HYPOTHETICAL LEARNING TRAJECTORY PADA PEMBELAJARAN BILANGAN NEGATIF BERDASARKAN TEORI SITUASI DIDAKTIS DI SEKOLAH MENENGAH

Nyiayu Fahriza Fuadiah

Abstract


Penelitian ini bertujuan untuk mendesain Hypothetical Learning Trajectory (HLT) pada pembelajaran bilangan negatif sebagai hasil dari tahap pertama Didactical Design Research yaitu Analisis Prospektif. HLT ini merupakan tindak lanjut dari hasil identifikasi Learning Obstacle yang yang dilakukan peneliti dalam pembelajaran bilangan negatif yang terintegrasi dalam materi Bilangan Bulat di kelas 7 sekolah menengah pertama. Observasi mendalam terhadap proses belajar mengajar di kelas yang diamati peneliti memperlihatkan kesulitan guru dalam menanamkan konsep bilangan negatif dan operasi bilangan yang melibatkan bilangan negatif serta beberapa kesalahan konstruksi konsep yang dialami oleh siswa. Istilah HLT merujuk pada rencana pembelajaran berdasarkan antisipasi belajar siswa yang mungkin dicapai dalam proses pembelajaran yang didasari pada tujuan pembelajaran matematika yang diharapkan pada siswa, pengetahuan, dan perkiraan tingkat pemahaman siswa, serta pilihan aktivitas matematika secara berurut. HLT ini disusun berdasarkan analisis terhadap Learning Obstacle, tahap berpikir siswa, dan analisis terhadap kurikulum dengan tetap berpijak pada konsep materi yang harus dipahami siswa.


This research aims to design Hypothetical Learning Trajectory (HLT) on learning of negative numbers as a result of the first stage on Didactical Design Research specifically in Prospective Analysis. This HLT is a follow up of the results of the identification of the Learning Obstacle conducted by researcher in learning negative numbers that integrated in the material Integer in the 7th grade secondary school. From the observations conducted by researcher on the teaching and learning process in the classroom showed the difficulties of teachers in embedding the concept of negative numbers and arithmetic operations involving negative numbers and several construction errors of concepts that experienced by the students. Term of HLT refers to a lesson plan based on the anticipation of student learning possibly achievable in the learning process which is based on mathematics learning goals expected on students, knowledge, estimates of the level of students understanding, and the selection of mathematical activity sequentially. This HLT is compiled based on an analysis of the Learning Obstacle, level of students thinking, and analysis of the curriculum that standing on the concept that must be understood by the students.


Keywords


Hypothetical Learning Trajectory; Theory of Didactical Situation; Negative Numbers; Mathematics Learning; Hypothetical Learning Trajectory; Teori Situasi Didaktis; Bilangan Negatif; Pembelajaran Matematika

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References


Almeida, R., dan Bruno, A. (2014). Strategies of pre-servise primary school teachers for solving addition problems with negative numbers. International Journal of Mathematical Education in Science and Technology, 45(5), 719-737. http://dx.doi.org/10.1080/002073999287482.

Altiparmak, K., dan Ozdogan, E. (2010). A Study on the teaching of the concept of negative numbers.International Journal of Mathematical Education in Science and Technology, 41(1): 31-47. http://dx.doi.org/10.1080/00207390903189179.

Artigue, M. (1994). Didactical Engineering as a framework for the conception of teaching product. In R. Biehler et al. (Eds.), Didactic of mathematics as a scientific discipline (pp. 27-39). Dorddrecht: Kluwer Academic Publishers.

Artigue, M., Haspekian, M., dan Corblin-Lenfant, A. (2014). Introduction to the theory of didactical situation (TDS). In: Ahsbahs dan Prediger (Eds.),Networking of theories as a research pratice in mathematics education (47 – 65). Switzerland: Springer International Publishing.

Blair, K. P., Rosenberg-Lee, M., Tsang, J.M., Schwartz, D.L., dan Menon, V. (2012). Beyond natural numbers: negative number representation in parietal cortex. Frontiers in Human Neuroscience, 6(7), 1–17. http://dx.doi.org/10.3389/fnhum.2012.0000.

Bofferding, L. (2014). Negative integer understanding: Characterizing first graders' mental models. Journal for Research in Mathematics Education, 45(2), 194-245. http://dx.doi.org/10.5951/jresematheduc.45.2.0194.

Brousseau, G. (2002). Theory of didactical situation in mathematics.Kluwer Academic Pulishers.

Clements, D., dan Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89.

Daro, P., et.al. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction.USA: Consortium for Policy Research in Education.

Fuadiah, N. F. (2015). Epistemological obstacles on mathematics’learning in junior high school students: a study on the operations of integer material. In Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2015 (ICRIEMS 2015), Yogyakarta State University, 17-19 May 2015. Fakultas MIPA Universitas Negeri Yokyakarta.

Gravemeijer, K. (1998). Developmental Research as a Research Method. Dalam J. Kilpatrick dan A. Sierpinska (Eds.), What is research in mathematics education and what are its results? (hal.277-295). Dordrecht: Kluwer.

Gravemeijer, K., dan Cobb. P. (2006). Design research from a learning design perspective. Dalam Jan van den Akker, et. Al. Educational Design Research. London: Routlege.

Kislenko, K. (2005.) Student’s beliefs about mathematics from the perspective of the theory of didactical situations. Dalam C. Winslow (ED.), Didactic of mathematics-the French way (83-96). Center For Naturfagenes Didaktis University of Copenhagen.

Lamb, L. L., Bishop, J. P., Philipp, R. A., Schappelle, B. P., Whitacre, I., dan Lewis, M. (2012). Developing symbol sense for the minus sign. Mathematics Teaching in the Middle School, 18(1), 5-9.

Larsen, J. (2012). Epistemological obstacles of negative numbers. Vector: The Official Journal of the BC Association of Mathematics Teachers, 53(2), 56-60 [online]. Retrieved from https://www.researchgate.net/publication/274310485_Epistemological_Obstacles_of_Negative_Numbers

Maloney, A. dan Confrey, J. (2013). A Learning trajectory framework for the mathematics common core: turnonccmath for interpretation, instructional planning, and collaboration. 17th annual conference of the association of mathematics teacher educators. Orlando: AMTE.

Manno, G. (2006). Embodiment and a-didactical situation in the teaching-learning of the perpendicular straight lines concept. Disertasi. Departement of Didactic Mathematics Comenius University Bratislava.

Sanchez dan Varcarcel. (1999). Science teachers’ views and practices in planning for teaching. Journal of Research in Science Teaching, 36(4), 493 – 513.

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

Subanji. (2015). Teori Kesalahan Konstruksi Konsep dan Pemecahan Masalah Matematika. Malang: Universitas Negeri Malang.

Suryadi, D. (2013). Didactical Design Research (DDR) dalam pengembangan pembelajaran matematika. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. Bandung: STKIP Siliwangi.

Sztajn, P., Confrey, J., Holt Wilson, P., dan Edgington, C. (2012). Learning trajectory based instruction: toward a theory of teaching. Educational Researcher, 41(5), 147–156.

Pöhler,B., dan Prediger, S. (2014). Intertwining lexical and conceptual learning trajectories – A design research study on dual macro - scaffolding towards percentages. Eurasia Journal of Mathematics, Science dan Technology Education, 11(6), 1697-1722.

Perrin-Glorian, M.J. (2008). From producing optimal teaching to analysing usual classroom situations development of a fundamental concept in the theory of didactic situations: the notion of milieu. [Online]. Retrieved from: https://www.unige.ch/math/EnsMath/Rome2008/WG5/Papers/PERRIN.pdf

Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555–570. http://dx.doi.org/10.1080/09515080802285552.

Wisdom, N. J. (2014). Meta-didactical slippages: a qualitative case study of didactical situations in a ninth grade mathematics classroom. Disertasi. Departement of Middle-Secondary Education and Instructional Technology Georgia State University.




DOI: https://doi.org/10.31980/mosharafa.v6i1.290

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