DEVELOPING MATHEMATICAL COMMUNICATION AND REPRESENTATION OF STUDENTS GRADE VII: A DESIGN RESEARCH

Dadang Juandi, Al Jupri

Abstract


ABSTRAK

Penelitian ini berfokus pada komunikasi matematika dan representasi melalui pembelajaran berbasis masalah yang dikembangkan melalui penelitian desain. Ada dua tujuan dari penelitian ini. Pertama, dalam jangka pendek, penelitian ini dilakukan untuk mengetahui: bagaimana komunikasi matematika dan representasi siswa berkembang, apakah budaya kelas mendukung pencapaian kompetensi dasar-, dan apa hambatan siswa untuk belajar. Kedua, dalam jangka panjang, penelitian ini dilakukan untuk mengembangkan “teori” dalam pendidikan matematika. Kedua tujuan tersebut diharapkan dapat dicapai melalui penelitian pengembangan (dalam hal ini menggunakan desain penelitian). Tujuan pertama dicapai dengan desain penelitian yang meliputi tiga tahap: desain awal, eksperimen, dan analisis retrospektif. Penelitian awal menunjukkan bahwa: (i) komunikasi matematika dan representasi dapat dikembangkan melalui bahan pembelajaran kontekstual, intervensi guru yang tepat itu, berbagai pengaturan belajar-mengajar, situasi didactical dikembangkan oleh guru, dan usaha guru dalam menghubungkan situasi didactical yakni antara bahan dan siswa belajar, dan antara mahasiswa dan guru, (ii) kesulitan siswa meliputi: kesulitan dalam berkomunikasi ide matematika secara lisan, mewakili ide matematika aljabar, menggunakan representasi matematis untuk memecahkan masalah, dan mengusulkan argumentasi, dan (iii) kesulitan guru adalah menganalisis komunikasi matematika dan representasi siswa.

ABSTRACT

This research studies mathematical communication and representation through problem based-learning which is developed by design research. There are two objectives of this research. First, in short term, the research is conducted to know: how students’ mathematical communication and representation develops, does classroom culture support the achievement of basic-competence, and what are students’ learning obstacles. Second, in long term, this research is conducted to develop “a theory” in mathematics education. These two objectives are expected to be achieved through developmental research (in this case using design research). The first objective is achieved by design research which includes three phases: preliminary design, experiment, and retrospective analysis. The preliminary research showed that: (i) mathematical communication and representation could be developed through contextual learning materials, proper teacher’s intervention, various learning-teaching settings, a didactical situation developed by the teacher, and the teacher’s effort in connecting didactical situations i.e., between learning materials and students, and between students and the teacher; (ii) students’ difficulties include: a difficulty in communicating mathematical idea verbally, representing mathematical idea algebraically, using mathematical representation to solve problems, and proposing argumentation; and (iii) the teacher’s difficulty is analyzing students’ mathematical communication and representations.


Keywords


hambatan belajar komunikasi matematika; rancangan penelitian; representasi matematika; learning obstacles; mathematical communication; mathematical representation; design research

Full Text:

PDF

References


Al Jupri, Yulianti, K., Rukmana, K., Saputra, C. (2007). Pengembangan Desain Pembelajaran Matematika Realistik untuk Menumbuhkembangkan Kemampuan Pemecahan Masalah dan Komunikasi Matematis Siswa Kelas VIII H SMP 22 Bandung. Bandung: Laporan Penelitian (Tidak dipublikasikan)

Al Jupri. (2008). Computational Estimation in Grade Four and Five: Design Research in Indonesia. Utrecht: Master Thesis at the Freudenthal Institute, Utrecht University (Unpublished).

Ansari, B. I. (2003).Menumbuhkembangkan Kemampuan Pemahaman dan Komunikasi Matematik Siswa SMU melalui Strategi Think-Talk-Write. Disertasi pada Program Pascasrjana UPI, Bandung: Tidak dipublikasikan.

As’ari, A.R. (2001). Representasi: Pentingnya dalam Pembelajaran Matematika. Jurnal MATEMATIKA, TAHUN VII, Nomor 2, Agustus 2001.

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht: Freudenthal Institute.

Cobb, P., Confrey, J., diSessa, A. A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

Cobb, P. & Bauersfeld, H. (Eds.) (1995). The Emergence of Mathematical Meaning: Interaction in classroom cultures. Hillsdale, New Jersey: Lawrence Erlbaum Associates, publishers.

Depdiknas. (2006). Kurikulum Tingkat Satuan Pendidikan. Jakarta:

Dekker, R. dan Moher, M.E.(2004). Teacher Interventions Aimed at Mathematical Level Raising during Collaborative Learning. Education Studies in Mathematics 56: 39-65. Netherlands: Kluwer Academic Publishers.

Delisle, R. (1997). How to Use Problem Based Learning in the Calssroom. New York: Association for Supervision and Curriculum Development.

Downs, J.M. dan Downs,M.(2002). Advanced Mathematical Thinking with a Special Reference to Reflection on Mathematical Structure. Dalam Handbook of International Research in Mathematics Education. English, L.D. (Ed). NCTM. London: Lawrence Erlbaum Associates Publisher.

Eisner, E. W. (1997). Cognition and Representation: A Way to Pursue the American Dream. Phi Delta Kappa, 349-353.

Emori, H. (2005). Constructing Original Mathematics Educationfor Keeping Thai Ethnic Identity. Panduan Workshop. Gunma University. Tidak diterbitkan.

Esty, W.W. & Teppo, A.R. (1996). Algebraic Thinking, Language, and Word Problems. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Fogarty, R. (1997). Problem Based-Learning and the Other Curriculum Models for Multiple Intelegences Clasroom. Hawker Brownlow Education.

Gijselaers, W. H.(1996). Connecting Problem-Based Practice with Educational Theory. Dalam Wilkerson, L.(Ed). New Direction for Teaching and Learning. No.68. Josey-Bass Publishers.

Goldin ,G.A. (2003). Representation in Mathematical Learning and Problem Solving. Dalam English, L.D. (Ed). Hanbook of International Research in Mathematics Education. NCTM. London: Lawrence Erlbaum Associates, Publisher.

Gravemeijer, K.P.E. (1994). Developing Realistic Mathematics Education. Utrecht: CD- Press. Freudenthal Institut.

Greenes, C. & Schulman, L. (1996). Communication Processes in Mathematical Explorations and Investigation. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Grouws, D.A. (1992). Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan Publishers.

Hendayana, S., et.al (2007). Lesson study: Suatu Strategi untuk Meningkatkan Keprofesionalan Pendidik (Pengalaman IMSTEP-JICA). Bandung: UPI Press.

House, P.A.(1996).Try a Little of the Write Stuff. Dalam Elliot, P.C. dan Kenney,M.J. (Eds). Communication in Mathematics,K-12 and Beyond.. Yearbook Virginia: NCTM.

Honebein, P. C. (1996). Seven Goals for the Design of Constructivist Learning Environments. Dalam Wilson, B.C. (Ed.), Constructivist Learning Environments: Case Studies in Instructional Design (pp. 11-24). Englewood Cliffs, NJ:Educational Technology Publications.

Howey, K.R., et.al (2001).Contextual Teaching and Learning:Preparing Teacher to Enhance Student Success in The Work Place and Beyond.Washington: ERIC Clearinghouse on Teaching and Teacher Education.

Huinker, D., & Laughlin, C. (1996). Talk Your Way into Writing. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Lester, F.K. (1980). Research on Mathematical Problem Solving. In R.J. Shumway (Ed.), Research in Mathematics Education.( pp. 286-323). Reston, Virginia: National Council of Teachers of Mathematics.

Linquist, M.M. (1996). Communication an Imperative for Change: A Coversation with Mary Lindquist. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Massingila, J.O. dan Wistiniowska,E.P.(1996).Developing and Assessing Mathematical Understanding in Calculus Through Writing. Dalam Elliot, P.C. dan Kenney,M.J. (Eds). Communication in Mathematics,K-12 and Beyond. Yerbook Virginia: NCTM.

McCoy, L.P., Baker, T.H., & Little, L.S., (1996). Using Multiple Representation to Communicate: An Algebra Challenge. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Monk, S. (2003). Representation in School Mathematics: Learning to Graph and Graphing to Learn. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp.250-262). Reston, NJ: NCTM.

NCTM (National Council of Teacher of Mathematics). (1989). Curriculum and Evaluation Standard for School Mathematics. Reston, Va: NCTM.

NCTM. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, Va: NCTM.

NCTM. (2000). Principles and Standadrs for School mathematics. Reston, VA:NCTM

Ngeow, K.K., dan San, Y. (1997). Learning to Learn: Preparing Teachers and Students for Problem–Based Learning.[On-Line], Tersedia: http// eric Indiana.Edu. ERIC Clearinghouse on Reading English and Communication Bloomington. IN.

Pierce, J.W. dan Jones, R.T. (2001). Problem-Based Learning: Learning and Teaching in Context of Problems. Dalam K.R. Howey, dkk. (Eds). Contextual Teaching and Learning: Preparing Teacher to Enhance Student Success in the Work Place and Beyond. (pp. 17-32). ERIC Clearinghouse on Teaching and Teacher Education.

Pugalee, D.K. (2004). A Comparison of Verbal and Written Description of Students’ Problem Solving Process. Educational Studies in Mathematics, 55: 22-47. Kluwer Academic Publishers.

Reidesel, C.A., Scwartz, J.E., & Clements, D.H. (1996). Teaching Elementary School Mathematics. Boston: Allyn and Bacon.

Sabandar, J. (2005). Pertanyaan Tantangan dalam Memunculkan Berpikir Kritis dan Kreatif dalam Pembelajaran Matematika. Makalah Disajikan pada Seminar MIPA di JICA: tidak diterbitkan.

Savery J.R. dan Duffy, T.M. (1996). Problem –Based Learning: An Instructional Model and Its Constructivist Framwork. .[On-Line], Tersedia: http//www. Soe.ecu.edu/Itdi/colaric/KB/PBLs.htm

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education. 26 (2), 114-145.

Shigeo, K. (2000). On Teaching Mathematical Thinking. In O.Toshio (Ed.), Mathematical Education in Japan (pp. 26-28). Japan: JSME.

Shimizu, N. (2000). An Analysis of “Make an Organized List” Strategy in Problem Solving Process. In T. Nakahara & M. Koyama (Eds.) Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 145-152). Hiroshima: Hiroshima University.

Siegel, M., Barosi, R., Fonzi, J.M., & Sanridge, L.G. (1996). Using Reading to Construct Mathematical Meaning. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Supriadi, D. (2001). Anatomi Buku Sekolah di Indonesia. Yogyakarta: Adi Cita

Smith, S. P. (2003). Representation in School Mathematics: Children’s Representations of Problems. Dalam J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 263-274). Reston, NJ: NCTM.

Sumarmo, U.(2002). Alternatif Pembelajaran Matematika dalam Menerapkan Kurikulum Berbasis Kompetensi. Makalah pada Seminar Nasional. FPMIPA UPI: Tidak dipublikasikan.

Shigeo, K. (2000). On Teaching Mathematical Thinking. In O.Toshio (Ed.), Mathematical Education in Japan (pp. 26-28). Japan: JSME.

Shimizu, N. (2000). An Analysis of “Make an Organized List” Strategy in Problem Solving Process. In T. Nakahara & M. Koyama (Eds.) Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 145-152). Hiroshima: Hiroshima University.

Usiskin, Z. (1996). Mathematics as a Language. In P.C. Elliot & M.J. Kenney (Eds). Communication in Mathematics, K-12 and Benyond (1996 Yearbook). Virginia: NCTM.

Wood,T. (1999).Creating a Context for Argument in Mathematics Class. Journal for Reasearch in Mathematics Education, 30 (2). 171-191.

Yamada, A. (2000). Two Patterns of Progress of Problem-Solving Process: From a Representational Perspective. In T. Nakahara & M. Koyama (Eds.) Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 289-296). Hiroshima: Hiroshima University.




DOI: https://doi.org/10.18269/jpmipa.v18i2.36128

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Jurnal Pengajaran MIPA

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

JPMIPA http://ejournal.upi.edu/index.php/jpmipa/index is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam (JPMIPA) or Journal of Mathematics and Science Teaching 

All rights reserverd. pISSN 1412-0917 eISSN 2443-3616

Copyright © Faculty of Mathematics and Science Education (FPMIPA) Universitas Pendidikan Indonesia (UPI)

 

View JPMIPA Stats