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Abstract
This study aims to generate trajectories of students in the learning addition dan subtraction fractions by using scales that evolved from the informal to the formal form. The method used in this study is a research design that consists of three stages, ie preliminary, design experiments and retrospective analysis. In this study, a series of learning is designed and developed based on the notion of the learning process and approach PMRI. This research was conducted in MI Al-Hilaliyah Palembang involving fourth graders totaling 30 siswa.penelitian produces Learning Trajectory (LT), which includes three activities, namely the activity 1. Considering the object and determine the equivalent fractions of fractions of known 2. define relationship occurred between two fractions to determine whether two fractions are equivalent fractions or not. Activity 3. solving the problems associated with fractional operation daily life - today. The results of the learning experiments showed that a series of activities that have been done to help improve students' understanding of the addition dan subtraction of learning fractions.
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References
- Akker, et al. 2006. Education Design Research. London : Routledge Taylor and Francis Group
- Ben-Chaim, Keret, & Ilany, 2012. Ratio Proportional.Sence Publishers Rotterdam Boston/TaipeiGravemeijer, K. 1994. Developing Realistic mathematics Education. Utrecht : Freudential Institute.
- Cramer, Kathleen; dkk. (2008). The Role of Representations in Fraction Addition and Subtraction. Jurnal: Mathematics Teaching In The Middle School, Vol. 13,
- Fazio, Lisa dan Siegler, Robert. (2011). Teaching Fraction Educational Practices Series-22. International Bureau Education
- Gravemeijer, K., & Cobb, P. 2006. Design Research from a Learning Design Perspective. In J. V. D Akker, K.P.E. Gravemeijer, S. McKenney, N. Nieven (Eds), Educational Design Research (pp. 17-51). London : Routledge
- Gravemeijer, K., & Van Eerde, D. 2009. Research as a Means for Building a Knowladge Base for Teaching In Mathematics Education. The Elementary School Journal. 109(5). 510-524
- H. Guershon & J. Confrey ( Eds.), The development of multiplicative rasoning in the learning mathematics (pp.89-120). Albany,
- Lamon, S. 1994. Ratio and Proportion : Cognitive Foundetions in Unitizing and norming. In Lesh, R.,Post, T. & Behr, M. (1988). Proportional reasoning. In A.Kelly & R.Lesh (Eds.), Number concepts and operations in the middle grades (pp. 93 - 118). Hillsdale, NJ:Lawrence Erlbaum, Practices Series-22. International Bureau Education
- Marhamah, 2011. Pengembangan Materi Ajar Pecahan Dengan Pendekatan Pmri Di Sd Negeri 21 Palembang. Makalah disajikan dalam Jurnal Pendidikan Matematika (JPM) Unsri vol.2 No.5 Tahun 2011. National Council of Teachers of Mathematics
- (NCTM). 2013 Teaching Ratio and Proportion the Middle Grades. Ratio and Proportion Research Brief
- Noer Hastuti Sri, 2007. Pembelajaran Open Ended untuk Meningkatkan Kemampuan Pemecahan Masalah Matematik dan Kemampuan Berfikir Kreatif. Tesis Penelitian Eksperimen pada Siswa Salah penelitian dari Universitas Lampung
- Tourniaire,F & Steven P.1985. Proportional Reasoning : A Review of the Literature Educational Studies in Mathematics,16,181-204. Calipornia:Group in Science and mathematics Education, Lawrence Hall of
- Ullya, 2010. Desain Bahan Ajar Penjumlahan Pecahan Berbasispendidikan Matematika Realistik Indonesia (Pmri) Untuk Siswa Kelas Iv Sekolah Dasar Negeri 23 Indralaya. Makalah ini disajikan dalam Jurnal Pendidikan Matematika (JPM) Unsri Vol.4 No.2 Tahun 2010
- Van De Walle, J.A. 2008. Matematika Sekolah Dasar Dan Menengah: Pengembangan Pengajaran. Jilid Kedua. Jakarta: Erlangga.Science, University of California
- Wijaya, Ariyadi. 2012. Pendidikan Matematika Realistik : Suatu Alternatif Pendekatan Pembelajaran Matematika. Yogyakarta : Graha Ilmu
- Zulkardi. 2006. RME suatu inovasi dalam pendidikan matematika d Indonesia. Makalah disajikan pada Konferensi Matematika Nasional XIII. Bandung ITB.
- Zulkardi. 2009. The “P” in PMRI : Progress and Problem. In Proceeding of IICMA 2009 Mathematics Education, pp. 773-780. Yogyakarta : IndoMs
- Zulkardi & Ilma, R. 2010. Pengembangan Blog Support untuk Membantu Siswa dan Guru Matematika Indonesia Belajar Pendidikan Matematika Realistik Indonesia (PMRI). Tersediaonline : http://eprints.unsri.ac.id/540/1/Prof.Dr.Zulkardi_Dr.Ratuilma_di_JIPP- Balitbang.pdf.
References
Akker, et al. 2006. Education Design Research. London : Routledge Taylor and Francis Group
Ben-Chaim, Keret, & Ilany, 2012. Ratio Proportional.Sence Publishers Rotterdam Boston/TaipeiGravemeijer, K. 1994. Developing Realistic mathematics Education. Utrecht : Freudential Institute.
Cramer, Kathleen; dkk. (2008). The Role of Representations in Fraction Addition and Subtraction. Jurnal: Mathematics Teaching In The Middle School, Vol. 13,
Fazio, Lisa dan Siegler, Robert. (2011). Teaching Fraction Educational Practices Series-22. International Bureau Education
Gravemeijer, K., & Cobb, P. 2006. Design Research from a Learning Design Perspective. In J. V. D Akker, K.P.E. Gravemeijer, S. McKenney, N. Nieven (Eds), Educational Design Research (pp. 17-51). London : Routledge
Gravemeijer, K., & Van Eerde, D. 2009. Research as a Means for Building a Knowladge Base for Teaching In Mathematics Education. The Elementary School Journal. 109(5). 510-524
H. Guershon & J. Confrey ( Eds.), The development of multiplicative rasoning in the learning mathematics (pp.89-120). Albany,
Lamon, S. 1994. Ratio and Proportion : Cognitive Foundetions in Unitizing and norming. In Lesh, R.,Post, T. & Behr, M. (1988). Proportional reasoning. In A.Kelly & R.Lesh (Eds.), Number concepts and operations in the middle grades (pp. 93 - 118). Hillsdale, NJ:Lawrence Erlbaum, Practices Series-22. International Bureau Education
Marhamah, 2011. Pengembangan Materi Ajar Pecahan Dengan Pendekatan Pmri Di Sd Negeri 21 Palembang. Makalah disajikan dalam Jurnal Pendidikan Matematika (JPM) Unsri vol.2 No.5 Tahun 2011. National Council of Teachers of Mathematics
(NCTM). 2013 Teaching Ratio and Proportion the Middle Grades. Ratio and Proportion Research Brief
Noer Hastuti Sri, 2007. Pembelajaran Open Ended untuk Meningkatkan Kemampuan Pemecahan Masalah Matematik dan Kemampuan Berfikir Kreatif. Tesis Penelitian Eksperimen pada Siswa Salah penelitian dari Universitas Lampung
Tourniaire,F & Steven P.1985. Proportional Reasoning : A Review of the Literature Educational Studies in Mathematics,16,181-204. Calipornia:Group in Science and mathematics Education, Lawrence Hall of
Ullya, 2010. Desain Bahan Ajar Penjumlahan Pecahan Berbasispendidikan Matematika Realistik Indonesia (Pmri) Untuk Siswa Kelas Iv Sekolah Dasar Negeri 23 Indralaya. Makalah ini disajikan dalam Jurnal Pendidikan Matematika (JPM) Unsri Vol.4 No.2 Tahun 2010
Van De Walle, J.A. 2008. Matematika Sekolah Dasar Dan Menengah: Pengembangan Pengajaran. Jilid Kedua. Jakarta: Erlangga.Science, University of California
Wijaya, Ariyadi. 2012. Pendidikan Matematika Realistik : Suatu Alternatif Pendekatan Pembelajaran Matematika. Yogyakarta : Graha Ilmu
Zulkardi. 2006. RME suatu inovasi dalam pendidikan matematika d Indonesia. Makalah disajikan pada Konferensi Matematika Nasional XIII. Bandung ITB.
Zulkardi. 2009. The “P” in PMRI : Progress and Problem. In Proceeding of IICMA 2009 Mathematics Education, pp. 773-780. Yogyakarta : IndoMs
Zulkardi & Ilma, R. 2010. Pengembangan Blog Support untuk Membantu Siswa dan Guru Matematika Indonesia Belajar Pendidikan Matematika Realistik Indonesia (PMRI). Tersediaonline : http://eprints.unsri.ac.id/540/1/Prof.Dr.Zulkardi_Dr.Ratuilma_di_JIPP- Balitbang.pdf.