Mathematics problem solving skill acquisition: Learning by Problem Posing or by Problem Solving?

 Endah Retnowati, Yazid Fathoni, Ouhao Chen

Abstract


Abstract:Problem posing is an instructional method where students are asked to create problems based on the given information, then solve them. While in an instructional method of problem solving, students learn by solving given problems. The aim of this study was to test: (1) the differences of efficacy between learning by problem posing and the problemsolving method of individual and small group instruction strategies; (2) the interaction effect of learning methods and grouping strategies.With regard to the independent variables, problemsolving skill or cognitive load, a quasi experiment with post-test-only-non-equivalent control group designwas used. Year 7 contextual mathematics problems were tested in this experiment, and one hundreds students, who had sufficient prior knowledge, participated. A 2 by 2 anova was employed for data analysis. The results showed that: (1) problem posing method was significantly more effective than problem-solving method; (2) there was no significant difference in efficacy between individualized instruction and small group instruction strategies; (3) the interaction between learning methods and grouping strategies, where it is more likely that learning problem posing was better than problem solving for individual instruction.

 

Keywords: cognitive load, individual, mathematics, problem posing, problem solving, small group

 

PENGUASAAN KETERAMPILAN PEMECAHAN MASALAH MATEMATIKA: BELAJAR MELALUI PROBLEM POSING ATAU PROBLEM SOLVING

 

Abstrak: Problem posing adalah suatu metode pembelajaran dimana siswa diminta untuk menciptakan masalah-masalah berdasarkan informasi yang diberikan, kemudian siswa diminta menyelesaikan masalah tersebut. Sedangkan dalam metode pembelajaran problem solving, siswa belajar melalui penyelesaian masalah yang telah ditentukan. Tujuan penelitian ini adalah untuk menguji: (1) perbedaan efektivitas metode pembelajaran problem posing dan problem soving secara individual atau kelompok; (2) Efek interaksi antara metode pembelajaran dan strategi pengelompokan belajar. Dengan meninjau pada variabel terikat, keterampilan pemecahan masalah dan muatan kognitif, kuasi eksperimen dirancang dengan desain post-test-only-non-equivalent control groups. Materi pembelajaran dalam eksperimen adalah masalah matematika kontekstual untuk kelas 7, dengan sampel sejumlah 100 siswa yang telah mempunyai pengetahuan awal yang memadai. Anova dua jalur digunakan untuk analisis data. Hasil penelitian menunjukkan bahwa: (1) ada perbedaan yang signifikan dari kedua metode pembelajaran, dimana problem posing lebih efektif daripada problem solving; (2) tidak ada perbedaan yang signifikan antara strategi belajar individu atau kelompok; (3) ada efek interaksi antara metode pembelajaran dengan strategi pengelompokan, dimana dalam strategi belajar individu, menggunakan problem posing lebih baik daripada menggunakan problem solving, tetapi ada kecenderungan sebaliknya untuk strategi belajar kelompok.

 

Kata kunci: muatan kognitif, individual, matematika, problem posing, problem solving, kelompok kecil

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References


Arikan, E. E., & Unal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educational Sciences: Theory and Practice, 15(5). doi: 10.12738/estp.2015.5.2678

Arterberry, M. E., Cain, K. M., & Chopko, S. A. (2007). Collaborative problem solving in five year old children: Evidence of social facilitation and social loafing. Educational Psychology, 27(5), 577-596. doi: 10.1080/01443410701308755

Avouris, N., Dimitracopoulou, A., & Komis, V. (2003). On Analysis of Collaborative Problem Solving: An Object-Oriented Approach. Computers in Human Behavior, 19, 147-167.

Destan, N., & Roebers, C. (2015). What are the metacognitive costs of young children’s overconfidence? Metacognition and Learning, 10(3), 347-374. doi: 10.1007/s11409-014-9133-z

Donovan, M. S., & Bransford, J. D. (Eds.). (2005). How students learn. Washington, DC: The National Academic Press.

Dowker, A., Sarkar, A., & Looi, C. Y. (2016). Mathematics Anxiety: What Have We Learned in 60 Years? Frontiers in Psychology, 7(508). doi: 10.3389/fpsyg.2016.00508

Hmelo-Silver, C. E. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235-266. doi: 10.1023/B:EDPR.0000034022.16470.f3

Kirschner, F., Paas, F., & Kirschner, P. A. (2011). Task complexity as a driver for collaborative learning efficiency: The collective working-memory effect. Applied Cognitive Psychology, 25(4), 615-624. doi: 10.1002/acp.1730

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86. doi: 10.1207/s15326985ep4102_1

Leung, S.-k. S. (2013). Teachers implementing mathematical problem posing in the classroom: challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. doi: 10.1007/s10649-012-9436-4

Lin, P. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. Proceeding of the 28th Conference of The International Group for The Psychology of Mathematics Education,3, 257-264.

NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Paas, F., & van Gog, T. (2006). Optimising worked example instruction: Different ways to increase germane cognitive load. Learning and Instruction, 16(2), 87-91. doi: 10.1016/j.learninstruc.2006.02.004

Paas, F., & van Merriënboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem solving skills: A cognitive load approach. Journal of Educational Psychology, 86(1), 122-133.

Polya, G. (1981). Mathematical discovery. New York, NY: John Wiley & Sons.

Retnowati, E., & Aqiila, A. (2017). Efektivitas strategi pengelompokan berpasangan dalam pembelajaran matematika model CORE. Jurnal Cakrawala Pendidikan, 36(1), 12-23. doi: 10.21831/cp.v35i1.12628

Retnowati, E., Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(3), 349-367. doi: 10.1080/01443411003659960

Retnowati, E., Ayres, P., & Sweller, J. (2016). Can Collaborative Learning Improve the Effectiveness of Worked Examples in Learning Mathematics? Journal of Educational Psychology, 109(5), 666. doi: 10.1037/edu0000167

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. doi: 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(5), 521-539. doi: 10.2307/749846

Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. New York, NY: Springer.

Youssef, A., Ayres, P., & Sweller, J. (2012). Using general problem-solving strategies to generate ideas in order to solve geography problems. Applied Cognitive Psychology, 26(6), 872-877. doi: 10.1002/acp.2888




DOI: https://doi.org/10.21831/cp.v37i1.18787

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