Meta-analysis of the Utilization of Problem-Posing Approach in Enhancing Students’ Academic Achievement: Direction for Mathematics Learning
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Abstract
This meta-analysis examined the effect of using the problem-posing approach on students’ academic achievement in Mathematics. Results from 16 studies showed that problem-posing has a large positive effect on students’ academic achievement (g=0.73) following a random-effects model. Subgroup analysis revealed that the positive effect is moderated by grade level and subject matter. Notably, the problem-posing approach has the largest effect at the tertiary level, relatively large at the senior and junior secondary level, and smallest at the primary level. In addition, problem-posing approach produces the largest effect when it is implemented in calculus and algebra and least effect in Geometry. Neither study sampling design (i.e., randomized, convenience, and purposive) nor the country from which the study is implemented moderates the effect of problem-posing on academic achievement. Consequently, this study recommends using a problem-posing approach in mathematics classrooms
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References
Akay, H., & Boz, N. (2009). The Effect of Problem Posing Oriented Calculus-II Instruction on Academic Success. Journal of the Korea Society of Mathematical Education, 13(2), 75–90.
Akay, H., & Boz, N. (2010). The Effect of Problem Posing Oriented Analyses-II Course on the Attitudes toward Mathematics and Mathematics Self-Efficacy of Elementary Prospective Mathematics Teachers. Australian Journal of Teacher Education, 35(1). https://doi.org/10.14221/ajte.2010v35n1.6
Balduzzi, S., Rücker, G., & Schwarzer, G. (2019). How to perform a meta-analysis with R: A practical tutorial. Evidence Based Mental Health, 22(4), 153–160. https://doi.org/10.1136/ebmental-2019-300117
Baumanns, L., & Rott, B. (2022). Developing a framework for characterising problem-posing activities: A review. Research in Mathematics Education, 24(1), 28–50. https://doi.org/10.1080/14794802.2021.1897036
Cabuquin, J. C., & Abocejo, F. T. (2023). Mathematics Learners’ Performance and Academic Achievement at a Public High School Institution in Leyte, Philippines. Formatif: Jurnal Ilmiah Pendidikan MIPA, 13(2). https://doi.org/10.30998/formatif.v13i2.17235
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., & 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. https://doi.org/10.1007/s10763-016-9758-2
Calabrese, J. E., Capraro, M. M., & Thompson, C. G. (2022). The Relationship Between Problem Posing and Problem Solving: A Systematic Review. International Education Studies, 15(4), 1. https://doi.org/10.5539/ies.v15n4p1
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. https://doi.org/10.1007/s10763-013-9433-9
Castillo, D., Carrión, J., Chamba, C., Jiménez, Y., Rodríguez-Álvarez, M. J., & Lakshminarayanan, V. (2024). Teaching Math: A Review of Effective Teaching and Learning Strategies in Higher Education. In Review. https://doi.org/10.21203/rs.3.rs-4708199/v1
Chang, K.-E., Wu, L.-J., Weng, S.-E., & Sung, Y.-T. (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. (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. F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing (pp. 309–329). Springer New York. https://doi.org/10.1007/978-1-4614-6258-3_15
Christidamayani, A. P., & Kristanto, Y. D. (2020). The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation. Indonesian Journal on Learning and Advanced Education (IJOLAE), 100–108. https://doi.org/10.23917/ijolae.v2i2.9981
Cohen, J. (2009). Statistical power analysis for the behavioral sciences (2. ed., reprint). Psychology Press.
Cooper, H. (2017). Research Synthesis and Meta-Analysis: A Step-by-Step Approach. SAGE Publications, Inc. https://doi.org/10.4135/9781071878644
Darlena, W., Susanta, A., Koto, I., & Susanto, E. (2022). Effect of problem posing on problem-solving ability in mathematics learning of elementary school students. International Journal of Trends in Mathematics Education Research, 5(4), 435–440. https://doi.org/10.33122/ijtmer.v5i4.169
De Winter, J. C. F., Zadpoor, A. A., & Dodou, D. (2014). The expansion of Google Scholar versus Web of Science: A longitudinal study. Scientometrics, 98(2), 1547–1565. https://doi.org/10.1007/s11192-013-1089-2
Divrik, R., Pilten, P., & Mentiş Taş, A. (2021). Effect of Inquiry-Based Learning Method Supported by Metacognitive Strategies on Fourth-Grade Students Problem-Solving and Problem-Posing Skills: A Mixed Methods Research. Lnternational Electronic Journal of Elementary Education, 13(2), 287–308. https://doi.org/10.26822/iejee.2021.191
Durlak, J. A. (2009). How to Select, Calculate, and Interpret Effect Sizes. Journal of Pediatric Psychology, 34(9), 917–928. https://doi.org/10.1093/jpepsy/jsp004
Eidlin-Levy, H., Avraham, E., Fares, L., & Rubinsten, O. (2023). Math anxiety affects career choices during development. International Journal of STEM Education, 10(1), 49. https://doi.org/10.1186/s40594-023-00441-8
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
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), 120–128. https://doi.org/10.1037/a0024445
Gehanno, J.-F., Rollin, L., & Darmoni, S. (2013). Is the coverage of google scholar enough to be used alone for systematic reviews. BMC Medical Informatics and Decision Making, 13(1), 7. https://doi.org/10.1186/1472-6947-13-7
Guvercin, S., Cilavdaroglu, A. K., & Savas, A. C. (2014). The Effect of Problem Posing Instruction on 9th Grade Students’ Mathematics Academic Achievement and Retention. The Anthropologist, 17(1), 129–136. https://doi.org/10.1080/09720073.2014.11891422
Guvercin, S., & Verbovskiy, V. (2014). The Effect of Problem Posing Tasks Used in Mathematics Instruction to Mathematics Academic Achievement and Attitudes Toward Mathematics. International Online Journal of Primary Education, 3(2), 59–65.
Haddaway, N. R., Collins, A. M., Coughlin, D., & Kirk, S. (2015). The Role of Google Scholar in Evidence Reviews and Its Applicability to Grey Literature Searching. PLOS ONE, 10(9), e0138237. https://doi.org/10.1371/journal.pone.0138237
Halevi, G., Moed, H., & Bar-Ilan, J. (2017). Suitability of Google Scholar as a source of scientific information and as a source of data for scientific evaluation—Review of the Literature. Journal of Informetrics, 11(3), 823–834. https://doi.org/10.1016/j.joi.2017.06.005
Helsa, Y., Suparman, Dadang, J., Turmudi, & Ghazali, M. B. (2023). A Meta-Analysis of the Utilization of Computer Technology in Enhancing Computational Thinking Skills: Direction for Mathematics Learning. International Journal of Instruction, 16(2), 735–758. https://doi.org/10.29333/iji.2023.16239a
Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003). Measuring inconsistency in meta-analyses. BMJ, 327(7414), 557–560. https://doi.org/10.1136/bmj.327.7414.557
Huedo-Medina, T. B., Sánchez-Meca, J., Marín-Martínez, F., & Botella, J. (2006). Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods, 11(2), 193–206. https://doi.org/10.1037/1082-989X.11.2.193
Juandi, D., Kusumah, Y. S., Tamur, M., Perbowo, K. S., & Wijaya, T. T. (2021). A meta-analysis of Geogebra software decade of assisted mathematics learning: What to learn and where to go? Heliyon, 7(5), e06953. https://doi.org/10.1016/j.heliyon.2021.e06953
Kadir, K. (2023). Students’ Mathematics Achievement Based on Performance Assessment through Problem Solving-Posing and Metacognition Level. Mathematics Teaching Research Journal, 15(3), 109–135.
Karasel, N., Ayda, O., & Tezer, M. (2009). Effect of problem posing method in mathematic education with computer assisted pictures on student success and attitudes. PROCEEDINGS of 9th INTERNATIONAL EDUCATIONAL TECHNOLOGY CONFERENCE9th International Educational Technology Conference, 731–737.
Kutlu, M. O., & Kültür, Y. Z. (2021). The effect of formative assessment on high school students mathematics achievement and attitudes. Journal of Pedagogical Research, 5(4), 155–171. https://doi.org/10.33902/JPR.2021474302
Laconde, F. D., & Lomibao, L. S. (2018). Comparing Learner Generated Examples and Problem Posing in Enhancing Students’ Conceptual Understanding in Mathematics. Sci.Int.(Lahore), 30(1), 117–121.
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(4), 723–735. https://doi.org/10.1007/s11858-021-01291-w
Lim, K.-S., Wong, C. H., McIntyre, R. S., Wang, J., Zhang, Z., Tran, B. X., Tan, W., Ho, C. S., & Ho, R. C. (2019). Global Lifetime and 12-Month Prevalence of Suicidal Behavior, Deliberate Self-Harm and Non-Suicidal Self-Injury in Children and Adolescents between 1989 and 2018: A Meta-Analysis. International Journal of Environmental Research and Public Health, 16(22), 4581. https://doi.org/10.3390/ijerph16224581
Lin, L., & Chu, H. (2018). Quantifying Publication Bias in Meta-Analysis. Biometrics, 74(3), 785–794. https://doi.org/10.1111/biom.12817
Lipsey, M. W., & Wilson, D. B. (2009). Practical meta-analysis (Nachdr.). SAGE Publ.
Maamin, M., Maat, S. M., & H. Iksan, Z. (2021). The Influence of Student Engagement on Mathematical Achievement among Secondary School Students. Mathematics, 10(1), 41. https://doi.org/10.3390/math10010041
Mahendra, R., Slamet, I., & Budiyono. (2017). Problem Posing with Realistic Mathematics Education Approach in Geometry Learning. Journal of Physics: Conference Series, 895, 012046. https://doi.org/10.1088/1742-6596/895/1/012046
Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & the PRISMA Group*. (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. Annals of Internal Medicine, 151(4), 264–269. https://doi.org/10.7326/0003-4819-151-4-200908180-00135
Muzayyanah, A., & Wutsqa, D. U. (2023). Effectiveness of problem posing and investigation in terms of problem solving abilities, motivation and achievement in mathematics. Annals of Mathematical Modeling, 1(2). https://doi.org/10.33292/amm.v1i2.7
Namkung, J., & Fuchs, L. (2019). Remediating Difficulty with Fractions for Students with Mathematics Learning Difficulties. Learning Disabilities: A Multidisciplinary Journal, 24(2), 36–48. https://doi.org/10.18666/LDMJ-2019-V24-I2-9902
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), 1–21. https://doi.org/10.14689/ejer.2018.78.6
Papadopoulos, I., Patsiala, N., Baumanns, L., & Rott, B. (2021). Multiple Approaches to Problem Posing: Theoretical Considerations Regarding its Definition, Conceptualisation, and Implementation. Center for Educational Policy Studies Journal. https://doi.org/10.26529/cepsj.878
Patac, A., & Herrera, F. (2019). Understanding pre-service teachers’ mathematical concepts representation for problem posing. SDSSU Multidisciplinary Research Journal, 5, 7–14.
Polat, H., & Özkaya, M. (2023). The effect of problem posing-based active learning activities on problem-solving and posing performance: The case of fractions. Journal of Pedagogical Research. https://doi.org/10.33902/jpr.202317880
R Core Team. (2024). R: A Language and Environment for Statistical Computing [Computer software]. R Foundation for Statistical Computing. https://www.R-project.org/
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), p227. https://doi.org/10.5539/ies.v7n13p227
Rothstein, H. R., Sutton, A. J., & Borenstein, M. (Eds.). (2005). Publication Bias in Meta‐Analysis: Prevention, Assessment and Adjustments (1st ed.). Wiley. https://doi.org/10.1002/0470870168
Sadak, M., Incikabi, L., Ulusoy, F., & Pektas, M. (2022). Investigating mathematical creativity through the connection between creative abilities in problem posing and problem solving. Thinking Skills and Creativity, 45, 101108. https://doi.org/10.1016/j.tsc.2022.101108
Sari, N., & Surya, E. (2017). Analysis Effectiveness of Using Problem Posing Model in Mathematical Learning. International Journal of Sciences: Basic and Applied Research, 33(3), 13–21.
Schoenfeld, A. H. (Ed.). (2013). Problem Formulating: Where Do Good Problems Come From? In Cognitive Science and Mathematics Education (0 ed., pp. 141–166). Routledge. https://doi.org/10.4324/9780203062685-9
Schwarzer, G., Chemaitelly, H., Abu‐Raddad, L. J., & Rücker, G. (2019). Seriously misleading results using inverse of Freeman‐Tukey double arcsine transformation in meta‐analysis of single proportions. Research Synthesis Methods, 10(3), 476–483. https://doi.org/10.1002/jrsm.1348
Semeraro, C., Giofrè, D., Coppola, G., Lucangeli, D., & Cassibba, R. (2020). The role of cognitive and non-cognitive factors in mathematics achievement: The importance of the quality of the student-teacher relationship in middle school. PLOS ONE, 15(4), e0231381. https://doi.org/10.1371/journal.pone.0231381
Silmi Juman, Z. A. M., Mathavan, M., Ambegedara, A. S., & Udagedara, I. G. K. (2022). Difficulties in Learning Geometry Component in Mathematics and Active-Based Learning Methods to Overcome the Difficulties. Shanlax International Journal of Education, 10(2), 41–58. https://doi.org/10.34293/education.v10i2.4299
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
Sterne, J. A. C., & Egger, M. (2001). Funnel plots for detecting bias in meta-analysis. Journal of Clinical Epidemiology, 54(10), 1046–1055. https://doi.org/10.1016/S0895-4356(01)00377-8
Suarlin, S., Negi, S., Ali, M. I., Bhat, B. A., & Elpisah, E. (2021). The Impact of Implication Problem Posing Learning Model on Students in High Schools. International Journal of Environment, Engineering and Education, 3(2), 69–74. https://doi.org/10.55151/ijeedu.v3i2.61
Tan, R. G. (2018). Strengthening The Students’ Achievement in Mathematics Through Problem Posing. Sci.Int.(Lahore), 30(2), 229–232.
Tan, R. G., Luna, C. A., & Namoco, R. A. (2018). The Effects of Problem Posing and Sense-Making on Students’ Conceptual Understanding and Anxiety towards Mathematics. Liceo Journal of Higher Education Research, 14(2). https://doi.org/10.7828/ljher.v14i2.1271
Varlik, S. (2023). An Investigation of Uncertainty Intolerance and Uncertainty Management Research in Educational Institutions: Meta-Analysis Study. Kastamonu Eğitim Dergisi, 31(2), 265–277. https://doi.org/10.24106/kefdergi.1271533
Viechtbauer, W. (2010). Conducting Meta-Analyses in R with the metafor Package. Journal of Statistical Software, 36(3). https://doi.org/10.18637/jss.v036.i03
Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM – Mathematics Education, 53(4), 937–949. https://doi.org/10.1007/s11858-021-01277-8
