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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika Journal of the Indonesian Mathematical Society AKSIOMA: Jurnal Program Studi Pendidikan Matematika JRPM (Jurnal Review Pembelajaran Matematika) JOHME: Journal of Holistic Mathematics Education JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Ilmiah Pendidikan Matematika Al Qalasadi Mosharafa: Jurnal Pendidikan Matematika PENA ABDIMAS : Jurnal Pengabdian Masyarakat
Rubono Setiawan
Department Of Mathematics Education, Universitas Sebelas Maret
Humanities Economics, Econometrics & Finance Education Mathematics Nursing Public Health Social Sciences Other

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Analisis Soal Latihan Transformasi Linier Dalam Buku Ajar Aljabar Linier Berdasarkan Teori Prakseologi Sujatmiko, Ponco; Aryuna, Dyah Ratri; Pramudya, Ikrar; Mardiyana, Mardiyana; Setiawan, Rubono
Jurnal Ilmiah Pendidikan Matematika Al Qalasadi Vol 9 No 2 (2025): JURNAL ILMIAH PENDIDIKAN MATEMATIKA AL QALASADI
Publisher : Prodi Pendidikan Matematika, Fakultas Tarbiyah dan Ilmu Keguruan IAIN Langsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32505/qalasadi.v9i2.12872

Abstract

Undergraduate students often struggle to shift froam procedural to conceptual understanding when learning linear transformation. They tend to focus on mechanical procedures while neglecting the underlying concepts. Textbooks play a crucial role in developing conceptual understanding through well-structured and meaningful exercises. Praxeological theory, which maps the relationship among mathematical tasks, techniques, supporting technologies, and underlying theories, provides a comprehensive framework for such analysis. This study aims to analyze linear transformation exercises in Elementary Linear Algebras (11th edition) by Howard Anton and Chris Rorres using a qualitative content analysis based on the praxeological framework. The findings reveal that most exercises have the potential to foster deep conceptual understanding, particularly when learning activities do not stop at the technical stage. Practically, the study offers insights for lecturers and textbook developers in designing exercises that balance procedural demands and conceptual reasoning, thereby enhancing meaningful learning of linear algebra in higher education.
Algebraic Thinking and Algebraic Reasoning in School Mathematics: A Systematic Literature Review Based on the Pirie–Kieren Theory Larasanti, Rida; Siswanto; Setiawan, Rubono
JRPM (Jurnal Review Pembelajaran Matematika) Vol. 11 No. 1 (2026)
Publisher : Department of Mathematics Education, Faculty of Tarbiyah and Teacher Training, UIN Sunan Ampel Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15642/jrpm.2026.11.1.15-36

Abstract

Algebraic thinking and algebraic reasoning are core competencies in mathematics education; however, students often exhibit procedural skills without adequate conceptual understanding. This study aims to synthesize empirical research on algebraic thinking and algebraic reasoning through the lens of the Pirie–Kieren theory of conceptual understanding. A Systematic Literature Review (SLR) was conducted using a structured and transparent protocol. Articles were collected from Google Scholar and Scopus databases using the keywords algebraic thinking and algebraic reasoning, covering publications from 2018 to 2026. From an initial pool of 400 articles, 32 empirical studies met the inclusion criteria and were analyzed using thematic coding. The findings show that algebraic thinking primarily develops in the early to intermediate layers of understanding, namely Primitive Knowing, Image Making, Image Having, and Property Noticing. In contrast, algebraic reasoning is more dominant in advanced layers, including Formalising, Observing, and Structuring. Students’ difficulties in algebra, such as errors in symbolization, limited generalization, and weak justification, reflect transitions between layers and frequently involve folding back processes. This study concludes that the Pirie–Kieren framework provides a coherent and dynamic perspective for integrating algebraic thinking and reasoning, with implications for designing algebra instruction that emphasizes conceptual growth and reflective learning.
Co-Authors Ario Wiraya Ayuningrum, Satya Mardi Budi Usodo Budiyastuti, Novita Ening Budiyono, Budiyono Budiyono, Budiyono Chrisnawati, Henny Ekana Dyah Ratri Aryuna Faizah, Farah Farida Nurhasanah Fauziah, Asma' Nurul Fitri Rahmawati Fitriana, Laila Getut Pramesti Handayani, Hesti Ikrar Pramudya, Ikrar Imam Sujadi Indriyani, Anita Jingga, Annisa Astra Kartika Maharani Dwi Astuti Kristanto, Matias Vico Anggoro Kurniawati, Cici Kuswardi, Yemi Laila Fitriana Landyasari Riffyanti Larasanti, Rida Mahardhikawati, Ema Mardiyana Mardiyana Maulia, Dityana Mila Meiliana, Cahyo Henny Mukti, Putri Sari Mulyani, Septiya Nasution, Nur Baiti Pramudya, Ikrar Pratama, Mahendra Dany Rokhim, Andrean Fajar Rosyada, Atina Setiawan, Muhammad Ridwan Setyorini, Intan Ayu Sigarini, Khofifah Aluh Siswanto Soeyono, Soeyono Sujatmiko, Ponco Sujatmiko, Ponco SYARIFAH ZAHRA Triyanto, Triyanto Valentina, Febriyani Warifdah, Yumna Yaumil Sitta Achir