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

Endah Retnowati, Department of Mathematics Education, Universitas Negeri Yogyakarta (Scopus ID: 36006825500), Indonesia
Yazid Fathoni, National Institute of Education, Singapore
Ouhao Chen, National Institute of Education, Singapore


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




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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