PENGARUH MODEL PEMBELAJARAN BERBASIS MASALAH DAN PENALARAN FORMAL TERHADAP KEMAMPUAN PEMECAHAN MASALAH MATEMATIKA (Eksperimen Pada Siswa Kelas VIII SMP Negeri 1 Tabanan)

Abstract

ABSTRAK

Penelitian ini bertujuan untuk mengetahui pengaruh model pembelajaran berbasis masalah dan penalaran formal terhadap kemampuan pemecahan masalah matematika siswa. Penelitian ini menggunakan metode eksperimen dengan desain faktorial 2x2. Variabel bebas dalam penelitian ini adalah model pembelajaran, sedangkan penalaran formal berperan sebagai variabel moderator, Sebagai variabel terikat dalam penelitian ini adalah kemampuan pemecahan masalah matematika. Instrumen berupa tes penalaran formal dan  tes kemampuan pemecahan masalah matematika.  Sampel penelitian berjumlah 88 orang siswa kelas VIII yang diambil secara acak dengan menggunakan tehnik pengambilan sampel secara bertahap. Analisis data menggunakan analisis varian dua jalur. Hasil penelitian menunjukkan bahwa: (1) terdapat perbedaan kemampuan pemecahan masalah matematika yang mengikuti model belajar berbasis masalah dengan siswa yang  mengikuti model pembelajaran langsung (F =  5,213; p<0,05), (2) untuk yang memiliki penalaran formal tinggi, terdapat perbedaan kemampuan pemecahan masalah matematika yang mengikuti model belajar berbasis masalah dengan siswa yang mengikuti model pembelajaran langsung , (3) untuk siswa yang memiliki penalaran formal rendah, terdapat perbedaan kemampuan pemecahan masalah matematika siswa yang mengikuti model pembelajaran langsung dengan siswa yang mengikuti model belajar berbasis masalah , dan (4) terdapat pengaruh interaksi yang signifikan antara model pembelajaran dan penalaran formal terhadap kemampuan pemecahan masalah matematika siswa (F =  27,018; p<0,05).  Oleh karena itu dapat disimpulkan bahwa model belajar berbasis masalah dan penalaran formal mempunyai pengaruh yang signifikan terhadap kemampuan pemecahan matematika, tetapi untuk siswa yang memiliki penalaran formal rendah akan mengalami kesulitan memahami masalah sehingga lebih memerlukan peran guru sehingga model pembelajaran langsung masih diperlukan pada pembelajaran matematika untuk siswa SMP Negeri 1 Tabanan.

Kata kunci  : Model Pembelajaran, Penalaran Formal, dan Pemecahan Masalah.

This study aimed at finding out the effect of problem-based teaching model and formal thinking upon students' ability to solve mathematic problems. This study was conducted at SMP Negeri 1 Tabanan by using an experimental method with 2x2 factorial design. The independent variable in this study was the teaching model. Then the teaching model was divided into two levels of factor, i.e., problem-based teaching model that was treated to the experiment group and direct teaching model that was treated to the control group while formal thinking played the role as a moderator variable. Then, the formal thinking was divided into two levels of factor, i.e., high formal thinking and low formal thinking . As the dependent variable in this study was ability to solve mathematic problems. The instruments in this study consisted of a test of formal thinking that was used to measure the students' formal thinking ability while a test of mathematic problems solving was used to measure the students' ability to solve mathematic problems. The sample was 88 students of Class VIII that were drawn randomly by using a stratified sampling technique. The data were analyzed by two-way analysis of variance. The results showed that (1) in general, there was a different ability to solve mathematic problems between the students who studied through problem­based teaching model and the students who studied through direct teaching model (F=5,213; p<0,05). (2) for the students who had a high formal thinking, there was a different  ability to solve mathematic problems between who studied through problem-based teaching model and the students who studied through direct teaching model (Q=5,290; p<0,05). (3) for the students who had a low formal thinking, there was a different  ability to solve mathematic problems between who studied through direct teaching model and who studied through problem-based teaching model (Q=2,061; p<0,05). (4) there was a significant interaction between teaching model and formal thinking upon the students' ability of solving mathematic problems (F=27,018; p<0,05). Hence it can be concluded that problem-based teaching model and formal thinking had a significant effect upon ability to solve mathematic problems, but for the students with a low formal thinking , they will experience a difficulty in understanding the problems so that they need the role of the teacher more. Thus in addition to using problem-based teaching model, direct teaching model is still needed in mathematic teaching for the students of SMP Negeri 1 Tabanan.

The key word : Learning Model, Formal Thinking, Solve Problem

ABSTRAK

Penelitian ini bertujuan untuk mengetahui pengaruh model pembelajaran berbasis masalah dan penalaran formal terhadap kemampuan pemecahan masalah matematika siswa. Penelitian ini menggunakan metode eksperimen dengan desain faktorial 2x2. Variabel bebas dalam penelitian ini adalah model pembelajaran, sedangkan penalaran formal berperan sebagai variabel moderator, Sebagai variabel terikat dalam penelitian ini adalah kemampuan pemecahan masalah matematika. Instrumen berupa tes penalaran formal dan  tes kemampuan pemecahan masalah matematika.  Sampel penelitian berjumlah 88 orang siswa kelas VIII yang diambil secara acak dengan menggunakan tehnik pengambilan sampel secara bertahap. Analisis data menggunakan analisis varian dua jalur. Hasil penelitian menunjukkan bahwa: (1) terdapat perbedaan kemampuan pemecahan masalah matematika yang mengikuti model belajar berbasis masalah dengan siswa yang  mengikuti model pembelajaran langsung (F =  5,213; p<0,05), (2) untuk yang memiliki penalaran formal tinggi, terdapat perbedaan kemampuan pemecahan masalah matematika yang mengikuti model belajar berbasis masalah dengan siswa yang mengikuti model pembelajaran langsung , (3) untuk siswa yang memiliki penalaran formal rendah, terdapat perbedaan kemampuan pemecahan masalah matematika siswa yang mengikuti model pembelajaran langsung dengan siswa yang mengikuti model belajar berbasis masalah , dan (4) terdapat pengaruh interaksi yang signifikan antara model pembelajaran dan penalaran formal terhadap kemampuan pemecahan masalah matematika siswa (F =  27,018; p<0,05).  Oleh karena itu dapat disimpulkan bahwa model belajar berbasis masalah dan penalaran formal mempunyai pengaruh yang signifikan terhadap kemampuan pemecahan matematika, tetapi untuk siswa yang memiliki penalaran formal rendah akan mengalami kesulitan memahami masalah sehingga lebih memerlukan peran guru sehingga model pembelajaran langsung masih diperlukan pada pembelajaran matematika untuk siswa SMP Negeri 1 Tabanan.

Kata kunci  : Model Pembelajaran, Penalaran Formal, dan Pemecahan Masalah.

This study aimed at finding out the effect of problem-based teaching model and formal thinking upon students' ability to solve mathematic problems. This study was conducted at SMP Negeri 1 Tabanan by using an experimental method with 2x2 factorial design. The independent variable in this study was the teaching model. Then the teaching model was divided into two levels of factor, i.e., problem-based teaching model that was treated to the experiment group and direct teaching model that was treated to the control group while formal thinking played the role as a moderator variable. Then, the formal thinking was divided into two levels of factor, i.e., high formal thinking and low formal thinking . As the dependent variable in this study was ability to solve mathematic problems. The instruments in this study consisted of a test of formal thinking that was used to measure the students' formal thinking ability while a test of mathematic problems solving was used to measure the students' ability to solve mathematic problems. The sample was 88 students of Class VIII that were drawn randomly by using a stratified sampling technique. The data were analyzed by two-way analysis of variance. The results showed that (1) in general, there was a different ability to solve mathematic problems between the students who studied through problem­based teaching model and the students who studied through direct teaching model (F=5,213; p<0,05). (2) for the students who had a high formal thinking, there was a different  ability to solve mathematic problems between who studied through problem-based teaching model and the students who studied through direct teaching model (Q=5,290; p<0,05). (3) for the students who had a low formal thinking, there was a different  ability to solve mathematic problems between who studied through direct teaching model and who studied through problem-based teaching model (Q=2,061; p<0,05). (4) there was a significant interaction between teaching model and formal thinking upon the students' ability of solving mathematic problems (F=27,018; p<0,05). Hence it can be concluded that problem-based teaching model and formal thinking had a significant effect upon ability to solve mathematic problems, but for the students with a low formal thinking , they will experience a difficulty in understanding the problems so that they need the role of the teacher more. Thus in addition to using problem-based teaching model, direct teaching model is still needed in mathematic teaching for the students of SMP Negeri 1 Tabanan.

The key word : Learning Model, Formal Thinking, Solve Problem