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IMPLEMENTATION OF LINEAR SYSTEM WITH TWO VARIABLES USING GEOMETRY
Corresponding Author(s) : Jesi Irwanto
Humanities & Social Sciences Reviews,
Vol. 8 No. 1 (2020): January
Abstract
Purpose: This study aims to understand the concept of a two-variable linear equation system by presenting material in the form of line drawings in the field of Cartesian, this is because at the 2013 Junior High School Examination National Examination many students received mathematical grades below the standard.
Methodology: In constructing the concept of a system of linear equations, two variables in the Cartesian plane are carried out in stages. The first stage is obtained four system concepts of two-variable linear equations which include the concept of a straight line position in the Cartesian plane, the concept of the point position towards intervals in the Cartesian plane, the concept of the point position towards the line am + bn = c, the concept of the relationship of two lines_1 m + b_1 n = c_1 and a_2 m + b_2 n = c_2.
Main Findings: The results of this study are the first stage of the concept of four systems of linear equations which include the concept of straight-line position in the cartesian plane, the concept of point position at intervals in the Cartesian plane, the concept of position points with lines, the concept of two-line relations.
Applications of this study: This study is applicable to the junior high school level.
Novelty/Originality of this study: a) Evaluating data about constants, intervals for variables and, relations of points with lines, relations of two lines. b) It provides data on stage (a) to visualize various lines determine the position of points against the line, intersect two lines. c) Provide a case for related points a and b to students for evaluation.
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- Ambarwati, R., Dwijanto, D., & Hendikawati, P. (2015). Keefektifan model Project-Based Learning Berbasis GQM Terhadap Kemampuan Komunikasi Matematis dan Percaya Diri Siswa Kelas VII. Unnes Journal of Mathematics Education, 4(2).
- Azis, A., & Sugiman, S. (2015). Analisis kesulitan kognitif dan masalah afektif siswa SMA dalam belajar matematika menghadapi ujian nasional. Jurnal Riset Pendidikan Matematika, 2(2), 162–174. https://doi.org/10.21831/jrpm.v2i2.7331 DOI: https://doi.org/10.21831/jrpm.v2i2.7331
- Chen, C.-T. (1998). Linear system theory and design. Oxford University Press, Inc.
- Cholik, S. (2004). Matematika untuk SMP kelas VII. Erlangga: Jakarta.
- Devlin, K. (1996). Mathematics: The science of patterns: The search for order in life, mind and the universe. Macmillan.
- Dewi, I. P., Mursida, L., & Marta, Y. R. (2017). The Development of Interactive multimedia-based Learning Media Using Adobe Flash Cs3 and Camtasia in Problem-solving Learning in Elementary Mathematics of in Student PGSD SKTIP Adzkia in Padang.
- Farihah, U., & Nashihudin, M. (2016). The analysis on students’errors in solving mathematical word problems of cube and block materials based on the stages of newman’s error analysis. Mathematics Education and Graph Theory, 449.
- Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in teaching geometry in Indonesian primary schools (p. 346). University Of Twente.
- Gao, F. (1995). Small perturbation Cramer methods and moderate deviations for Markov processes. Acta Mathematica Scientia, 15(4), 394–405. https://doi.org/10.1016/S0252-9602(18)30062-6 DOI: https://doi.org/10.1016/S0252-9602(18)30062-6
- Gearhart, M., & Saxe, G. B. (2004). When teachers know what students know: Integrating mathematics assessment. Theory into Practice, 43(4), 304–313. https://doi.org/10.1207/s15430421tip4304_9 DOI: https://doi.org/10.1207/s15430421tip4304_9
- Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2018). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569-578. https://doi.org/10.12973/ejmste/76959 DOI: https://doi.org/10.12973/ejmste/76959
- Laurillard, D. (2013). Rethinking university teaching: A conversational framework for the effective use of learning technologies. Routledge. https://doi.org/10.4324/9781315012940 DOI: https://doi.org/10.4324/9781315012940
- Mezirow, J. (2008). An overview of transformative learning. In Lifelong learning (pp. 40–54). Routledge.
- Mezirow, J. (2018). Transformative learning theory. In Contemporary Theories of Learning (pp. 114–128). Routledge. https://doi.org/10.4324/9781315147277-8 DOI: https://doi.org/10.4324/9781315147277-8
- Oliveri, G. (1997). Mathematics. A science of patterns? Synthese, 112(3), 379–402. DOI: https://doi.org/10.1023/A:1004906107430
- Orton, A. (2004). Learning mathematics: Issues, theory, and classroom practice. Bloomsbury Publishing. https://doi.org/10.1023/A:1004906107430 DOI: https://doi.org/10.1023/A:1004906107430
- Pulungan, R. R. (2019). Analysis of student’s misconceptions in solving the system of linear equation in two variables. Journal of Physics: Conference Series, 1157(4), 42113. IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042113 DOI: https://doi.org/10.1088/1742-6596/1157/4/042113
- Purcell, E. J., & Varberg, D. (1994). Kalkulus dan Geometri Analitis Jilid 1 dan 2. Terjemahan: I Nyoman Susila, Kartasasmita Bana, Jakarta: Erlangga.
- Resnik, M. D. (1997). Mathematics as a Science of Patterns. Oxford University Press.
- Romberg, T. A. (Ed.). (1995). Reform in school mathematics and authentic assessment. SUNY Press.
- Rugh, W. J., & Rugh, W. J. (1996). Linear system theory (Vol. 2). prentice hall Upper Saddle River, NJ.
- Semadiartha, I. K. S. (2012). Pengembangan media pembelajaran berbasis komputer dengan Microsoft Excel yang berorientasi teori Van Hiele pada Bahasan Trigonometri kelas X SMA untuk Meningkatkan Prestasi dan Motivasi Belajar Matematika Siswa. Jurnal Pendidikan Dan Pembelajaran Matematika Indonesia, 1(2).
- Soviawati, E. (2011). Pendekatan matematika realistik (pmr) untuk meningkatkan kemampuan berfikir siswa di tingkat sekolah dasar. Jurnal Edisi Khusus, 2(2), 79-85.
- Stipek, D. (2002). Good instruction is motivating. In Development of achievement motivation (pp. 309–332). Elsevier. https://doi.org/10.1016/B978-012750053-9/50014-0 DOI: https://doi.org/10.1016/B978-012750053-9/50014-0
- Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem-solving. Research Ideas for the Classroom: High School Mathematics, 57, 78.
- Wu, Y. T., & Mohanty, S. (2006). Variable screening and ranking using sampling-based sensitivity measures. Reliability Engineering & System Safety, 91(6), 634–647. https://doi.org/10.1016/j.ress.2005.05.004 DOI: https://doi.org/10.1016/j.ress.2005.05.004
References
Ambarwati, R., Dwijanto, D., & Hendikawati, P. (2015). Keefektifan model Project-Based Learning Berbasis GQM Terhadap Kemampuan Komunikasi Matematis dan Percaya Diri Siswa Kelas VII. Unnes Journal of Mathematics Education, 4(2).
Azis, A., & Sugiman, S. (2015). Analisis kesulitan kognitif dan masalah afektif siswa SMA dalam belajar matematika menghadapi ujian nasional. Jurnal Riset Pendidikan Matematika, 2(2), 162–174. https://doi.org/10.21831/jrpm.v2i2.7331 DOI: https://doi.org/10.21831/jrpm.v2i2.7331
Chen, C.-T. (1998). Linear system theory and design. Oxford University Press, Inc.
Cholik, S. (2004). Matematika untuk SMP kelas VII. Erlangga: Jakarta.
Devlin, K. (1996). Mathematics: The science of patterns: The search for order in life, mind and the universe. Macmillan.
Dewi, I. P., Mursida, L., & Marta, Y. R. (2017). The Development of Interactive multimedia-based Learning Media Using Adobe Flash Cs3 and Camtasia in Problem-solving Learning in Elementary Mathematics of in Student PGSD SKTIP Adzkia in Padang.
Farihah, U., & Nashihudin, M. (2016). The analysis on students’errors in solving mathematical word problems of cube and block materials based on the stages of newman’s error analysis. Mathematics Education and Graph Theory, 449.
Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in teaching geometry in Indonesian primary schools (p. 346). University Of Twente.
Gao, F. (1995). Small perturbation Cramer methods and moderate deviations for Markov processes. Acta Mathematica Scientia, 15(4), 394–405. https://doi.org/10.1016/S0252-9602(18)30062-6 DOI: https://doi.org/10.1016/S0252-9602(18)30062-6
Gearhart, M., & Saxe, G. B. (2004). When teachers know what students know: Integrating mathematics assessment. Theory into Practice, 43(4), 304–313. https://doi.org/10.1207/s15430421tip4304_9 DOI: https://doi.org/10.1207/s15430421tip4304_9
Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2018). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569-578. https://doi.org/10.12973/ejmste/76959 DOI: https://doi.org/10.12973/ejmste/76959
Laurillard, D. (2013). Rethinking university teaching: A conversational framework for the effective use of learning technologies. Routledge. https://doi.org/10.4324/9781315012940 DOI: https://doi.org/10.4324/9781315012940
Mezirow, J. (2008). An overview of transformative learning. In Lifelong learning (pp. 40–54). Routledge.
Mezirow, J. (2018). Transformative learning theory. In Contemporary Theories of Learning (pp. 114–128). Routledge. https://doi.org/10.4324/9781315147277-8 DOI: https://doi.org/10.4324/9781315147277-8
Oliveri, G. (1997). Mathematics. A science of patterns? Synthese, 112(3), 379–402. DOI: https://doi.org/10.1023/A:1004906107430
Orton, A. (2004). Learning mathematics: Issues, theory, and classroom practice. Bloomsbury Publishing. https://doi.org/10.1023/A:1004906107430 DOI: https://doi.org/10.1023/A:1004906107430
Pulungan, R. R. (2019). Analysis of student’s misconceptions in solving the system of linear equation in two variables. Journal of Physics: Conference Series, 1157(4), 42113. IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042113 DOI: https://doi.org/10.1088/1742-6596/1157/4/042113
Purcell, E. J., & Varberg, D. (1994). Kalkulus dan Geometri Analitis Jilid 1 dan 2. Terjemahan: I Nyoman Susila, Kartasasmita Bana, Jakarta: Erlangga.
Resnik, M. D. (1997). Mathematics as a Science of Patterns. Oxford University Press.
Romberg, T. A. (Ed.). (1995). Reform in school mathematics and authentic assessment. SUNY Press.
Rugh, W. J., & Rugh, W. J. (1996). Linear system theory (Vol. 2). prentice hall Upper Saddle River, NJ.
Semadiartha, I. K. S. (2012). Pengembangan media pembelajaran berbasis komputer dengan Microsoft Excel yang berorientasi teori Van Hiele pada Bahasan Trigonometri kelas X SMA untuk Meningkatkan Prestasi dan Motivasi Belajar Matematika Siswa. Jurnal Pendidikan Dan Pembelajaran Matematika Indonesia, 1(2).
Soviawati, E. (2011). Pendekatan matematika realistik (pmr) untuk meningkatkan kemampuan berfikir siswa di tingkat sekolah dasar. Jurnal Edisi Khusus, 2(2), 79-85.
Stipek, D. (2002). Good instruction is motivating. In Development of achievement motivation (pp. 309–332). Elsevier. https://doi.org/10.1016/B978-012750053-9/50014-0 DOI: https://doi.org/10.1016/B978-012750053-9/50014-0
Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem-solving. Research Ideas for the Classroom: High School Mathematics, 57, 78.
Wu, Y. T., & Mohanty, S. (2006). Variable screening and ranking using sampling-based sensitivity measures. Reliability Engineering & System Safety, 91(6), 634–647. https://doi.org/10.1016/j.ress.2005.05.004 DOI: https://doi.org/10.1016/j.ress.2005.05.004