Learning trajectory berbasis proyek pada materi definisi himpunan

Widi Astuti, SMP Negeri 2 Pejawaran, Kabupaten Banjarnegara, Provinsi Jawa Tengah, Indonesia
Ariyadi Wijaya, Jurusan Pendidikan Matematika, Universitas Negeri Yogyakarta, Indonesia

Abstract


Tujuan penelitian ini adalah untuk mendeskripsikan learning trajectory ber­basis proyek yang dilalui siswa untuk memahami definisi himpunan. Penelitian desain ini menggunakan model Gravemeijer dan Cobb dengan tahapan yang terdiri atas: (1) preparing for the experiment yang mencakup penyusunan hypo­thetical learning trajectory (HLT); (2) design experiment yang mencakup pe­laksanaan pembelajaran berdasarkan HLT yang telah dirancang; dan (3) retro­spective analysis, yaitu membandingkan HLT dengan pembelajaran yang dilak­sanakan. Pengembangan HLT menjadi learning trajectory diperoleh melalui serangkaian aktivitas yang dilaksanakan dengan pengumpulan data melalui dokumentasi, observasi, dan wawancara dengan guru dan siswa untuk meng­klarifikasi dan mengonfirmasi alur belajar. Hasil penelitian mengindikasikan bahwa pembelajaran berbasis proyek dapat memfasilitasi siswa dalam mema­hami definisi himpunan. Learning trajectory definisi himpu­nan berbasis proyek diperoleh melalui serangkaian aktivitas dengan empat level pemodelan. Level situasional berupa aktivitas survei kumpulan objek di sekolah. Pada level refe­rensial, istilah “ciri-ciri yang sama”, “dapat didefinisikan”, dan “objek tambah­an”, dan “kesepakatan” muncul melalui diskusi. Pada level generalisasi, siswa me­nuliskan himpunan dalam bentuk yang lebih umum. Ter­akhir, pada level for­mal, pemahaman yang siswa peroleh dari setiap aktivitas merupakan modal un­tuk membangun konsep tentang definisi himpunan.


Project-based learning trajectory on the definition of the set topic

Abstract

This research aimed to describe the project-based learning trajectory pass­ed through by students to understand the set definition. This design research used Gravemeijer and Cobb model with stages: (1) preparing for the experiment that includes developing hypothetical learning trajectory (HLT); (2) design of expe­riments which includes learning practices implementation based on the deve­loped HLT; and (3) retrospective analysis, which was to compare HLT with learning practices. The development of HLT into a learning trajectory was ob­tained through a series of activities carried out by collecting data through docu­mentation, observation, and interviews with the teacher and students to clarify and confirm the learning trajectory. The results indicated that project-based learning could facilitate students to understand the definition of set. The lear­ning trajectory was obtained through a series of acti­vities with four levels of modeling. The situational level was in the form of a survey activity aimed to collect objects in the school area. At the referential level, the terms “common features”, “definable”, “additional objects”, and “agree­ment” emerged thro­ugh discussion. At the generalization level, students wrote the set in a more general form. Lastly, at the formal level, the under­standing that students get from each activity was a provision to construct a concept about set definition.


Keywords


lintasan belajar; definisi himpunan; pembelajaran berbasis proyek; penelitian desain; learning trajectory; hypothetical learning trajectory; definition of set; design research

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References


Aisah, L. S. (2019). Learning trajectory konsep volume prisma pada pembelajaran Matematika SMP. Prosiding Seminar Nasional Pendidikan Matematika, 1(1), 223–234. http://www.fkip-unswagati.ac.id/ejournal/index.php/snpm/article/view/814

Azizah, I. N., & Widjajanti, D. B. (2019). Keefektifan pembelajaran berbasis proyek ditinjau dari prestasi belajar, kemampuan berpikir kritis, dan kepercayaan diri siswa. Jurnal Riset Pendidikan Matematika, 6(2), 233–243. https://doi.org/10.21831/jrpm.v6i2.15927

Barnett, R. A., Ziegler, M. R., & Byleen, K. E. (2008). Finite mathematics for business, economics, life sciences, and social sciences. Pearson.

Billstein, R., Libeskind, S., & Lott, J. W. (1990). A problem solving approach to mathematics for elementary school teachers (4th ed.). Benjamin/Cummings.

Chang, C. S., Wong, W. T., & Chang, C. Y. (2011). Integration of project-based learning strategy with mobile learning: Case study of mangrove wetland ecology exploration project. Tamkang Journal of Science and Engineering, 14(3), 265–273. https://doi.org/10.6180/jase.2011.14.3.10

Clement, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1

Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. CD-ß Press/Freudenthal Institute.

Gravemeijer, K. P. E., & Cobb, P. (2006). Design research from a learning design perspective. In J. Van den Akker, K. P. E. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17–51). Routledge.

Holmes, V. L., & Hwang, Y. (2016). Exploring the effects of project-based learning in secondary mathematics education. The Journal of Educational Research, 109(5), 449–463. https://doi.org/10.1080/00220671.2014.979911

Kemendikbud. (2014). Peraturan menteri pendidikan dan kebudayaan Republik Indonesia nomor 58 tahun 2014 tentang kurikulum 2013 sekolah menengah pertama/madrasah tsanawiyah. https://jdih.kemdikbud.go.id/arsip/Permendikbud%20Nomor%2058%20Tahun%202014-digabungkan.pdf

Manurung, M. M., Windria, H., & Arifin, S. (2018). Desain pembelajaran materi himpunan dengan pendekatan realistic mathematics education (RME) untuk kelas VII. Jurnal Derivat: Jurnal Mate¬matika dan Pendidikan Matematika, 5(1), 19–29. https://doi.org/10.31316/j.derivat.v5i1.143

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Author.

Nursyahidah, F., Saputro, B. A., Albab, I. U., & Aisyah, F. (2020). Pengembangan learning trajectory-based instruction materi kerucut menggunakan konteks megono gunungan. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 47–58. https://doi.org/10.31980/mosharafa.v9i1.560

Puspendik. (n.d.). Laporan hasil ujian nasional: Penguasaan materi ujian nasional. Kementerian Pendi¬dikan dan Kebudayaan. https://hasilun.puspendik.kemdikbud.go.id/

Risdiyanti, I., Prahmana, R. C. I., & Shahrill, M. (2019). The learning trajectory of social arithmetic using an Indonesian traditional game. Elementary Education Online, 18(4), 2094–2108. http://ilkogretim-online.org.tr/index.php/io/article/view/3026

Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91-104. https://doi.org/10.1207/s15327833mtl0602_2

Suryadi, D. (2011). Didactical design research (DDR) dalam pengembangan pembelajaran matematika. Joint conference UPI-UiTM: Strengthening research collaboration on education (pp. 1–12). http://a-research.upi.edu/operator/upload/pros_ui-uitm_2011_didi_didactical_design_research.pdf

Tamim, S. R., & Grant, M. M. (2013). Definitions and uses: Case study of teachers implenting project-based learning. Interdiciplinary Journal of Problem Based Learning, 7(2), 72–101. https://doi.org/10.7771/1541-5015.1323

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Pearson.

Wibowo, A. (2017). Pengaruh pendekatan pembelajaran matematika realistik dan saintifik terhadap prestasi belajar, kemampuan penalaran matematis dan minat belajar. Jurnal Riset Pendidikan Matematika, 4(1), 1–10. https://doi.org/10.21831/jrpm.v4i1.10066

Wijaya, A. (2012). Pendidikan matematika realistik: Suatu alternatif pendekatan pembelajaran mate-matika. Graha Ilmu.

Wijaya, A., Elmaini, E., & Doorman, M. (2021). A learning trajectory for probability: A case of game-based learning. Journal on Mathematics Education, 12(1), 1–16. http://doi.org/10.22342/jme.11.1.10225.157-166

Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003

Yee, L. P., & Hoe, L. N. (2009). Teaching secondary school mathematics: A resource book (2nd ed.). McGraw-Hill Education.




DOI: https://doi.org/10.21831/jrpm.v7i2.16483

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