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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika Jurnal Pendidikan Matematika Jurnal Infinity Prosiding Universitas PGRI Palembang Jurnal Pendidikan Matematika RAFA Suska Journal of Mathematics Education AdMathEduSt: Jurnal Ilmiah Mahasiswa Pendidikan Matematika PYTHAGORAS: Jurnal Program Studi Pendidikan Matematika E-Dimas: Jurnal Pengabdian kepada Masyarakat Journal of Honai Math Indiktika : Jurnal Inovasi Pendidikan Matematika JEMST: Journal of Education in Mathematics, Science, and Technology Faktor Jurnal Ilmiah Kependidikan Lentera Sriwijaya : Jurnal Ilmiah Pendidikan Matematika Edumatica: Jurnal Pendidikan Matematika Abdi Cendekia: Jurnal Pengabdian Masyarakat JNPM (Jurnal Nasional Pendidikan Matematika) Jurnal Infinity Mathematics Education Journal
Retni Paradesa
Program Studi Pendidikan Matematika, Universitas Islam Negeri Raden Fatah Palembang
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The Ability to Prove of Real Analysis Problems: Investigation with APOS Conception Afgani, Muhammad Win; Paradesa, Retni; Fitrianti, Yuli
Edumatica : Jurnal Pendidikan Matematika Vol 16 No 2 (2026): Edumatica: Jurnal Pendidikan matematika (Agustus 2026)
Publisher : Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jambi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22437/edumatica.v16i2.52319

Abstract

Proving is an important ability for pre-service mathematics teachers. However, previous studies have rarely examined proving in Real Analysis using the APOS framework, which provides insight into students’ cognitive development in constructing mathematical proofs. Although Real Analysis plays an important role in developing proving abilities, students’ proving abilities from an APOS perspective remain unclear. Therefore, this study aims to analyze pre-service mathematics teachers’ proving abilities in Real Analysis based on the APOS framework. This qualitative study involved 59 university students. Data were collected through a test consisting of four proof problems representing different levels of reasoning in Real Analysis. The data were analyzed using content and thematic analysis guided by APOS indicators: action, process, object, and schema. The results indicate that students constructed proofs without deep reflection and had difficulty identifying appropriate proof methods. Some students used examples to justify general statements, indicating limited understanding of mathematical proof. Most students remained at the action conception, only a few reached the process conception, and none demonstrated the object or schema conception. These findings indicate that students mainly relied on procedural manipulation rather than conceptual understanding. Therefore, instruction should strengthen prerequisite abilities and provide opportunities to construct various Real Analysis proofs to facilitate students’ transition from action to higher APOS levels.
Co-Authors Agustiany Dumeva Putri, Agustiany Dumeva Ali Syahbana Angge Sapto Mubharokh Anggraini Putri Utami Arfin Efriani Budi Mulyono Ceria, R. Evenda Darmawijoyo Darmawijoyo Darmawijoyo, Darmawijoyo Dini Damayanti Dwi Nisa oktarisa Dyah Agustin Ely Susanti Fadiyah Syafigah Fitrianti, Yuli Fitrianti, Yuli Gusmelia Testiana Khan, Adnan Shahid Lestaria N, Yunika Maha Reihani Muhammad Win Afgani Nanda Nabila Al Jannah Nery, Rieno Septa Putri, Ade Yuni R. Evenda Ceria Ratu Ilma Indra Putri Ratu Ilma Indra Putri Siti Naziroh Sonia Juniarti Sujinal Arifin Suzana Paranita Syutaridho Syutaridho Syutaridho Syutaridho Utari, Septi Yunika Lestaria Ningsih Zuhdiyah Zuhdiyah Zulkardi Zulkardi Zulkardi Zulkardi Zulkardi Zulkardi Zulkardi