Abstract

This study aims to examine the effect of problem posing-based active learning activities on students' problem-posing skills and problem-solving achievement. To this aim, an experimental design with pre-test post-test control group was employed. The participants consisted of two groups of sixth graders, one experimental group (N=23) and one control group (N=25). Students in the experimental group were exposed to seven problem-based active learning activities over the course of six weeks. The study used problem-solving and problem-posing tests to collect data. The results revealed that eventhough the intervention was not statistically significant, the increase in the problem-solving mean score of the experimental groups was higher than that of the control group. Problem posing pre- and post-test scores of the experimental group differed statistically significantly with a high level of effect size (η2=0.80 ). Finally, educational implications are discussed, and recommendations are made for future research.

Keywords

References

• Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
• Angelini, M., Prescott, A., Schuck, S., Rai, T., Lee, C., & Coupland, M. (2018, January). “Maths Inside”: A Project to Raise Interest in Mathematics. In Mathematics Education Research Group of Australasia, 40th Annual Conference. MERGA: Mathematics Education Research Group of Australasia.
• Bédard, D., Lison, C., Dalle, D., Côté, D., & Boutin, N. (2012). Problem-based and project-based learning in engineering and medicine: Determinants of students’ engagement and persistance. Interdisciplinary Journal of Problem-based Learning, 6(2), 8. https://doi.org/10.7771/1541-5015.1355
• Bilgin, T., & Acar, C. (2007). The generalization of using active learning methods in teaching mathematics at junior high school level. Journal of Sakarya University Faculty of Education, 14, 115-130.
• Brown, G., & Quinn, R. J. (2006). Algebra students' difficulty with fractions. Australian Mathematics Teacher, 62(4), 28–40.
• Büyüköztürk, Ş. (2013). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences]. Pegem Akademi.
• 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.
• 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.
• Chen, L., Dooren, W. V., & 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: 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, 37(3), 149–158. https://doi.org/10.1007/s11858-005-0004-6
• De Boeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. Springer.
• Duan, N., Bhaumik, D. K., Palinkas, L. A., & Hoagwood, K. (2015). Optimal design and purposeful sampling: Complementary methodologies for implementation research. Administration and Policy in Mental Health and Mental Health Services Research, 42(5), 524-532. https://doi.org/10.1007/s10488-014-0596-7
• 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(3), 183-217. http://doi.org/10.1023/A:1002963618035
• Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78-84. http://dx.doi.org/10.1111/j.1949-8594.1994.tb12295.x
• Hansen, N., Jordan, N. C., & Rodrigues, J. (2017). Identifying learning difficulties with fractions: A longitudinal study of student growth from third through sixth grade. Contemporary Educational Psychology, 50, 45-59. https://doi.org/10.1016/j.cedpsych.2015.11.002
• Işık, C. (2011). Conceptual analysis of multiplication and division problems infractions posed by preservice elementary mathematics teachers. Hacettepe University Journal of Education, 41, 231-243.
• Işık, C., & Kar, T. (2012). An error analysis in division problems in fractions posed by pre-service elementary mathematics teachers. Educational Sciences in Theory and Practice, 12(3), 2289-2309.
• Işık, C., & Kar, T. (2015). The analysis of the problems posed by the sixth grade students for open-ended verbal story about fractions. Turkish Journal of Computer and Mathematics Education, 6(2), 230-249.
• 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. https://doi.org/10.1080/0020739X.2015.1021394
• Kar, T., & Işık, C. (2014). Analyzing problems posed by seventh grade middle school students for subtraction operation with fractions. Elementary Education Online, 13(4), 1223-1239.
• Karaaslan, K. G. (2018). Investigation of students' algebra learning and problem posing skills in a mathematics classroom supported by problem posing approach (Publication No. 516120) [Unpublished doctoral dissertation, Hacettepe University, Ankara]. National Thesis Center of the Council of Higher Education.
• Karaoglan Yilmaz, F. G., Özdemir, B. G., & Yasar, Z. (2018). Using digital stories to reduce misconceptions and mistakes about fractions: an action study. International Journal of Mathematical Education in Science and Technology, 49(6), 867-898. https://doi.org/10.1080/0020739X.2017.1418919
• Katrancı, Y. (2014). The effect of problem posing studies on mathematical understanding and problem solving achievement in cooperative learning environments (Publication No. 372290) [Unpublished doctoral dissertation, Marmara University-İstanbul]. National Thesis Center of the Council of Higher Education.
• Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., ... 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
• Kyriacou, C. (1992). Active learning in secondary school mathematics. British Educational Research Journal, 18(3), 309-318. https://doi.org/10.1080/0141192920180308
• Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. https://doi.org/10.2307/2529310
• Lavy, I. (2015). Problem-posing activities in a dynamic geometry environment: When and how. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 393–410). Springer.
• Lowrie, T. (2002). Designing a framework for problem posing: Young children generating open-ended tasks. Contemporary Issues in Early Childhood, 3(3), 354-364. https://doi.org/10.2304/ciec.2002.3.3.4
• Miller, C. J., Smith, S. N., & Pugatch, M. (2020). Experimental and quasi-experimental designs in implementation research. Psychiatry Research, 283, 112452. https://doi.org/10.1016/j.psychres.2019.06.027
• Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim program (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum -Primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8]. Author.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Author.
• Nicolaou, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing, and mathematics achievement. Focus on Learning Problems in Mathematics, 29(4), 48-70.
• Örnek, T. (2020). The assessment of problem posing learning model designed for the development of problem posing skill (Publication No. 624464) [Unpublished doctoral dissertation, Atatürk University, Erzurum]. National Thesis Center of the Council of Higher Education.
• Örnek, T., & Soylu, Y. (2021). A model design to be used in teaching problem posing to develop problem-posing skills. Thinking Skills and Creativity, 41, 100905. https://doi.org/10.1016/j.tsc.2021.100905
• Özgen, K., Aparı, B., & Zengin, Y. (2019). Problem posing based learning approaches of eighth grade students: ımplementation of active learning framework supported by GeoGebra. Turkish Journal of Computer and Mathematics Education,10(2), 501-538. https://doi.org/10.16949/turkbilmat.471760
• Polya, G. (1957). How to solve it: A new aspect of mathematical method . Princeton University Press.
• Rotgans, J. I., & Schmidt, H. G. (2011). Situational interest and academic achievement in the active-learning classroom. Learning and Instruction, 21(1), 58-67. https://doi.org/10.1016/j.learninstruc.2009.11.001
• Şahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178
• Sarıer, Y. (2020). The effect of active teaching methods, on mathematics achievement: A meta-analysis study. Abant İzzet Baysal University Journal of the Faculty of Education, 20(1), 115-132. https://doi.org/10.17240/aibuefd.2020.20.52925-526900
• 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(1), 157–162. https://doi.org/10.1007/s10649-013-9477-3
• Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Mathematics Education Research Group of Australasia.
• Tekin, H. (2008). Eğitimde ölçme ve değerlendirme [Measurement and evaluation in education]. Yargı.
• Terzi, A. (2021). The effect of active learning framework-based teaching on the development of problem solving and posing performance of 6th grade students (Publication No. 690752) [Unpublished master’s thesis, Recep Tayyip Erdoğan University, Rize]. National Thesis Center of the Council of Higher Education.
• Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing, Teaching and Teacher Education, 25, 166–175. https://doi.org/10.1016/j.tate.2008.08.003
• Turhan, B. (2011). Examination of effects of mathematics teaching with problem posing approach on sixth grade students' problem solving success, problem posing abilities and views towards mathematics (Publication No. 296603) [Unpublished master’s thesis, Anadolu University, Eskişehir]. National Thesis Center of the Council of Higher Education.
• Turhan, B., & Güven, M. (2014). The effect of mathematics instruction with problem posing approach on problem solving success, problem posing ability and views towards mathematics. Journal of Çukurova University Faculty of Education, 43(2), 217-234.
• van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally. Pearson.

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