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All Journal Jurnal Penelitian dan Pengembangan Pendidikan Publikasi Pendidikan Kreano, Jurnal Matematika Kreatif-Inovatif Jurnal S2 Pendidikan Matematika Journal of Mathematics and Mathematics Education Union: Jurnal Ilmiah Pendidikan Matematika Journal of Mathematics and Mathematics Education (JMME) Jurnal Pembelajaran Matematika KACANEGARA Jurnal Pengabdian pada Masyarakat Journal of Educational Research and Evaluation Surya Abdimas Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) Abdimas Galuh: Jurnal Pengabdian Kepada Masyarakat Mosharafa: Jurnal Pendidikan Matematika Journal of Educational Management and Instruction (JEMIn) International Journal on Education Insight Prosiding SNPBS (Seminar Nasional Pendidikan Biologi dan Saintek) Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya INCOME: Indonesian Journal of Community Service and Engagement Pedagogy Review Jurnal Pendidikan MIPA Mathematics Education Journal
Imam Sujadi
Sebelas Maret University
Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Economics, Econometrics & Finance Education Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Nursing Public Health Social Sciences Other

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Journal : Mathematics Education Journal

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Utilizing Length Models and Number Lines to Enhance Students’ Understanding of Fractions Putri, Amellia; Sujadi, Imam; Nursanti, Yuli Bangun
Mathematics Education Journal Vol. 20 No. 1 (2026): Mathematics Education Journal
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Fractions are abstract mathematical concepts that often challenge students due to their various representations. While fraction instruction in schools typically emphasizes area models, it is crucial to incorporate other models, such as length models and number lines. This study aims to 1) identify the learning obstacles students encounter in representing fractions with length and number line models, 2) develop didactic designs to address these learning obstacles, and 3) evaluate the effectiveness of the designs. Employing a qualitative approach grounded in the Didactical Design Research (DDR) framework, the study comprised three stages: prospective, metapedadidactic, and retrospective analysis. Data were collected through tests administered to 20 seventh-grade bilingual students, in-depth interviews with those experiencing difficulties, and an analysis of their learning resources. All the collected data on learning obstacles were then analyzed using the Miles & Huberman method, which involves the stages of data reduction, data display, and conclusion drawing. The findings indicate that students relied predominantly on area models due to limited instructional exposure, leading to learning obstacles when representing fractions using the length model and locating them on the number line. When asked to use the length model, students tended to revert to area representations, reflecting conceptual constraints. Based on these obstacles, a didactic design was developed in which the length model and number line were introduced sequentially and in an interconnected manner. The design proved effective, as no further learning obstacles were identified after its implementation. These findings suggest that systematically integrating both representations strengthens students’ conceptual understanding of fractions.
Co-Authors A.A. Ketut Agung Cahyawan W Abdul Aziz Agus Darmawan Agus Margono Aji Permana Putra Andriawan Nurcahyo, Andriawan Asip Cakra Buana, Asip Cakra Bambang Sugaiarto Budi Usodo BUDIYONO Budiyono Budiyono Burhan Mustaqim Dalud Daeka Dewi Retno Sari S Dian Fitri Argarini, Dian Fitri Diari Indriati Dona Dinda Pratiwi Dwi Retnowati Dwiani Listya Kartika, Dwiani Listya Elywati Elywati Endah Asmarawati, Endah Eva Tri Wahyuni Exacta, Annisa Prima Farida Nurhasanah Fauzi Mulyatna Fitri Andika Nurussafa’at, Fitri Andika Fransiskus Xaverius Agus Siswanto, Fransiskus Xaverius Frasetyana, Anita Diah Getut Pramesti Habib Ratu Perwira Negara Hadi Prayitno, Hadi Hartono Hartono Hasan S Negara Hendriyanto, Agus Hirtanto Hirtanto, Hirtanto Ikrar Pramudya, Ikrar Indra Kurniawan Ira Kurniawati Isnandar Slamet, Isnandar Janah, Rahmawati Fatkhul Juwita Rini Kharisma Ardhy W KOMARUDIN Laila Fitriana Laksono Trisnantoro Luthfiana Mirati, Luthfiana Mania Roswitha Mardiyana Mardiyana Mardodo Mardodo Muh. Zuhair Zahid Muhammad Zuhair Zahid, Muhammad Zuhair Muhtarom Ningsih, Maya Kristina Nugroho Arif Sudibyo Nuraini Muhassanah Nurmalitasari Nurmalitasari Nursanti, Yuli Bangun Nurul Amalia K W Nurul Hidayati Shaliha, Nurul Hidayati Pangadi Pangadi Priyogo, Adi Puspitasari, Norma Puteri, Hanifa Alifia Putri, Amellia Putri, Astiwi Comastika Rahmadiansyah, Fatkhunur Fariza Rahmawati Masruroh, Rahmawati Retno Sari Riki Andriatna Rima Aksen Cahdriyana Rina Agustina Riyadi Riyadi Rofiah, Faizatur Rubono Setiawan Salsabila, Unik Hanifah Selvi Marcellia Siswanto Siti Khoiriyah Siti Komsatun Siti Suprihatiningsih Soeyono Soeyono Sri Subanti Sukamto, Ika Sumiyarsi Sukowiyono Sukowiyono Sulaiman Sulaiman Tajuddin, Annas Tasyah Tika Karlina R Tri Atmojo Kusmayadi Tri Yuliana Triana Harmini Tunggu Biyarti Ulfa Masamah, Ulfa Vera Dewi Susanti Wahyu Nofiansyah, Wahyu Wahyuni, Fina Tri Warifdah, Yumna Widodo Widodo Wulandari, Arum Nur Zainnur Wijayaanto Zamroni Zamroni Zulfa, Faradina Nilam