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Exploring Ethnomathematical Geometry in Indonesian Shadow Puppetry Gunungan: Philosophical and Educational Implications Miftakhul Djannah; Naufal Ishartono; Argenti Agung Hayuni; Atikah Mufidah; Suliadi Fidaus bin Sufahani; Mohamad Waluyo
Jurnal VARIDIKA Volume 36 No 1, June 2024
Publisher : Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/varidika.v36i1.5661

Abstract

This study delves into the philosophical dimensions of traditional architecture and the ethnomathematical geometry inherent in the mountains of shadow puppets, a significant aspect of Indonesia's cultural heritage. Utilizing a qualitative methodology with an ethnographic design, data were collected through observations and interviews with primary, secondary, and additional informants. The objective of this research is to uncover the mathematical concepts embedded in the mountains of shadow puppets, including geometry, algebra, arithmetic, and statistics, using an ethnographic approach that addresses four principal inquiries: "Where should I begin my investigation?", "How do I proceed with the search?", "How can I identify significant findings?", and "How do I interpret these findings?". The results indicate that among the four mathematical concepts investigated, only geometric concepts are present in the puppet mountains, as validated by a geometer. The geometric sub-concepts identified encompass (1) geometric transformations such as translation and reflection, (2) plane geometry including rhombuses, rectangles, triangles, and circles, and (3) congruence and symmetry. This research holds significant implications for enhancing students' mathematical education by incorporating geometric examples from local cultural contexts. Integrating ethnomathematics into school curricula can expand students' artistic horizons, boost their engagement in learning, and deepen their comprehension of mathematical concepts.
Pengembangan Alat Peraga Papan Transformasi Geometri (PATOGE) untuk Meningkatkan Pemahaman Konsep Siswa Kelas IX SMP Nawfa, Zulfatun; Waluyo, Mohamad
JOEAI (Journal of Education and Instruction) Vol. 7 No. 1 (2024): JOEAI (Journal of Education and Instruction)
Publisher : Institut Penelitian Matematika, Komputer, Keperawatan, Pendidikan dan Ekonomi (IPM2KPE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31539/joeai.v7i1.8798

Abstract

Transformasi geometri merupakan salah satu materi matematika yang penting untuk dipelajari di tingkat SMP. Namun, materi ini sering dianggap sulit oleh siswa karena abstrak dan kurang kongkret. Salah satu upaya untuk mengatasi kesulitan ini adalah dengan menggunakan alat peraga. Penelitian ini bertujuan untuk mengembangkan alat peraga papan transformasi geometri untuk meningkatkan pemahaman konsep siswa kelas IX SMP. Alat peraga ini terdiri dari dua bagian utama, yaitu papan dasar dan papan transformasi. Papan dasar terbuat dari tripleks, sedangkan papan transformasi terbuat dari seng yang dilapisi dengan stiker. Alat peraga ini dapat digunakan untuk memvisualisasikan berbagai macam transformasi geometri, seperti refleksi, rotasi, translasi, dan dilatasi. Penelitian ini menggunakan metode eksperimen. Sampel penelitian adalah 17 siswa kelas IX SMP. Hasil penelitian menunjukkan bahwa penggunaan alat peraga papan transformasi geometri dapat meningkatkan pemahaman konsep siswa kelas IX SMP. Hal ini dibuktikan dengan peningkatan nilai rata-rata hasil belajar siswa dari 57,65 menjadi 79,41. Kata Kunci : Transformasi Geometri, Alat Peraga, Papan, Pengembangan
Development of GeoGebra-Based PjBL Activities Containing Ethnomathematics in Spatial Geometry to Improve Mathematical Communication Fajrul Falah; Mohamad Waluyo
Proceeding International Conference on Mathematics and Learning Research 2025: Proceeding International Conference on Mathematics and Learning Research
Publisher : Universitas Muhammadiyah Surakarta

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Abstract

The low mathematical communication skills of junior high school students, particularly in presenting mathematical ideas and arguments in writing, form the background of this study. As a solution, a Project-Based Learning (PjBL) activity that integrates ethnomathematics content and is assisted by GeoGebra software was developed. This research is a development study (R&D) that adopted the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). The aim of this research is to develop ethnomathematics-based Project-Based Learning activities and teaching tools assisted by GeoGebra on the topic of three-dimensional flat-sided shapes (cubes, cuboids, prisms, and pyramids), as well as to test their validity. The ethnomathematics context used is the architecture of the Dieng Temple to study the concept of surface area. The resulting product was assessed by subject matter and media experts. The validation results show an average score of 0.8542, which falls into the highly valid category. Therefore, the developed learning product is declared valid and feasible for use to support mathematical communication.
Assessment of Mathematics Proof Construction: Preservice Mathematics Teacher Training and Upper Secondary School Students Mohamad Waluyo; S Sutama; Nining Setyaningsih
Proceeding International Conference on Mathematics and Learning Research 2025: Proceeding International Conference on Mathematics and Learning Research
Publisher : Universitas Muhammadiyah Surakarta

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Abstract

Constructing valid mathematical proofs is a fundamental yet persistent challenge for students. This study investigates the developmental trajectory of proof construction abilities among Indonesian students, spanning from upper secondary school (Grades 10-11) to undergraduate mathematics levels. Adopting a descriptive cross-sectional design, data were collected from 479 participants using open-ended proof construction tasks and a survey on proof perception. The results reveal a pervasive dominance of empirical proof schemes, where students rely on specific numerical examples rather than generalized logical arguments. Notably, formal proof construction was virtually non-existent at the secondary level, highlighting a significant pedagogical gap. While the frequency of formal proof attempts increased among university students, valid execution remained limited, indicating a disconnect between students' strategic knowledge and their normative understanding of "correct" proof. Furthermore, findings show a critical misalignment between perception and performance; students often recognized formal algebraic arguments as superior yet reverted to empirical methods in practice. The study concludes that the transition from inductive to deductive reasoning does not occur naturally and requires explicit instructional interventions to bridge the cognitive rupture between secondary calculation-based mathematics and tertiary formal reasoning.