PROFIL GENERALISASI SISWA OPERASIONAL KONKRET BERDASARKAN PERSPEKTIF SEMIOTIK
Keywords:
Generalisasi pola, Semiotik, Berpikir logis, Operasional konkretAbstract
Penelitian ini bertujuan untuk mengeksplorasi generalisasi pola berdasarkan perspektif semiotik pada siswa operasional konkret. Material semiotik yang akan dianalisis meliputi, gestur, ucapan dan tulisan. Penelitian kualitatif eksploratif ini dilaksanakan di salah satu SMP swasta di Tuban Jawa Timur Indonesia. Subjek dalam penelitian ini adalah seorang siswa Kelas VII berjenis kelamin laki-laki dan kemampuan berpikir logis berada pada tahap operasional konkret. Subjek dipilih dengan menggunakan instrument GALT (Group of Assessment of Logical Thinking). Data dikumpulkan dengan think aloud, yaitu saat menyelesaikan tugas generalisasi pola, siswa menyatakan proses berpikirnya secara lisan. Selain itu, juga dilakukan wawancara. Data yang telah terkumpul kemudian dianalisis dengan menggunakan teknik analisis data kualitatif. Hasil penelitian menunjukkan bahwa siswa operasional konkret melalui tiga tahapan proses generalisasi, yaitu menemukan keteraturan, mengkonfirmasi keteraturan dan menghasilkan rumus umum. Tahapan membuktikan kebenaran rumus umum tidak dilakukan oleh siswa. Siswa menyatakan produk generalisasi dalam bentuk kalimat sederhana berdasarkan pada konteks gambar yang dilihat
References
Tikekar, V, G. 2009. Deceptive patterns in mathematics. International Journal Mathematic Science Education. Vol 2 No.1: 13-21.
Orton, A. 1999. Pattern in the teaching and learning of mathematics. London: Cassel.
Zazkis, Rina & Liljedahl, Peter. 2002. Generalization of patterns: The Tension Between Algebraic Thinking and Algebraic Notation. Educational Studies in Mathematics. Vol 49: 379-402.
Mason, J. 1996. Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp. 65–86). Dordrecht: Kluwer.
Blanton, M. L. & Kaput, J. J. 2011. Functional Thinking as a Route Algebra in the Elementary Grade. Dalam Cai, Jinva & Knuth, Eric (Eds.), Early Algebraization: A Global Dialogue from Multiple Perspectives. New York: Springer Heidelberg Dordrecht.
Healy, L., & Hoyles, C. 1996. Seeing, doing and expressing: An evaluation of task sequences for supporting algebraic thinking. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th International Conference of the International Group for the Psychology of Mathematics Education. Vol. 3: 67-74. Valencia, Spain.
Presmeg, N. 2006. Research on visualization in learning and teaching mathematics: Emergence from psychology. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education. 205-235. Dordrecht: Sense Publishers.
Fadiana, Mu’jizatin. 2016b. Strategi Generalisasi Pola Siswa SMP Kelas VII. Prosiding Seminar Nasional Matematika X Tahun 2016. Semarang : FMIPA Universitas Negeri Semarang
Ernest, Paul. 2006. A Semiotic Perspective of Mathematical Activity: The Case of Number. Educational Studies in Mathematics. 61:67-1001.
Tarasenkova, N & Kovalenka, O. 2015. Content and Semiotic Features of Mathematical Problems Used as a Means of Training the Primary School Education Students. American Journal of Educational Research. Vol. 3: 31-35.
Inganah, S. & Subanji. 2013. Semiotik dalam Proses Generalisasi Pola. Prosiding: Konferensi Nasional Matematika dan Pendidikan Matematika V. FMIPA Universitas Negeri Malang. 27-30 Juni. ISBN: 978-602-97895-8-4. Hal. 431-438.
Orton, A. & Orton, J. 1999. Pattern and the Approach to Algebra. In A. Orton (Ed.) Pattern in the Teaching and Learning of Mathematics. Cassell, London.
Labinowicz, E. 1985. Learning from children: new beginnings for teaching numerical thinking. Menlo Park, CA: Addison-Wesley
Atherson, J.S. 2013. Learning and teaching: Piaget’s developmental theory [Online :UK]. Diakses 29 Desember 2016 dari http://www.learningandteaching.info/learning/piaget.htm
[Minderovic, Z. 2001. Logical Thinking. Encyclopedia of Psychology, April 2006. [Online]. Diakses 13 April 2016 dari :http//findarticles.com/p/article/mi_g2600/ix_is_0005/ai_269000536/ ?tag-content;coll,
Roadrangka, V., Yeany, R. H., & Padilla, M. J. 1982. GALT, Group test of logical thinking. University of Georgia, Athens, GA.
Stacey, K. And Macgregor, M. 1994. Algebraic Sums And Products: Students’ Concepts And Symbolism’, In J.P. Da Ponte And J.F. Matos (Eds.), Proceedings Of The Eighteenth Inter- Understanding Algebraic Notation 19 National Conference For The Psychology Of Mathematics Education (Vol. Iv), University Of Lisbon, Portugal: PME. 289–296.
Inganah, S. 2012. Generalisasi Pola dalam Berpikir Secara Aljabar. Prosiding: Conference on Applied Mathematics and Education: Membangun Kreativitas dan Kemandirian Bangsa Melalui Matematika. Hal. 349-355. Yogyakarta: UIN Sunan Kalijaga.
Fadiana, M. Amin, S,M & Lukito, A. 2017. Generalization of Visual Pattern. IOSR Journal of Research & Method in Education. Vol 7. 6 (III): 29-32
Radford, L. 2003. Gestures, speech and the sprouting of signs. Mathematical Thinking and Learning. 5(1), 37-70.
Fadiana, M. 2016. Peran Gestur dalam Pembelajaran Matematika. Prosiding Seminar Nasional MASIF II FPMIPATI. Semarang : Universitas PGRI Semarang
Radford, L. 2002. The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.
Botzer G. & Yerushalmy M. 2008. Embodied Semiotic Activities and their Role in the Construction of Mathematical Meaning of Motion Graphs. International Journal of Computers for Mathematical Learning. Vol 13. No 2: 111–134.