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All Journal Jurnal VARIDIKA Jurnal Didaktik Matematika
Miftakhul Djannah
Universitas Muhammadiyah Surakarta
Education Languange, Linguistic, Communication & Media Mathematics Other

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Defragmentation of Students' Conceptual Understanding in Solving Non-Routine Mathematics Problems Miftakhul Djannah; Nining Setyaningsih; Muhammad Noor Kholid; Mark Angelo C Reotutar
Didaktik Matematika Vol 11, No 2 (2024): OCTOBER 2024
Publisher : Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jdm.v11i2.38383

Abstract

This study investigated the impact of concept fragmentation on students' understanding of mathematics and examines efforts to reduce it. Concept fragmentation hinders problem-solving abilities, often occurring when students struggle to create meaningful connections or new representations from existing ones. Limited interventions, such as cognitive conflict and scaffolding, are suggested to address this issue. This study employed a qualitative descriptive approach, focusing on two seventh-grade students in Sukoharjo, Indonesia, who exhibited concept fragmentation. Data collection involved tests, interviews, and observations, with analysis following qualitative methods. The findings indicate two main types of fragmentation: translational thinking fragmentation and meaningless connection fragmentation. These arise when students attempt to build new representations but make errors due to disconnected prior knowledge. Interventions revealed a pattern of developing schemas, where students knit together concepts to minimize problem-solving errors. Techniques such as rereading problems and substituting information into formulas improved concept comprehension. The study concludes that defragmentation aids students in connecting existing knowledge with new information, enhancing their problem-solving strategies. Future research should investigate other fragmentation types and effective interventions for reducing fragmentation in mathematics learning.
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.
Co-Authors Argenti Agung Hayuni Atikah Mufidah Mark Angelo C Reotutar Mohamad Waluyo Muhammad Noor Kholid Naufal Ishartono Nining Setyaningsih Suliadi Fidaus bin Sufahani