Main Article Content

Abstract

This research aims at developing local instruction theory for learning combinations by using Realistic Mathematics Education (RME). This research uses a design research approach, Hypothetical Learning Trajectory (HLT), developed from a series of activities to obtain a better understanding about combinations at Senior High School (SHS) students. Theoretical development is supported by an interactive process in designing learning activities, conducting teaching experiment and conducting retrospective analysis to contribute to combinations of Local Instruction Theory (LIT). An understanding of combinations emerges and develops during classroom learning activities. Qualitative analysis of teaching experiments shows that by using local instruction theory teaching materials that characterize RME students are able to develop their understanding about a combination.

Keywords

Combinations HLT Local Instruction Theory RME

Article Details

References

  1. Azhar, E. & Kusumah, Y. S. (2011). Pengembangan Perangkat Pembelajaran Teori Peluang Berbasis RME Untuk Meningkatkan Pemahaman, Penalaran, dan Komunikasi Matematik Siswa SLTA. Prosiding Seminar Nasoinal Matematika dan Pendidikan Matematika 2011, Pendidikan Matematika FMIPA UNY, Yogyakarta, 3 Desember 2011, 213-222.
  2. Ben-Hur, M. (2006). Concept-rich mathematics instruction: Building a strong foundation for reasoning and problem solving. Alexandria, VA: Association for Supervision and Curriculum Development.
  3. Busadee, N., & Laosinchai, P. (2013). Authentic problems in high school probability lesson: Putting research into practice. Procedia-Social and Behavioral Sciences, 93, 2043-2047.
  4. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational researcher, 32(1), 9-13.
  5. Eizenberg, M. M., & Zaslavsky, O. (2004). Students' verification strategies for combinatorial problems. Mathematical Thinking and learning, 6(1), 15-36.
  6. Fischbein, H. (1975). The intuitive sources of probabilistic thinking in children (Vol. 85). Springer Science & Business Media.
  7. Fitria, N. L. (2013). Pengembangan Lembar Kerja Siswa (LKS) Materi Permutasi Dan Kombinasi Menggunakan Masalah Kontekstual. SKRIPSI Jurusan Matematika-Fakultas MIPA UM.
  8. Freudenthal, H. (1991). Revisiting Mathematics Education: China lectures. Kluwer Academic Publishers. Dordrecht, the Netherlands.
  9. Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for research in Mathematics Education, 19(1), 44-63.
  10. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical thinking and learning, 1(2), 155-177.
  11. Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical thinking and learning, 6(2), 105-128.
  12. Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Educational design research (pp. 29-63). Routledge.
  13. Herman, T. (2007). Pembelajaran berbasis masalah untuk meningkatkan kemampuan berpikir matematis tingkat tinggi siswa sekolah menengah pertama. Educationist, 1(1), 47-56.
  14. Meika, I., & Suryadi, D. (2018). Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling. In Journal of Physics: Conference Series, 948(1), 012060.
  15. Van de Walle, J. A. (2008). Matematika sekolah dasar dan menengah. Terjemahan Suyono). Jakarta: Penerbit Erlangga.
  16. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 458-477.
  17. Yulianti, Y., Zulkardi, Z., & Ilma, R. (2014). Pengembangan Perangkat Pembelajaran Peluang Berbasis Reciprocal Teaching Untuk Melatih Kemampuan Berpikir Kritis Siswa Kelas XI Smk Negeri 3 Lubuklinggau. Jurnal Pendidikan Matematika, 4(2).