International Conference on Mathematical Education into the 21st century: Social Challenges, Issues and Approaches, (Vol. 2, pp.1–8), Cairo, Egypt.
  • American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for educational and psychological testing.
  • Arikan, E. E., & Ünal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educational Sciences: Theory and Practice, 15 (5) , 1403–1416 doi: https://doi.org/10.12738/estp.2015.5.2678.
  • Armstrong, A. C. (2013). Problem posing as storyline: Collective authoring of mathematics by small groups of middle school students (Doctoral dissertation). University of British Columbia.
  • Bakker, A., Cai, J., English, L., Kaiser, G., Mesa, V., & Van Dooren, W. (2019). Beyond small, medium, or large: Points of consideration when interpreting effect sizes. Educational Studies in Mathematics, 102(1), 1–8. https://doi.org/10.1007/s10649-019-09908-4
  • Bernacki, M. L., & Walkington, C. (2018). The role of situational interest in personalized learning. Journal of Educational Psychology, 110(6), 864. https://doi.org/10.1037/edu0000250
  • Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105(3), 457–485. https://doi.org/10.1007/s10649-020-09995-8
  • Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37–55. https://doi.org/10.1007/s10649-012-9441-7
  • Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. A John Wiley and Sons, Ltd., Publication.
  • Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Erlbaum.
  • Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37–50. https://doi.org/10.1007/BF03217121
  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior. 21(4), 401–421 https://doi.org/10.1016/s0732-3123(02)00142-6.
  • Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: 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., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics, 105(3), 287–301. https://doi.org/10.1007/s10649-020-10008-x
  • 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, 1–8. https://doi.org/10.1016/j.ijer.2019.01.001
  • Cankoy, O., & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal of Education, 38, 11–24 https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.4670&rep=rep1&type=pdf.
  • Chang, K., Wu, L., Weng, S., & Sung, Y. (2012). Embedding game-based problem-solving phase into problem-posing system for mathematics learning. Computers & Education, 58(2), 775–786. https://doi.org/10.1016/j.compedu.2011.10.002
  • 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
  • Cifarelli, V. V., & Sevim, V. (2015). Problem posing as reformulation and sense- making within problem solving. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 177–194). New York, NY: Springer. https://doi.org/10.1007/978-1-4614-6258-3
  • Cohen, J. (1969). Statistical power analysis for the behavioral sciences. Academic Press.
  • Cotič, M., & Zuljan, M. V. (2009). Problem‐based instruction in mathematics and its impact on the cognitive results of the students and on affective‐motivational aspects. Educational Studies, 35(3), 297–310. https://doi.org/10.1080/03055690802648085
  • 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
  • Demir, B. B. (2005). The effect of instruction with problem posing on tenth grade students’ probability achievement and attitudes toward probability (Master’s thesis). Middle East Technical University.
  • Dickerson, V. M. (1999). The impact of problem-posing instruction on the mathematical problem-solving achievement of seventh graders (Doctoral dissertation). Emory University.
  • Dominguez, H. (2016). Mirrors & windows into student noticing. Teaching Children Mathematics, 22(6), 358–365. https://doi.org/10.5951/teacchilmath.22.6.0358
  • Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL model. Educational Psychologist, 46(1), 6–25. https://doi.org/10.1080/00461520.2011.538645
  • 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
  • Ellerton, N. F., Singer, F. M., & Cai, J. (2015). Problem posing in mathematics: Reflecting on the past, energizing the present, and foreshadowing the future. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 547–556). New York: Springer.
  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217. https://doi.org/10.1023/A:1002963618035
  • English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106. https://doi.org/10.2307/749719
  • Ferguson, C. J., & Brannick, M. T. (2012). Publication bias in psychological science: Prevalence, methods for identifying and controlling, and implications for the use of meta-analyses. Psychological Methods, 17(1), 120. https://doi.org/10.1037/a0024445
  • Gade, S., & Blomqvist, C. (2015). From problem posing to posing problems via explicit mediation in grades 4 and 5. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 195–213). New York: Springer.
  • Guo, M., Leung, F. K., & Hu, X. (2020). Affective determinants of mathematical problem posing: The case of Chinese Miao students. Educational Studies in Mathematics, 105(3), 367–387. https://doi.org/10.1007/s10649-020-09972-1
  • Hedges, L. (1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128. https://doi.org/10.3102/10769986006002107
  • Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111–127. https://doi.org/10.1207/s15326985ep4102_4
  • Kapur, M. (2015). The preparatory effects of problem solving versus problem posing on learning from instruction. Learning & Instruction, 39, 23–31. https://doi.org/10.1016/j.learninstruc.2015.05.004
  • Karnaina, T., Bakara, M. N., Siamakania, S. Y. M., Mohammadikiaa, H., & Candrab, M. (2014). Exploring the metacognitive skills of secondary school students’ use during problem posing. Jurnal Teknologi, 67(1), 27–32. https://journals.utm.my/jurnalteknologi/article/download/1847/2144
  • Keşan, C., Kaya, D., & Güvercın, S. (2010). The effect of problem posing approach to the gifted student’s mathematical abilities. International Online Journal of Educational Sciences, 2 (3) , 677–687. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.657.9699&rep=rep1&type=pdf
  • Kitchings, C. N. (2014). Problem posing in middle-grades mathematics classes (Doctoral dissertation). University of Georgia.
  • Kojima, K., Miwa, K., & Matsui, T. (2015). Experimental study of learning support through examples in mathematical problem posing. Res Pract Technol Enhanc Learn, 10(1), 1. https://doi.org/10.1007/s41039-015-0001-5
  • Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behavior, 31(1), 149–161. https://doi.org/10.1016/j.jmathb.2011.11.002
  • Kopparla, M., & Capraro, M. M. (2018). Portrait of a second-grade problem poser. European Journal of STEM Education, 3(2), 03.https://doi.org/10.20897/ejsteme/2684
  • Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., Caldwell, C., Capraro, M. M., & Capraro, R. M. (2019). The effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 708–725. https://doi.org/10.1080/03055698.2018.1509785
  • Lin, K. M., & Leng, L. W. (2008). Using problem-posing as an assessment tool. In 10th Asia-Pacific Conference on Giftedness, Singapore (pp. 1-15).
  • Mahendra, R., Slamet, I., & Budiyono, B. (2017). The effect of problem posing and problem solving with realistic mathematics education approach to the conceptual understanding and adaptive reasoning. International Conference and Workshop on Mathematical Analysis and its Applications (ICWOMAA 2017) AIP Conference Proceedings 1913, Malang, Indonesia (AIP Publishing LLC.)https://doi.org/10.1063/1.5016659 .
  • Martin, F., Sun, T., & Westine, C. D. (2020). A systematic review of research on online teaching and learning from 2009 to 2018. Computers & Education, 159, 104009. https://doi.org/10.1016/j.compedu.2020.104009
  • Mihaela, S. F., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: new questions and directions. Educational Studies in Mathematics, 83(1), 1–7 doi:10.1007/s10649-013-9478-2.
  • Mitchell, M. (1993). Situational interest: Its multifaceted structure in the secondary school mathematics classroom. Journal of Educational Psychology, 85(3), 424. https://doi.org/10.1037/0022-0663.85.3.424
  • Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. J. T. I. P. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms Theory Into Practice. 31(2), 132–141. https://doi.org/10.1080/00405849209543534
  • Ozdemir, A. S., & Sahal, 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. https://doi.org/10.14689/ejer.2018.78.6
  • Pigott, T. D., & Polanin, J. R. (2019). Methodological guidance paper: High-quality meta-analysis in a systematic review. Review of Educational Research, 90(1), 24–46. https://doi.org/10.3102/0034654319877153
  • Priest, D. J. (2009). A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students (Doctoral dissertation). Queensland University of Technology.
  • Retnowati, E., Fathoni, Y., & Chen, O. (2018). Mathematics problem solving skill acquisition: Learning by problem posing or by problem solving? Jurnal Cakrawala Pendidikan, 37(1), 1–10. https://journal.uny.ac.id/index.php/cp/article/view/18787
  • Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The effects of problem posing on student mathematical learning: A meta-analysis. International Education Studies, 7(13), 227–241. https://doi.org/10.5539/ies.v7n13p227
  • Salman, E. (2012). The impact of problem posing activities in elementary mathematics instruction on students? problem solving achievement and attitudes. (master’s thesis). Erzincan University.
  • Schloemer, C. G. (1996). Integrating problem posing into instruction in advanced algebra: Feasibility and outcomes (Unpublished doctoral dissertation). University of Pittsburg, PA. https://elibrary.ru/item.asp?id=5631446
  • Silver, E. A., & Marshall, S. P. (1990). Mathematical and scientific problem solving: Findings, issues and instructional implications. In B. F. Jones & C. Idol (Eds.), Dimensions of thinking and cognitive instruction (pp. 265–290). Lawrence Erlbaum.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14 (1) , 19–28. https://www.jstor.org/stable/40248099?origin=JSTOR-pdf
  • 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. https://doi.org/10.2307/749846
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135. https://doi.org/10.5951/TCM.12.3.0129
  • Singer, F. M., Ellerton, N. F., & Cai, J. (2015). Mathematical problem posing. Springer.
  • Smith, M. S., & Stein, M. K. (1998). Reflections on practice: Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350 https://doi.org/10.5951/MTMS.3.5.0344.
  • Smithson, M. (2002). Confidence Intervals (Vol. 140): Sage Publications. https://doi.org/10.4135/9781412983761
  • StataCorp. (2019). Stata statistical software: Release 16. College Station, TX: StataCorp LLC
  • Stoyanova, E. (1999). Extending students’ problem solving via problem posing. Australian Mathematics Teacher, 55 (3) , 29–35. https://search.informit.org/doi/10.3316/informit.249619636969136
  • Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory (Cognitive Load Theory). Springer New York.
  • Tanner-Smith, E. E., & Tipton, E. (2014). Robust variance estimation with dependent effect sizes: Practical considerations including a software tutorial in Stata and spss. Research Synthesis Methods, 5(1), 13–30. https://doi.org/10.1002/jrsm.1091
  • Ümit, K. U. L., & Çelik, S. (2020). A meta-analysis of the impact of problem posing strategies on students’ learning of mathematics. Revista Romaneasca Pentru Educatie Multidimensionala, 12(3), 341–368. https://doi.org/10.18662/rrem/12.3/325
  • Walkington, C., & Bernacki, M. (2015). Students authoring personalized “algebra stories”: Problem-posing in the context of out-of-school interests. The Journal of Mathematical Behavior, 40(B), 171–191. https://doi.org/10.1016/j.jmathb.2015.08.001
  • Walkington, C. (2017). Design research on personalized problem posing in Algebra. In E. Galindo & J. Newton (Eds.), Proceedings for the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 195-202). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
  • Walkington, C., & Hayata, C. A. (2017). Designing learning personalized to students’ interests: Balancing rich experiences with mathematical goals. ZDM, 49(4), 519–530. https://doi.org/10.1007/s11858-017-0842-z
  • Walkington, C., & Bernacki, M. (2021). Making classroom learning personalized. APA Division 15 Policy Brief Series, 1(4), 1–6. https://par.nsf.gov/servlets/purl/10274025
  • Walkington, C., Nathan, M. J., Wang, M., Swart, M., Holcomb-Webb, K., & Washington, J. (2022). Collaborative problem posing of geometric movements in a motion capture game. Manuscript submitted for publication.
  • Wang, M., Walkington, C., & Dhingra, K. (2021). Facilitating student-created math walks. Mathematics Teacher: Learning and Teaching PK-12, 114(9), 670–676. https://doi.org/10.5951/MTLT.2021.0030
  • Xia, X., Lü, C., & Wang, B. (2008). Research on mathematics instruction experiment based problem posing. Journal of Mathematics Education, 1(1), 153–163. https://www.educationforatoz.com/images/_12_Xia_-_Research_on_Mathematics_Instruction_Experiment.pdf
  • Zakaria, E., & Ngah, N. (2011). A preliminary analysis of students’ problem-posing ability and its relationship to attitudes towards problem solving. Research Journal of Applied Sciences, Engineering and Technology, 3(9), 866–870. https://maxwellsci.com/print/rjaset/v3-866-870.pdf

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.