A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics

Authors

DOI:

https://doi.org/10.18662/rrem/12.3/325

Keywords:

problem posing, meta-analysis, learning outcomes, teaching mathematics

Abstract

This is a review of experimental research in which students have been taught to pose mathematical problems as a means of developing their learning. Hence, the aim of the research is to combine the empirical evidence regarding the functionality of problem posing strategies and to explore the aspects which could influence the integration of problem posing in mathematical education. In this direction, a meta-analysis approach was utilized in this study. 20 experimental research published between years of 2000 and 2020 are contained in this research and 31 effect sizes were computed. According to random effects model, it was found that problem posing strategy has significant impact on learners’ problem-solving skills, mathematics achievement, level of problems posed, and attitudes towards mathematics (ES = 1.328; 1.142; 1.152; 0.643; p=0.05). These effects also were analyzed according to methodological and instructional variables. The findings obtained in the research was discussed in the light of the literature and suggestions were made for the future studies.

References

Akay, H., & Boz, N. (2009). The effect of problem posing oriented calculus-II instruction on academic success. Research in Mathematical Education, 13(2), 75-90. https://www.koreascience.or.kr/article/JAKO200922951808540.page

Akay, H., & Boz, N. (2010). The effect of problem posing oriented Analysis-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 59-75. https://doi.org/10.14221/ajte.2010v35n1.6

Altun, M. (2012). İlköğretim ikinci kademede (6., 7. ve 8. sınıflarda) matematik öğretimi [Teaching of Middle school mathematics]. Alfa Aktüel.

Barlow, A. T., & Cates, J. M. (2006). The impacts of problem posing on elementary teachers’ belief about mathematics and mathematics teaching. School Science and Mathematics, 106, 64-73. http://dx.doi.org/10.1111/j.1949-8594.2006.tb18136.x

Borenstein, M., Hedges, L., & Rothstein, H. (2007). Meta-analysis fixed effects vs. random effects. Meta-analysis. https://www.meta-analysis.com/downloads/M-a_f_e_v_r_e_sv.pdf

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. F. Ellerton, & J. Cai (Eds.), Mathematical problem solving: From research to effective practice (pp. 3-34). Springer.

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. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.4670&rep=rep1&type=pdf

Cantürk-Günhan, B., Geçici, M. E., & Günkaya, B. (2019). The effect of problem posing based mathematics teaching on students’ success: A Meta-Analysis Study. Necatibey Fculty of Education Electronic Journal of Science and Mathematics Education 13(2), 1042-1062. https://doi.org/10.17522/balikesirnef.614345

Capar, G., & Tarim, K. (2015). Efficacy of the cooperative learning method on mathematics achievement and attitude. A Meta-Analysis Research. Educational Sciences: Theory and Practice, 15(2), 553-559. https://doi.org/10.12738/estp.2015.2.2098

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: From research to effective practice (pp. 309–329). Springer.

Chin, C., Brown, D. E., & Bruce, B. C. (2002). Student-generated questions: a meaningful aspect of learning in science. International Journal of Science Education, 24(5), 521–549. https://doi.org/10.1080/09500690110095249

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Lawrence Erlbaum Associates.

Cooper, H. (2010). Research synthesis and meta-analysis: A step-by-step approach. Sage Publications.

Cooper, H. M., Hedges, L. V., Valentine, J., & Hedges, L. V. (Eds.), (2009). The Handbook of Research Synthesis and meta-analysis. The Russell Sage Foundation.

Çoğaltay, N., Karadağ, E., & Öztekin, Ö. (2014). The effect of school principals’ transformational leadership behaviors on teachers’ organizational commitment: a meta analysis study. educational administration: Theory and Practice, 20(4), 483-500. https://doi.org/10.14527/kuey.2014.019

Drake, J. M., & Barlow, A. T. (2008). Assessing students’ levels of understanding multiplication through problem writing. Teaching Children Mathematics, 14(5), 272–277. https://eric.ed.gov/?id=EJ781359

El Sayed, R. A. E. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69. https://inst.eecs.berkeley.edu/~cs375/fa18/resources /Oman-problemssolving.pdf

Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics 17, 261–271. https://doi.org/10.1007/BF00305073

English, L. D. (1997). The development of fifth-grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183-217. http://dx.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. https://doi.org/10.1111/j.1949-8594.1994.tb12295.x

Güzel, R., & Biber, A.Ç. (2019). The effect of the problem posing approach for academic success in the teaching of inequalities. Kastamonu University Faculty of Education, 27(1), 199-208. https://doi.org/10.24106/kefdergi.2464

Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3) 242-273. https://doi.org/10.2307/749120

Kaya, D. R. (2016). Problem solving based learning in math educati̇on: Meta - analysis study [Unpublished master’s thesis]. Recep Tayyip Erdoğan University, Rize.

Kock, A. (2009). A guideline to meta-analysis. TIM Working Paper Series, 2, 1-39. https://www.tim.tu-berlin.de/fileadmin/fg101/TIM_Working_Paper_Series/Volume_2/TIM_WPS_Kock_2009.pdf

Kojima, K., Miwa, K. & Matsui, T. (2015). Experimental study of learning support through examples in mathematical problem posing. Research and Practice in Technology Enhanced Learning, 10(1), 1-18. https://doi.org/10.1007/s41039-015-0001-5

Kul, U., Çelik, S., & Aksu, Z. (2018). The impact of educational material use on mathematics achievement: A Meta-Analysis. International Journal of Instruction, 11(4), 303-324. https://doi.org/10.12973/iji.2018.11420a

Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 3, 129- 136. PME.

Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14, 87-98. http://dx.doi.org/10.1007/BF03217355

Malofeeva, E. V. (2005). Meta-analysis of mathematics instruction with young children [Unpublished doctoral dissertation]. University of Notre Dame.

Milli Eğitim Bakanlığı [Ministry of National Education]. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı [ Middle School Mathematics Curriculum]. MEB Basımevi. Ankara.

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standard for school mathematics. National Council of Teachers of Mathematics.

Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton University Press.

Rosenshine, B., Meister, C., & Chapman, S. (1996). Teaching students to generate questions: A review of the intervention studies. Review of Educational Research, 66(2), 181-221. https://doi.org/10.3102/00346543066002181

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. https://doi.org/10.5539/ies.v7n13p227

Sanchez-Elez, M., Pardines, I., Garcia, P., Miñana, G., Roman, S., Sanchez, M., & Risco, J. L. (2014). Enhancing students’ learning process through self-generated tests. Journal of Science Education and Technology, 23(1), 15–25. https://doi.org/10.1007/s10956-013-9447-7

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28. https://doi.org/10.2307/749366

Singer, F., & Voica, C. (2012). 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

Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing [Unpublished doctoral dissertation]. Indiana University, School of Education, Indiana.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia.

Suarsana, I M., Lestari, I. A. P. D., & Mertasari, N. M. S. (2019). The Effect of Online Problem Posing on Students’ Problem-Solving Abilitiy in Mathematics. International Journal of Instruction, 12(1), 809-820. https://eric.ed.gov/?id=EJ1201188

Tichá, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. SouryLavergne, & 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.

Toluk- Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175. https://doi.org/10.1016/j.tate.2008.08.003

Turhan, B., & Güven, M. (2014). The effect of mathematics ınstruction with problem posing approach on problem solving success, problem posing ability and views towards mathematics. Çukurova University Journal of Faculty of Education, 43(2), 217-234. https://doi.org/10.14812/cufej.2014.021

Üstün, U., & Eryılmaz, A. (2014). A research methodology to conduct effective research syntheses: Meta-analysis. Education & Science, 39(174). 1-32. https://doi.org/10.15390/EB.2014.3379

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. https://doi.org/10.1007/s10649-012-9456-0

Downloads

Published

2020-10-05

How to Cite

KUL, Ümit, & ÇELİK, 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

Publish your work at the Scientific Publishing House LUMEN

It easy with us: publish now your work, novel, research, proceeding at Lumen Scientific Publishing House

Send your manuscript right now