Keywords:-
Article Content:-
Abstract
Mathematical literacy skills of Indonesian students are still below the OECD average (PISA 2022) , where students face difficulties relating their mathematical knowledge to real-life contexts. This indicates that learning is still dominated by a mechanistic approach. This research aims to design worked examples in mathematical literacy skills for solving contextual problems in the Pythagorean Theorem material. The research method used is design and development research with the ADDIE model (Analyze, Design, Development). The problem design was developed based on the three main processes of OECD mathematical literacy: formulating, employing, and interpreting. The results yielded a problem design that provides systematic and contextual solution steps , while minimizing cognitive load by avoiding split-attention and redundancy effects. This worked example strategy is recommended for novice learners because it serves as scaffolding that guides students to understand the reasoning process and application of concepts systematically in real-world situations
References:-
References
Anggraeni, N. D., Alviana, W. K. D., Wahyuni, D. F., Ainurrosyidah, L. D. K., Mahardika, I. K., Sutarto, Wicaksono, I. (2024). Analisis Perkembangan Peserta Didik Menurut Teori Jean Piaget dan Pengimplementasianya pada Pembelajaran IPA SMP. Edusaintek: Jurnal Pendidikan, Sains dan Teknologi, 11(3), 1503 – 1519.
https://doi.org/10.47668/edusaintek.v11i3.1252
Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from Examples: Instructional Principles from the Worked Examples Research. In Review of Educational Research Summer2000 (Vol. 70, Issue 2).
https://doi.org/10.3102/00346543070002181
Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783.
https://doi.org/10.1037/0022-0663.95.4.774
Ayres, P., & Cierniak, G. (2012). Split-Attention Effect, In Encyclopedia of the Sciences of Learning (pp. 3172- 3175).
Ayres, P. (2011). Worked Example Effect. In Encyclopedia of the Science of Learning. Springer
Ayres, P., & Sweller, J. (2013). Worked examples. In J. Hattie & E. Anderman (Eds.), The International Handbook of Student Achievement (p. 408). UK: Routledge.
Azizah, N., & Retnowati, E. (2017). Desain Worked Example untuk Mengajarkan Matematika pada Siswa Disabilitas Netra. Seminar Matematika Dan Pendidikan Matematika Uny, 517–524.
CESE. (2018). Cognitive load theory in practice: Examples for the classroom. Australia: Centre for Education Statistics and Evaluation.
Chen, O. Retnowati, E., Chan, B. B. K. Y., & Kalyuga, S. (2023). The Effect of Worked Examples on Learning Solution Steps and Knowledge Transfer, Educational Psychology, 43 (8), 914–928.
https://doi.org/10.1080/01443410.2023.2273762
Cooper, G. (1990). Cognitive load theory as an aid for instructional design. Australasian Journal of Educational Technology, 6(2).
https://doi.org/10.14742/ajet.2322
Hartmann, C., van Gog, T., & Rummel, N. (2021). Preparatory effects of problem solving versus studying examples prior to instruction. Instructional Science: An International Journal of the Learning Sciences, 49(1).
https://doi.org/10.1007/s11251-020-09528-Z
Irwansyah, M. F., & Retnowati, E. (2019). Efektivitas worked example dengan strategi pengelompokan siswa ditinjau dari kemampuan pemecahan masalah dan cognitive load. Jurnal Riset Pendidikan Matematika, 6(1), 62-74.https://doi.org/10.21831/jrpm.v6i1.21452
Julianingsih, E., Retnowati, E., & Ng, K. T. (2023). A Worked Example Design with ARCS Motivational Model. Learning Science and Mathematics, 0832(18), 32-45.http://www.recsam.edu.my/sub_lsmjournal
Manson, E., & Ayres, P. (2021). Investigating how errors should be flagged and worked examples structured when providing feedback to novice learners of mathematics. Educational Psychology, 41(2), 153–171.https://doi.org/10.1080/01443410.2019.1650895
Marinda, L. (2020). Teori Perkembangan Kognitif Jean Piaget dan Problematikanya pada Anak Usia Sekolah Dasar. An-Nisa’: Jurnal Kajian Perempuan & Keislaman, 13(1), 116-152.
https://doi.org/10.35719/annisa.v13i1.26
Matty, A. N. (2016). A study on how inquiry based instruction impacts student achievement in mathematics at the high school level. ProQuest Dissertations Publishing.
https://www.proquest.com/openview/da895b80797c90f9382f0c9a948f7f68/1?pqorigsite=gscholar&cbl=18750
McLaren, B. M., Van Gog, T., Ganoe, C., Karabinos, M., & Yaron, D. (2016). The efficiency of worked examples compared to erroneous examples, tutored problem solving, and problem solving in computer-based learning environments. Computers in Human Behavior, 55, 87-99
https://doi.org/10.1016/j.chb.2015.08.038
Nurmayunita, Soeprianto, H., Junaidi, & Patmi, S. (2024). Analisis kesulitan siswa dalam menyelesaikan soal cerita pada materi teorema Pythagoras. Griya Journal of Mathematics Education and Application, 4(1), 75–81.
https://doi.org/10.29303/griya.v4i1.432
OECD. (2023). PISA 2022 Asessment and analytical. OECD.
https://doi.org/10.1787/dfe0bf9c-en
Parvaneh, H., & Duncan, G. J. (2021). The role of robotics in the development of creativity, critical thinking and algorithmic thinking. Australian Primary Mathematics Classroom, 26(3), 9–13.
https://eric.ed.gov/?id=EJ1365642
Plass, J. L., Moreno, R., Br¨unken, R. (2010). Cognitive Load Theory. New York: Cambridge University Press.
Rabaza, M., & Hamilton, J. (2022), the Effect of the Euclidean Geometry Short Learning Programme Using the Worked-Out Examples Teaching Approach on Mathematics Teachers Performance, JOHME: Journal of Holistic Mathematics Education, 6(1),
https://doi.org/10.19166/johme.v6i1.5264
Rafiepour, A., & Faramarzpour, N. (2023). Investigation of the mathematical connection’s ability of 9th grade students. Journal on Mathematics Education, 14(2), 339–352.
https://doi.org/10.22342/jme.v14i2.pp339-352
Renkl, A., & Atkinson, R. K. (2010). Learning from worked-out examples and problem solving. In Cognitive Load Theory (pp. 89–108). United States of America by Cambridge University Press. https://doi.org/10.1017/CBO9780511844744.007
Retnowati, E., Endah, Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(3), 349–367. https://doi.org/10.1080/01443411003659960
Retnowati, E., & Fadlila, N. (2023). The Compound Area of Quadrilaterals and Triangles: A Worked Example Based Learning Design. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(1), 150-159. https://doi.org/10.31764/jtam.v7i1.11678
Ritonga, E. D. S., & Hasibuan, L. R. (2022). Analisis Kesulitan Siswa dalam Pembelajaran Matematika Materi Teorema Pythagoras Ditinjau dari Minat Belajar Siswa di SMP Negeri 1 Rantau Utara. Jurnal Cendekia: Jurnal Pendidikan Matematika, 6(2), 1449–1460.
https://doi.org/10.31004/cendekia.v6i2.1341
Rodiawati, A., & Retnowati, E. (2019). How to Design Worked Examples for Learning Patterns in Mathematics. Journal of Physics: Conference Series, 1320(1).
https://doi.org/10.1088/1742-6596/1320/1/012045
Schworm, S., & Renkl, A. (2019), Learning by Solved Example Problems: Instructional Explanations Reduce Self-Explanation Activity. In Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society
https://doi.org/10.4324/9781315782379-175
Stacey, K., & Turner, r. (2015). Assessing Mathematical Literacy. Springer International Publishing. https://doi.org/10.1007/978-3-319-10121-7
Sweller, J, Ayres, P., & Kalyuga, S. (2011). Cognitive Load Theory. Springer.
Sweller, J. (2019). Cognitive load theory and educational technology. Educational Technology Research and Development, 68(1), 1–16.
https://doi.org/10.1007/s11423-019-09701-3
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive Architecture and Instructional Design: 20 Years Later. Educational Psychology Review, 31(2), 261–292.
https://doi.org/10.1007/s10648-019-09465-5
Van Garderen, D., Scheuermann, A., Sadler, K., Hopkins, S., & Hirt, S. M. (2021). Preparing pre-service teachers to use visual representations as strategy to solve mathematics problems: What did they learn?. Teacher Education and Special Education, 44(4), 319–339.
https://doi.org/10.1177/0888406421996070
Van Gog, T., Kester, L., & Paas, F. (2011). Effects of worked examples, example-problem, and problemexample pairs on novices’ learning. Contemporary Educational Psychology, 36(3), 212–218.
https://doi.org/10.1016/j.cedpsych.2010.10.004
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word Problems in Mathematics Education: A Survey. ZDM – Mathematics Education, 52(1), 1-23. https://doi.org/10.1007/s11858-020-01130-4
Wittwer, J., & Renkl, A. (2010). How Effective are Instructional Explanations in Example-Based Learning? A Meta-Analytic Review. Educational Psychology Review, 22(4), 393-409.
https://psycnet.apa.org/doi/10.1007/s10648-010-9136-5
Wijaya, A. (2016). Student’s information literacy: a perpective for mathematical literacy. Journal on Mathematics Education, 720, 73-82.
Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Wulandari, L., & Riajanto, M. L. E. J. (2020). Analisis Kesulitan Siswa SMP dalam Menyelesaikan Soal Materi Teorema Pythagoras. Jurnal Riset Pendidikan Dan Inovasi Pembelajaran Matematika, 3(2), 61–67.
https://doi.org/10.26740/jrpipm.v3n2.p61-67
Yeo, L, M., & Tzeng, Y. T. (2020). Cognitive Effect of Tracing Gesture in the Learning from Mathematics Worked Examples. International Journal of Science and Mathematics Education, 18(4), 733-751.