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The Effect of Realistic Mathematic Education on Students’ Conceptual Understanding of Linear Progamming ()

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DOI: 10.4236/ce.2015.622251 3,375 Downloads 4,816 Views Citations

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Riyan Hidayat^*, Zanaton H. Iksan

Affiliation(s)

Faculty of Education, Universiti Kebangsaan Malaysia, Bangi, Malaysia.

ABSTRACT

A number of national and international scale surveys showed that the mathematics achievements of Indonesian secondary school students were in the lower level. One of the indicators of this low achievement was the insufficient level of understanding of mathematical concepts of the students. Understanding of mathematical concepts could be integrated through Realistic Mathematics Education (RME). Therefore, the quasi-experimental study was conducted to examine the effectiveness of Realistic Mathematical Education towards the conceptual understanding of linear programming. The study also investigated the relationship between conceptual understanding and mathematics achievement and investigated the misconceptions on linear programming. This study involved 65 students of Madrasah Aliyah Negeri 1 Pekanbaru, Indonesia. Test conceptual understanding programming topics had Cronbach’s alpha reliability of 0.80. The data were collected by using a test question conceptual understanding of linear programming. Quantitative data analysis involved a descriptive and inferential analysis using SPSS 21.0. The descriptive analysis included the percentage, mean and standard deviation while inferential analysis involving independent t-test and Pearson correlation analysis. The results revealed that there were significant differences between the treatment and control groups toward conceptual understanding. There was a significant relationship between conceptual understanding and mathematics achievement of linear programming. Misconception toward linear programming for the treatment group was lower than the control group. The implications of this study were useful for educators to help their students to understand concept of mathematics through open and contextual questions so that the students though through the mathematics, not worked in the mathematics.

KEYWORDS

Realistic Mathematics Education, Conceptual Understanding, Misconception, Linear Programming

Cite this paper

Hidayat, R. and Iksan, Z. (2015) The Effect of Realistic Mathematic Education on Students’ Conceptual Understanding of Linear Progamming. Creative Education, 6, 2438-2445. doi: 10.4236/ce.2015.622251.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2] Bayazit, I. (2013). An Investigation of Problem Solving Approaches, Strategies, and Models Used by the 7th and 8th Grade Students When Solving Real-World Problems. Educational Sciences: Theory & Practice, 13, 1-25.
http://dx.doi.org/10.12738/estp.2013.3.1419

[3] Bull, S., Jackson, T. J., & Lancaster, M. J. (2010). Students’ Interest in Their Misconceptions in First Year Electrical Circuits and Mathematics Courses. International Journal of Electrical Engineering Education, 47, 307-318.
http://dx.doi.org/10.7227/IJEEE.47.3.6

[4] Costu, S., Arslan, S., Catlioglu, H., & Birgin, O. (2009). Perspectives of Elementary School Teachers and Their Students about Relating and Contextualizing in Mathematics. Procedia-Social and Behavioral Sciences, 1, 1692-1696.
http://dx.doi.org/10.1016/j.sbspro.2009.01.300

[5] Daryanto, & Tasrial (2012). Konsep Pembelajaran Kreatif. Yogyakarta: Gava Media.

[6] Dogan-Dunlap, H. (2010). Linear Algebra Students’ Modes of Reasoning: Geometric Representations. Linear Algebra and Its Applications, 432, 2141-2159.
http://dx.doi.org/10.1016/j.laa.2009.08.037

[7] Dudley, P. (2013). Teacher Learning in Lesson Study: What Interaction-Level Discourse Analysis Revealed about How Teachers Utilised Imagination, Tacit Knowledge of Teaching and Fresh Evidence of Pupils Learning, to Develop Practice Knowledge and So Enhance Their Pupils’ Lea. Teaching and Teacher Education, 34, 107-121.
http://dx.doi.org/10.1016/j.tate.2013.04.006

[8] Ernest, P. (1991). The Philosophy of Mathematics Education. London: The Falmer Press.

[9] Fatimah, R., Norazzila, S., & Rohani, A. T. (2013). Exploring Student’s In-Depth Learning Difficulties in Mathematics through Teachers’ Perspective. Procedia—Social and Behavioral Sciences, 97, 339-345.
http://dx.doi.org/10.1016/j.sbspro.2013.10.243

[10] Fruedenthal, H. (1991). Revisiting Mathematics Education. Dordrecht: Kluwer Academic Publishers.

[11] Gravemeijer, K. (1994). Developing Realistic Mathematic Education. Ultrec: Freudenthal Institute.

[12] Hajiyati, S. (2008). Peningkatan pemahaman konsep simteri melalui model pembelajaran kreatif dengan permainan matematik. Skripsi, Sukoharjo: Universitas Muhammadiyah Surakarta.

[13] Herman, T. (2007). Pembelajaran Berbasis Masalah untuk Meningkatkan Kemampuan Berpikir Matematis Tingkat Tinggi Siswa Sekolah Menengah Pertama. Educationist, I, 47-56.

[14] Hidayati, F. (2010). Kajian Kesulitan Belajar Siswa Kelas VII SMP Negeri 16 Yogyakarta Dalam Mempelajari Aljabar. Caturtunggal: Universitas Negeri Yogyakarta.

[15] I Made Asih (2011). Peningkatan kemampuan siswa sman 8 Denpasar dalam menyelesaikan soal cerita pokok bahasan Program Linier mata pelajaran Matematika. Jurnal Udayana Mengabdi, 10, 67-71.

[16] Istikomah, E., & Nor Sakinah, M. (2013). Kesan integrasi geometer’s sketchpad dalam pengajaran ke atas pemahaman konsep trasformasi. Jurnal Pendidikan Matematik, 1, 1-13.

[17] Joseph, Y. K. K. (2011). An Exploratory Study of Primary Two Pupils’ Approach to Solve Word Problems Mathematics Curriculum in Schools with a Primary Aim to Enable Students to. Journal of Mathematics Education, 4, 19-30.

[18] Karagoz. M., & Cakir, M. (2011). Problem Solving in Genetics: Conceptual and Procedural Difficulties. Summer, 11, 1668-1674.

[19] Kawuryan, S., Sutijan, & Budiharto, T. (2012). Pemahaman konsep bangun ruang melalui pendekatan matematika realistik. Tesis Sarjana, Surakarta: Jabatan Pendidikan Matematik, Unversitas sebelas Maret.

[20] Leong, K. E. (2013). Factors That Influence the Understanding of Good Factors That Influence the Understanding of Good Mathematics Teaching. Eurasia Journal of Mathematics, Science & Technology Education, 9, 319-328.
http://dx.doi.org/10.12973/eurasia.2013.939a

[21] Lim, C. H. (2007). Penyelidikan Pendidikan. Pendekatan Kuantitatif dan Kualitatif. Kuala Lumpur: McGraw-Hill Education.

[22] Marlina, A., & Nurhidayah, U. (2010). Tahap kefahaman pelajar tingkatan dua bagi topik nombor negatif. Johor: Universiti Teknologi Malaysia.

[23] Miswanto (2011). Penerapan model pembelajaran berbasis proyek pada materi Program Linier siswa kelas X SMK Negeri 1 Singosari. Jurnal Penelitian Dan Pemikiran Pendidikan, 1, 60-68.

[24] Muzakkir (2010). Kesan pendekatan matematik realistik (PMR) ke atas pencapian dan sikap pelajar terhadap pelajaran matematik. Tesis Sarjana, Bangi Selangor: Universiti Kebangsaan Malaysia.

[25] Ndlovu, M. C. (2011). University-School Partnerships for Social Justice in Mathematics and Science Education: The Case of the SMILES Project at IMSTUS. South African Journal of Education, 31, 419-433.

[26] Nesusin, N., Intrarakhamhaeng, P., Supadol, P., Piengkes, N., & Poonpipathana, S. (2014). Development of Lesson Plans by the Lesson Study Approach for the 6th Grade Students in Social Study Subject Based on Open Approach Innovation. Procedia—Social and Behavioral Sciences, 116, 1411-1415.
http://dx.doi.org/10.1016/j.sbspro.2014.01.407

[27] Nurhayati, A. N., & Maulana (2009). Penerapan pendekatan matematika realistik dalam penanaman konsep perkalian dan pembagian bilangan bulat. Makalah dibentangkan pada Konferensi Pendidikan Dasar I Tingkat Internasional pada tanggal 10-11 Oktober 2009 di UPI Kampus Sumedang. Universitas Pendidikan Indonesia.

[28] Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An Analysis of Elementary School Students’ Difficulties in Mathematical Problem Solving. Procedia—Social and Behavioral Sciences, 116, 3169-3174.
http://dx.doi.org/10.1016/j.sbspro.2014.01.728

[29] Searle, J., & Barmby, P. (2012). Evaluation Report on the Realistic Mathematics Education Pilot Project at Manchester Metropolitan University. Durham: Durham University.

[30] Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26, 114-145.
http://dx.doi.org/10.2307/749205

[31] Smart, A. M. (2009). Introducing Angles in Grade Four: A Realistic Approach Based on the van Hiele Model. Canadian Journal for New Scholars in Education, 2, 1-20.

[32] Subhan, A. (2007). Meningkatkan pemahaman konsep dan sikap peserta didik melalui pelatihan guru dengan VCD pemodelan dan pendampingan pada pembelajaran matematik bercirikan pendayagunaan alat peraga bahan pengahajarn pokok luas bangun datar kelas V SD Sekaran 2 TA 2006/2007. Skripsi, Malang dan Blitar: Unversiti Negeri Malang.

[33] Sumitro, N. K. (2008). Pembelajaran matematika realistik untuk pokok bahasan kesebangunan di Kelas 3 SMP Negeri 3 Porong. Paradigma, 8, 204-218.

[34] Tanjungsari, R. D., Soedjoko, E., & Mashuri (2012). Diagnosis kesulitan belajar matematika SMP pada materi persamaan garis lurus. Unnes Journal of Mathematics Education, 1, 53-58.

[35] Win Afgani, M., Darmawijoyo, & Purwoko, M. S. (2008). Pengembangan media website pembelajaran materi program linear untuk siswa sekolah menengah atas. Jurnal Pendidikan Matematika, 2, 47-61.

[36] Wiwin, S. H., & Nurwiani (2009). Analisis kesalahan menyelesaikan soal program linear siswa kelas XI SMK Tribuana Jombang Tahun 2008/2009. Tesis Sarjana, Sekolah Tinggi Keguruan dan Ilmu Pendidikan PGRI Jombang.

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[1]	Afri, Mukhni, & Sofia (2011). Penerapan pendekatan matematik realistik ke atas kemahiran pemecahan masalah murid kelas 2 SMP Negeri 3 Painan tahun pelajaran 2012/2013. STKIP PGRI Sumatera Barat.

[2]	Bayazit, I. (2013). An Investigation of Problem Solving Approaches, Strategies, and Models Used by the 7th and 8th Grade Students When Solving Real-World Problems. Educational Sciences: Theory & Practice, 13, 1-25. http://dx.doi.org/10.12738/estp.2013.3.1419

[3]	Bull, S., Jackson, T. J., & Lancaster, M. J. (2010). Students’ Interest in Their Misconceptions in First Year Electrical Circuits and Mathematics Courses. International Journal of Electrical Engineering Education, 47, 307-318. http://dx.doi.org/10.7227/IJEEE.47.3.6

[4]	Costu, S., Arslan, S., Catlioglu, H., & Birgin, O. (2009). Perspectives of Elementary School Teachers and Their Students about Relating and Contextualizing in Mathematics. Procedia-Social and Behavioral Sciences, 1, 1692-1696. http://dx.doi.org/10.1016/j.sbspro.2009.01.300

[5]	Daryanto, & Tasrial (2012). Konsep Pembelajaran Kreatif. Yogyakarta: Gava Media.

[6]	Dogan-Dunlap, H. (2010). Linear Algebra Students’ Modes of Reasoning: Geometric Representations. Linear Algebra and Its Applications, 432, 2141-2159. http://dx.doi.org/10.1016/j.laa.2009.08.037

[7]	Dudley, P. (2013). Teacher Learning in Lesson Study: What Interaction-Level Discourse Analysis Revealed about How Teachers Utilised Imagination, Tacit Knowledge of Teaching and Fresh Evidence of Pupils Learning, to Develop Practice Knowledge and So Enhance Their Pupils’ Lea. Teaching and Teacher Education, 34, 107-121. http://dx.doi.org/10.1016/j.tate.2013.04.006

[8]	Ernest, P. (1991). The Philosophy of Mathematics Education. London: The Falmer Press.

[9]	Fatimah, R., Norazzila, S., & Rohani, A. T. (2013). Exploring Student’s In-Depth Learning Difficulties in Mathematics through Teachers’ Perspective. Procedia—Social and Behavioral Sciences, 97, 339-345. http://dx.doi.org/10.1016/j.sbspro.2013.10.243

[10]	Fruedenthal, H. (1991). Revisiting Mathematics Education. Dordrecht: Kluwer Academic Publishers.

[11]	Gravemeijer, K. (1994). Developing Realistic Mathematic Education. Ultrec: Freudenthal Institute.

[12]	Hajiyati, S. (2008). Peningkatan pemahaman konsep simteri melalui model pembelajaran kreatif dengan permainan matematik. Skripsi, Sukoharjo: Universitas Muhammadiyah Surakarta.

[13]	Herman, T. (2007). Pembelajaran Berbasis Masalah untuk Meningkatkan Kemampuan Berpikir Matematis Tingkat Tinggi Siswa Sekolah Menengah Pertama. Educationist, I, 47-56.

[14]	Hidayati, F. (2010). Kajian Kesulitan Belajar Siswa Kelas VII SMP Negeri 16 Yogyakarta Dalam Mempelajari Aljabar. Caturtunggal: Universitas Negeri Yogyakarta.

[15]	I Made Asih (2011). Peningkatan kemampuan siswa sman 8 Denpasar dalam menyelesaikan soal cerita pokok bahasan Program Linier mata pelajaran Matematika. Jurnal Udayana Mengabdi, 10, 67-71.

[16]	Istikomah, E., & Nor Sakinah, M. (2013). Kesan integrasi geometer’s sketchpad dalam pengajaran ke atas pemahaman konsep trasformasi. Jurnal Pendidikan Matematik, 1, 1-13.

[17]	Joseph, Y. K. K. (2011). An Exploratory Study of Primary Two Pupils’ Approach to Solve Word Problems Mathematics Curriculum in Schools with a Primary Aim to Enable Students to. Journal of Mathematics Education, 4, 19-30.

[18]	Karagoz. M., & Cakir, M. (2011). Problem Solving in Genetics: Conceptual and Procedural Difficulties. Summer, 11, 1668-1674.

[19]	Kawuryan, S., Sutijan, & Budiharto, T. (2012). Pemahaman konsep bangun ruang melalui pendekatan matematika realistik. Tesis Sarjana, Surakarta: Jabatan Pendidikan Matematik, Unversitas sebelas Maret.

[20]	Leong, K. E. (2013). Factors That Influence the Understanding of Good Factors That Influence the Understanding of Good Mathematics Teaching. Eurasia Journal of Mathematics, Science & Technology Education, 9, 319-328. http://dx.doi.org/10.12973/eurasia.2013.939a

[21]	Lim, C. H. (2007). Penyelidikan Pendidikan. Pendekatan Kuantitatif dan Kualitatif. Kuala Lumpur: McGraw-Hill Education.

[22]	Marlina, A., & Nurhidayah, U. (2010). Tahap kefahaman pelajar tingkatan dua bagi topik nombor negatif. Johor: Universiti Teknologi Malaysia.

[23]	Miswanto (2011). Penerapan model pembelajaran berbasis proyek pada materi Program Linier siswa kelas X SMK Negeri 1 Singosari. Jurnal Penelitian Dan Pemikiran Pendidikan, 1, 60-68.

[24]	Muzakkir (2010). Kesan pendekatan matematik realistik (PMR) ke atas pencapian dan sikap pelajar terhadap pelajaran matematik. Tesis Sarjana, Bangi Selangor: Universiti Kebangsaan Malaysia.

[25]	Ndlovu, M. C. (2011). University-School Partnerships for Social Justice in Mathematics and Science Education: The Case of the SMILES Project at IMSTUS. South African Journal of Education, 31, 419-433.

[26]	Nesusin, N., Intrarakhamhaeng, P., Supadol, P., Piengkes, N., & Poonpipathana, S. (2014). Development of Lesson Plans by the Lesson Study Approach for the 6th Grade Students in Social Study Subject Based on Open Approach Innovation. Procedia—Social and Behavioral Sciences, 116, 1411-1415. http://dx.doi.org/10.1016/j.sbspro.2014.01.407

[27]	Nurhayati, A. N., & Maulana (2009). Penerapan pendekatan matematika realistik dalam penanaman konsep perkalian dan pembagian bilangan bulat. Makalah dibentangkan pada Konferensi Pendidikan Dasar I Tingkat Internasional pada tanggal 10-11 Oktober 2009 di UPI Kampus Sumedang. Universitas Pendidikan Indonesia.

[28]	Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An Analysis of Elementary School Students’ Difficulties in Mathematical Problem Solving. Procedia—Social and Behavioral Sciences, 116, 3169-3174. http://dx.doi.org/10.1016/j.sbspro.2014.01.728

[29]	Searle, J., & Barmby, P. (2012). Evaluation Report on the Realistic Mathematics Education Pilot Project at Manchester Metropolitan University. Durham: Durham University.

[30]	Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26, 114-145. http://dx.doi.org/10.2307/749205

[31]	Smart, A. M. (2009). Introducing Angles in Grade Four: A Realistic Approach Based on the van Hiele Model. Canadian Journal for New Scholars in Education, 2, 1-20.

[32]	Subhan, A. (2007). Meningkatkan pemahaman konsep dan sikap peserta didik melalui pelatihan guru dengan VCD pemodelan dan pendampingan pada pembelajaran matematik bercirikan pendayagunaan alat peraga bahan pengahajarn pokok luas bangun datar kelas V SD Sekaran 2 TA 2006/2007. Skripsi, Malang dan Blitar: Unversiti Negeri Malang.

[33]	Sumitro, N. K. (2008). Pembelajaran matematika realistik untuk pokok bahasan kesebangunan di Kelas 3 SMP Negeri 3 Porong. Paradigma, 8, 204-218.

[34]	Tanjungsari, R. D., Soedjoko, E., & Mashuri (2012). Diagnosis kesulitan belajar matematika SMP pada materi persamaan garis lurus. Unnes Journal of Mathematics Education, 1, 53-58.

[35]	Win Afgani, M., Darmawijoyo, & Purwoko, M. S. (2008). Pengembangan media website pembelajaran materi program linear untuk siswa sekolah menengah atas. Jurnal Pendidikan Matematika, 2, 47-61.

[36]	Wiwin, S. H., & Nurwiani (2009). Analisis kesalahan menyelesaikan soal program linear siswa kelas XI SMK Tribuana Jombang Tahun 2008/2009. Tesis Sarjana, Sekolah Tinggi Keguruan dan Ilmu Pendidikan PGRI Jombang.