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All Journal Jurnal Pendidikan dan Pembelajaran Khatulistiwa (JPPK) KADIKMA JURNAL PENDIDIKAN DASAR PERKHASA JPMI (Jurnal Pendidikan Matematika Indonesia) KACANEGARA Jurnal Pengabdian pada Masyarakat VOX EDUKASI: Jurnal Ilmiah Ilmu Pendidikan JURNAL MATHEMATIC PAEDAGOGIC Jurnal Ilmiah Aquinas J-PiMat : Jurnal Pendidikan Matematika Jurnal Pengabdian Masyarakat Khatulistiwa Jurnal Pendidikan Dasar Perkhasa Jurnal PEKA (Pendidikan Matematika) JUTECH : Journal Education and Technology Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram Jurnal Riset Pendidikan Matematika Jakarta Riemann : Research of Mathematics and Mathematics Education
Olenggius Jiran Dores, Olenggius Jiran
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Arts Humanities Biochemistry, Genetics & Molecular Biology Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Physics Public Health Social Sciences Other

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Rasch-Based Diagnostic Instrument for Mathematical Abstraction in Linear Equations: Development and Initial Validation Beni Setiawan; Olenggius Jiran Dores
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.273

Abstract

Mathematical abstraction is a foundational cognitive competency for junior high school students, yet diagnostic instruments that map students’ positions along the Concrete–Representational–Abstract (CRA) continuum are still limited. This study developed and initially validated a Rasch-based diagnostic instrument for mathematical abstraction in single-variable linear equations. Participants were 222 Grade 8 students from seven junior secondary schools in Sintang Regency, West Kalimantan, Indonesia. The instrument consisted of 18 constructed-response items scored 0–3 and administered using an overlapping multi-booklet design; each student completed 9 items, with valid responses per item ranging from 56 to 166. Data were analyzed with the Partial Credit Model using the TAM package in R. Seventeen of 18 items met the acceptable fit criteria, while item A2 (Outfit MNSQ = 1.519) required further review. EAP Person Reliability was 0.755, WLE Reliability 0.674, and Item Separation Reliability 0.889, indicating adequate psychometric quality for classroom diagnosis. Unidimensionality was supported (MADaQ3 = 0.137). The Wright Map classified students into four diagnostic zones: Zone 1 pre-transition Concrete (14.41%), Zone 2 Concrete-to-Representational transition (53.60%), Zone 3 Representational-to-Abstract transition (26.58%), and Zone 4 established Abstract (5.41%). Local dependency appeared between R1 and R4 (Q3 = 1.000). Sensitivity analysis showed that removing R4 only slightly reduced EAP reliability (0.751) while lowering the maximum Q3 to 0.498. A lower-ability measurement gap was also found, with 11 students (4.95%) having WLE standard errors above 1.0. The instrument is an initial diagnostic prototype that requires refinement through R4 revision, additional easier Concrete items, and validation with a larger sample.
Co-Authors A.A. Ketut Agung Cahyawan W Ahmad Supendi Aming Aming Ana, Rupina Mila Maria Anastasia Helina Lina Andri Andri Andri Andri Anita Sri Rejeki Hutagaol Anita Sri Rejeki Hutagaol, Anita Sri Rejeki Bahasa Indonesia, Bahasa Indonesia Beni Setiawan BENI SETIAWAN Bistari Bustami, Yakobus Chris Robert Langgi Damianus Sopian Dwi Cahyadi Wibowo Dwi Cahyadi Wibowo Dwi Cahyadi Wibowo, Dwi Cahyadi Fatkhan Amirul Huda Fransiska Fransiska Frederykus Ege Hadidi, Hadidi Handayani, Ayu Fitri Markus Iyus Supiandi Melinda Rismawati Melinda Rismawati, Melinda Merayang, Martinus Viensius Nanda Dwi Natalia Nurapni Sopia Nurapni Sopia Oktavia Vorina Rupina Mila Maria Ana Rusita Riana Sirilus Sirhi, Sirilus Sopia, Nurapni Sopia, Nurapni Sopia Sugiatno . Surendra, Rosalia Vera Susi Susanti Tara, Santa Aktavia Ursula Dwi Oktaviani Yakobus Bustami Yasinta Lisa, M.Cs Yuliana Deta Zul Zagir Zul Zagir, Zul