Perbandingan keefektifan pendekatan problem solving dan problem posing dalam pembelajaran matematika pada siswa SMP

Harinda Nurril Falach

doi:10.21831/pg.v11i2.10635

Perbandingan keefektifan pendekatan problem solving dan problem posing dalam pembelajaran matematika pada siswa SMP

Harinda Nurril Falach, SMK Bina Harapan Jalan Kaliurang KM. 10 Gentan, Ngaglik, Sleman, Yogyakarta, Indonesia

10.21831/pg.v11i2.10635

Abstract

Penelitian ini bertujuan untuk mendeskripsikan: 1) keefektifan pendekatan problem solving terhadap kemampuan pemahaman dan penalaran matematis; 2) keefektifan pendekatan problem posing terhadap kemampuan pemahaman dan penalaran matematis; 3) perbandingan keefektifan antara pendekatan pembelajaran problem solving dan problem posing terhadap kemampuan pemahaman dan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar. Penelitian ini merupakan penelitian eksperimen semu (quasi experiment). Data dianalisis menggunakan one sample t test, uji MANOVA rumus T² Hotteling, dan uji t kriteria Bonferroni. Hasil penelitian menunjukkan bahwa: 1) pendekatan problem solving efektif terhadap kemampuan pemahaman dan penalaran matematis; 2) pendekatan problem posing efektif terhadap kemampuan pemahaman dan penalaran matematis; 3) pendekatan problem solving lebih efektif dibandingkan problem solving terhadap kemampuan pemahaman matematis tetapi pendekatan problem solving tidak lebih efektif dibandingkatn problem posingterhadap kemampuan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar.

Kata kunci: pendekatan problem solving, pendekatan problem posing, kemampuan pemahaman matematis, dan kemampuan penalaran matematis.

The effectiveness comparison of problem solving and problem posing approaches in mathematics learning towards junior high school students

Abstract

The aim of this study is to describe: 1) the effectiveness of problem solving approach on mathematical understanding and reasoning ability; 2) the effectiveness of problem posing approach on mathematical understanding and reasoning ability; 3) the comparison effectiveness of polyhedral learning using problem solving approach and problem posing approach on mathematical understanding and reasoning ability of State Junior High School. This study was a quasi experiment. The data were analyzed using one-sample t test, MANOVA test with T² Hotteling's formula, and t-test with Bonferroni criterion. The results of the study show that: 1) the problem solving approach has an effect on mathematical understanding and reasoning ability; 2) the problem posing approach has an effect on mathematical understanding and reasoning ability; and 3) the problem solving approach is more effective than the problem posing approach on mathematical understanding ability, but the problem solving approach is not more effective in polyhedral learning than the problem posing approach on mathematical reasoning ability of State Junior High.

Keywords: problem solving approach, problem posing approach, mathematical understanding ability, and mathematical reasoning ability

Keywords

pendekatan problem solving, pendekatan problem posing, kemampuan pemahaman matematis, dan kemampuan penalaran matematis.

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References

Allen, M.J., & Yen, W.M. (1979), Introduction to measurement theory.Monterey, California: Brooks/Cole Publishing Company.

Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2007). How Can We Asses Mathematical Understanding? Procedings of the 31" Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 pp. 41-48. Seoul: PME.

Brown, S. I., dan Walter, M. L. (2005). The art of problem posing. Mahwah, NJ: Lawrence Erlbaum associates Publishers.

Dahlan, .J. A. (2004). Meningkatkan Kemampuan Penalaran dan Pemahaman Matematika Siswa Sekolah Lanjutan Tingkat Pertama Melalui Pendekatan Pembelajaran Open-Ended. Disertasi. Bandung: Sekolah Pascasarjana, Universitas Pendidikan Indonesia.

De Lange, J., & Romberg, T.A. (2004). Monitorong student progress. In T. A. Romberg (Ed.), Standard-based mathematics assessment in middle school: Rethingking classroom practice (p. 5-21). New York: Teacher College Press.

Depdiknas. (2006). Peraturan Menteri Pendidikan Nasional Rl Nomor 22 Tahun 2006, tentang Standar lsi untuk Satuan Pendidikan Dasar dan Menengah.

Depdiknas. (2007). Peraturan Menteri Pendidikan Nasional Rl Nomor 41 Tahun 2007, tentang Standar Proses untuk Satuan Pendidikan Dasar dan Menengah.

Depdiknas. (2007). Laporan ujian nasional tahun pelajaran 2006/2007.

Depdiknas. (2008). Laporan ujian nasional tahun pelajaran 2007/2008.

Depdiknas. (2009). Laporan ujian nasional tahun pelajaran 2008/2009.

Depdiknas. (2010). Laporan ujian nasional tahun pelajaran 2009/2010.

Depdiknas. (2011). Laporan ujian nasional tahun pelajaran 2010/2011.

Driver, R. & Leach, J. (1993). A Constructivist View of Learning : Children’s and Nature of Science. Journal NSTA : What Research Says to the Science Teacher – The Science, Technology, Society Movement (3), 103-112.

English, L. D. (2009). Mathematical Reasoning: Analogies, Metaphors, and Images. Madison Ave, New York: Routledge.

Suherman, E., Turmudi, Suryadi, D., Herman, T., Suhendra, Prabawanto, S., Nurjanah, & Rohayati, A. (2003). Strategi pembelajaran matematika kontemporer (Rev.ed.). Bandung: JICA.

Glass, G. V., & Hopkins, K. D. (1984). Statistical Methods in Education and Psycology (2nd ed). New Jersey : Prentice Hall, Inc.

Haylock, D., & Cockbum, A. (2008). Understanding Mathematics for Young Children: A Guide For Fondation Stage and Lower Primary Teacher. London: SAGE Publication Inc.

Haylock, D., & Thangata, F. (2007). Key concepts in teaching primary mathematics. Thousand Oaks: SAGE Publication.

Jacobsen, D.A., Eggen P., dan Kauchak D. (2009). Metode-metode pengajaran meningkatkan belajar siswa tk-sma (edisi ke-8). (Terjemahan Achmad Fawaid & Khoirul Anam). Upper Saddle River, NJ: Pearson Education. (Buku asli diterbitkan tahun 2009).

Johnson, R.A. dan Wichern, D.W. (2007). Applied multivariate statistical analysis. Upper Saddle River, NJ: Pearson Education.

Keraf, G. (1982). Argumen dan Narasi. Komposisi Lanjutan III. Jakarta: Gramedia

Lavy, 1., & Shriki, A. (2007). Problem posing as a model means for developing mathematical knowledge of prospective teachers. Proceeding of the 31st Conference of the Intemational Group for the Psychology of Mathematics Education, Seoul, 3, 129-136.

Lithner, 1. (2012). Learning Mathematics by Creative or Imitative Reasoning. Journal 12st International Congress on Mathematical Education. Seoul, Korea.

Martin, W.G., & Kasmer, Lisa. (2009). Focus in High School Mathematics: Reasoning and Sense Making. Teaching Children Mathematics, Vol.16 No.5, p.284-291.

Mullis, I.V.S., Martin, M.O., Foy, P., Olson, J.F., Preuschoff, C., Erberber, E., Arora, A., Galia, J. (2008). TIMSS 2007 international mathematics report: finding from lEA's trends in international mathematics and science study at the fourth and eight grades. Chestnut Hill, MA: TIMSS & PIlLSIntemational Study Center.

Melianingsih, N. & Sugiman. (2015). Keefektifan Pendekatan Open-Ended dan Problem Solving Pada Pembelajaran Bangun Ruang Sisi Datar di SMP. Jurnal Riset Pendidikan Matematika, Vol. 2 No. 2, 211-223. Diakses pada tanggal 22 April 2016 dari http://journal.uny.ac.id/index.php/jrpm/article/view/7335/6318

Michener, E.R. (1978). Understanding Understanding Mathematics. Cognitive Science 2.

NCTM. (2000). Principles and standarts .for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Nugraha, T. S. & Mahmudi, A. (2015). Keefektifan Pembelajaran Berbasis Masalah dan Problem Posing Ditinjau dari Kemampuan Berpikir Logis dan Kritis. Jurnal Riset Pendidikan Matematika, Vol. 2 No. 1, 107-120. Diakses pada tanggal 22 April 2016 dari http://journal.uny.ac.id/index.php/jrpm/article/view/7154/6171

OECD. (2010). Pisa 2009 results: what students know and can do student performance in reading, mathematics and science (volume 1). Corrigenda.

Orlich, D.C, Harder, R.J., Callahan, R.C., Trevisan, M.S., Brown, A.H., & Miller, D.E. (2012). Teaching strategies: a guide to effective instruction (10th edition). Belmount, CA: Wadsworth Cengage Learning.

O’Shea, J. (2010). Teaching mathematical problem solving in the primary school. Resource & Research Guides Vol. 2 No. 5. Limerick: National centre for excellence in mathematics and science and learning.

Posamentier, A.S. , Smith, B.S., & Stepelman, J. (2010). Teaching secondary mathematics techniques and enrichment units (eight ed.). Boston, MA: Pearson Education, Inc.

Sanjaya, W. (2007). Strategi pembelajaran berorientasi standar proses pendidikan. Jakarta: Kencana.

Shanti, W. N. & Abadi, A. M. (2015). Keefektifan Pendekatan Problem Solving dan Problem Posing dengan Setting Kooperatif dalam Pembelajaran Matematika. Jurnal Riset Pendidikan Matematika, Vol. 2 No. 2, 121-134. Diakses pada tanggal 22 April 2016 dari http://journal.uny.ac.id/index.php/jrpm/article/view/7155/6172

Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, Vol. 27, No.5, 521-539.

Silver, E. A., Downs, J. M., Leung, S. S., et al. (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27(3), 293-309.

Stevens, J. (2002). Applied multivariate statistics for the social sciences (4th ed.). Mahwah: Lawrence Erlbaum Associates, Inc.

Xia, X., Lu, C., & Wang, B.B. (2008). Research on mathematics instruction experiment based problem posing. Journal of mathematics education. Vol.1, no.1, p.153-163.

DOI: https://doi.org/10.21831/pg.v11i2.10635