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All Journal Jurnal Pendidikan dan Pembelajaran Khatulistiwa (JPPK) Al-Jabar : Jurnal Pendidikan Matematika Jurnal Pendidikan Informatika dan Sains KALAMATIKA Jurnal Pendidikan Matematika Jurnal Pembelajaran Prospektif SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan JPMI (Jurnal Pendidikan Matematika Indonesia) EDUKATIF : JURNAL ILMU PENDIDIKAN Pena Kreatif : Jurnal Pendidikan GANDRUNG: Jurnal Pengabdian Kepada Masyarakat Jurnal AlphaEuclidEdu Mosharafa: Jurnal Pendidikan Matematika Jurnal Inovasi Pengabdian dan Pemberdayaan Masyarakat Jurnal Pengabdian Masyarakat Bangsa Cendikia Pendidikan Jurnal Armada Pendidikan Trigonometri: Jurnal Matematika dan Ilmu Pengetahuan Alam
Metia Novianti
Universitas Tanjungpura
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Exploring learning trajectories in trigonometric identity proof construction through didactic transposition Ade Mirza; Winarji, Agus; Metia Novianti; Ferah Ningtias; Muhammad Arjuna
Al-Jabar: Jurnal Pendidikan Matematika Vol 17 No 1 (2026): Al-Jabar : Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v17i1.30223

Abstract

Purpose: This study aims to analyze students’ learning trajectories in constructing proofs of trigonometric identities through the lens of didactic transposition. Method: This research employed a descriptive qualitative design involving undergraduate students enrolled in a mathematics education program who were taking a trigonometry course. Participants were selected purposively based on their active engagement in proof-related learning activities. Data were collected through classroom observations, analysis of students’ written proof documents, and in-depth interviews to capture students’ reasoning processes and conceptual interpretations. The collected data were analyzed through qualitative procedures consisting of data reduction, data display, and conclusion drawing to identify patterns in students’ learning trajectories during the proof construction process. Findings: The findings indicate that students’ learning trajectories in constructing trigonometric identity proofs develop through three interconnected phases. The first phase involves exploring the meaning of trigonometric ratios within geometric contexts. The second phase focuses on formalizing the relationships among trigonometric ratios and identities. The third phase involves constructing deductive arguments to establish the fundamental identity , reflecting a shift from empirical reasoning to formal mathematical proof. Significance: The didactic transposition process plays a crucial role in transforming students’ understanding from procedural manipulation toward deeper conceptual meaning. This process facilitates the emergence of structured learning trajectories that support reflective reasoning and higher-order mathematical thinking. The findings suggest that trigonometry instruction should emphasize conceptual learning trajectories grounded in didactic transposition to strengthen students’ proof construction abilities and promote meaningful mathematical understanding.
Analysis of Initial Ability and Visual Thinking Ability of Grade X High School Students in Trigonometry Competence Nur Khotibah; Ahmad Yani T; Agus Winarji; Mohammad Rif'at; Metia Novianti
JPMI (Jurnal Pendidikan Matematika Indonesia) Vol 11, No 2 (2026): Volume 11 Number 2, September 2026
Publisher : STKIP Singkawang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26737/jpmi.v11i2.8899

Abstract

This study investigated students’ prior knowledge, visual thinking ability, and the relationship between both aspects in learning trigonometry among tenth-grade students at SMAN 10 Pontianak. The study was motivated by the importance of prerequisite knowledge in supporting conceptual understanding and by the role of visual thinking in interpreting abstract trigonometric concepts. A qualitative approach with a case study design was employed. Six students from class X-A were selected purposively to represent high, moderate, and low levels of visual thinking ability. Data were collected through prior knowledge tests, visual thinking tests, and semi-structured interviews. Visual thinking was examined through four indicators: looking, seeing, imagining, and showing and telling. The data were analyzed using data reduction, data display, and conclusion drawing techniques. The findings revealed that students’ prior knowledge and visual thinking ability were categorized into high, moderate, and low levels. Students with strong prior knowledge were generally able to construct accurate visual representations and apply concepts systematically. In contrast, students with limited prior knowledge experienced difficulties, particularly in the imagining stage, because they struggled to connect prerequisite concepts with visual problem-solving processes. The study indicates that prior knowledge contributes to the quality of students’ visual representations and influences the consistency of concept application in solving trigonometry problems. Therefore, strengthening prerequisite concepts is necessary to support the development of visual thinking skills in mathematics learning.Analisis Kemampuan Awal dan Kemampuan Berpikir Visual Peserta Didik Kelas X SMA pada Kompetensi TrigonometriABSTRAKPenelitian ini bertujuan untuk menganalisis kemampuan awal, kemampuan berpikir visual, serta keterkaitan antara kemampuan awal dan kemampuan berpikir visual peserta didik kelas X SMAN 10 Pontianak pada materi trigonometri. Penelitian ini dilatarbelakangi oleh pentingnya kemampuan awal sebagai dasar pemahaman konsep serta peran kemampuan berpikir visual dalam membantu peserta didik merepresentasikan konsep trigonometri yang bersifat abstrak. Penelitian menggunakan pendekatan kualitatif dengan jenis studi kasus. Subjek penelitian terdiri dari enam peserta didik kelas X-A yang dipilih menggunakan teknik purposive sampling berdasarkan kategori kemampuan berpikir visual tinggi, sedang, dan rendah. Data diperoleh melalui tes kemampuan awal, tes kemampuan berpikir visual, dan wawancara semi terstruktur. Kemampuan berpikir visual dianalisis berdasarkan indikator looking, seeing, imagining, serta showing and telling. Data dianalisis melalui tahap reduksi data, penyajian data, dan penarikan kesimpulan. Temuan penelitian memperlihatkan adanya perbedaan tingkat penguasaan kemampuan awal dan kemampuan berpikir visual peserta didik yang dapat dikelompokkan ke dalam kategori tinggi, sedang, dan rendah. Peserta didik dengan kemampuan awal tinggi cenderung mampu membangun representasi visual secara tepat dan sistematis. Sebaliknya, peserta didik dengan kemampuan awal rendah mengalami kesulitan pada indikator imagining karena belum mampu menghubungkan konsep prasyarat dengan visualisasi penyelesaian masalah. Temuan penelitian menunjukkan bahwa kemampuan awal memengaruhi kualitas representasi visual dan konsistensi penggunaan konsep dalam penyelesaian soal trigonometri. Oleh karena itu, penguatan konsep prasyarat perlu dilakukan untuk mendukung kemampuan berpikir visual peserta didik dalam pembelajaran trigonometri.Kata Kunci :Kemampuan Awal; Kemampuan Berpikir Visual; Trigonometri
Penerapan model reciprocal teaching dengan pendekatan metakognitif untuk meningkatkan kemampuan literasi matematis mahasiswa Ahmad Yani T; Nadya Febriani Meldi; Agus Winarji; Metia Novianti; Mahmuda Sumarno
Jurnal Pendidikan Informatika dan Sains Vol. 13 No. 2 (2024): Jurnal Pendidikan Informatika dan Sains
Publisher : Universitas PGRI Pontianak

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31571/saintek.v13i2.7865

Abstract

Penelitian ini bertujuan untuk meningkatkan literasi matematis mahasiswa pada mata kuliah persamaan differensial biasa (PDB) melalui penerapan Reciprocal Teaching dengan pendekatan metakognitif. Reciprocal Teaching merupakan pembelajaran menggunakan empat strategi pemahaman yaitu: merangkum dari bahan ajar, mencermati dan membuat pertanyaan, mencatat istilah atau konsep-konsep yang dijelaskan dan membuat catatan masalah yang kurang logis atau membuat kesimpulan. Penelitian ini menggunakan mixed method, yaitu penggabungan metode kuantitatif dan kualitatif untuk mendapatkan pemahaman secara mendalam tentang kemampuan literasi matematis. Untuk desain penelitian ini ialah explanatory sequential, dengan mendahulukan fase kuantitatif kemudian dilanjuti dengan fase kualitatif. Desain yang digunakan pada fase kuantitatif yaitu Experimental Design Pre Test Post Test. Subjek penelitian adalah mahasiswa Program Studi Pendidikan Matematika PMIPA FKIP Untan semester genap tahun akademik 2023-2024. Instrumen penelitian menggunakan tes literasi matematis dan wawancara serta dokumentasi sehingga memperoleh data kemampuan literasi Mahasiswa yang kemudian data yang diperoleh diolah dengan uji t. Hasil dari uji T diperoleh sig .001 < .005 sehingga dapat ditarik kesimpulan bahwa penerapan Model Reciprocal Teaching dengan pendekatan metakognitif efektif untuk meningkatkan kemampuan literasi matematis mahasiswa. Hasil penelitian ini diperoleh bahwa terdapat perbedaan rata-rata dari kelas dengan metode konvensional dan kelas bermetodekan Reciprocal Teaching dengan pendekatan metakognitif yang berarti kemampuan literasi matematis mahasiswa terjadi peningkatan.
Deep Learning Workshop Based On Moral Messages In Mathematics Learning: Design, Implementation And Assessment For Junior High School Teachers In Sanggau District Edy Yusmin; Revi Lestari Pasaribu; Ade Mirza; Dona Fitriawan; Nadya Febriani Meldi; Metia Novianti; Agus Winarji; Bistari; Dede Suratman
GANDRUNG: Jurnal Pengabdian Kepada Masyarakat Vol. 7 No. 1 (2026): GANDRUNG: Jurnal Pengabdian Kepada Masyarakat
Publisher : Fakultas Olahraga dan Kesehatan, Universitas PGRI Banyuwangi

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Mathematics education plays a crucial role in shaping critical thinking skills and the character of 21st-century students. However, mathematics learning at the junior high school level, particularly in Sanggau Regency, still faces challenges in implementing methods that promote in-depth understanding and application. One relevant approach to address this issue is moral-based Deep Learning, which emphasizes not only cognitive aspects but also affective aspects and character values. This Community Service (PKM) activity was conducted by lecturers from the Mathematics Education Study Program, Faculty of Teacher Training and Education, Tanjungpura University, with the aim of improving the competence of junior high school teachers in designing, implementing, and evaluating Deep Learning-based mathematics learning. The activity methods included workshops, mentoring, and practical training in developing learning tools that integrate moral values. The results of the activity showed an increase in teachers' understanding of the Deep Learning concept and their ability to develop meaningful, contextual, and character-based learning designs. This activity is expected to contribute to improving the quality of mathematics learning in Sanggau Regency and encourage the emergence of a generation of students who are intellectually intelligent and strong in morality.
Exploring cognitive pathways of mathematics education students in solving contextual modular arithmetic problems Metia Novianti; Dede Suratman; Christy Oktavany Siambaton Munthe
KALAMATIKA Jurnal Pendidikan Matematika Vol 11 No 1 (2026): KALAMATIKA April 2026
Publisher : FKIP Universitas Muhammadiyah Prof. DR. HAMKA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22236/KALAMATIKA.vol11no1.2026pp178-196

Abstract

Understanding how university students grasp modular arithmetic in real-world contexts remains underexplored, particularly regarding their use of cognitive pathways in solving contextualized problems. This study aims to examine the cognitive pathways utilized by mathematics education students when solving context-based modular arithmetic problems. 32 undergraduate students in the early stage of a mathematics education program who had successfully completed course in Number Theory were asked to solve three real-world-based problems involving work cycle patterns, container multiples, and congruence systems. The tasks were designed to represent fundamental real-world structures of modular arithmetic and to explore how contextual representations influence students’ cognitive pathways. The analysis was conducted using a descriptive qualitative approach through Cognitive Task Analysis (CTA) to identify five key cognitive pathways: quantitative reasoning, linguistic processing, working memory, pattern recognition, and cognitive flexibility. The result show that the first three pathways were consistently used across all task, indicating stable patterns in numerical reasoning, language processing, and information management. In contrast, pattern recognition and flexibility varied depending on how the problems were presented. Contextual narratives encouraged more reflective and adaptive thinking, whereas symbolic forms tended to limit exploration and reduce conceptual engagement. These results highlight the importance of problem design in supporting diverse cognitive approaches. The study's practical implications include the development of assessments and learning strategies that foster flexible and meaningful thinking, especially when understanding abstract mathematical concepts. Future research is encouraged to explore the integration of digital technologies and multiple representations to enhance students' cognitive flexibility.
Co-Authors Ade Mirza Ade Mirza Agung Hartoyo Agus Winarji Agus Winarji Agus Winarji Ahmad Yani T Ahmad Yani T Alghozi, Hakiimul Hilmiy Alvina Yolanda Aprilia, Angela Florisa Aprilyani, Safitri Bistari Christy Oktavany Siambaton Munthe Dede Suratman Dewi Ismu Purwaningsih Dian Ahmad Dian Ahmad Dona Fitriawan Dwi Purwanto Edy Yusmin Edy Yusmin Febriani Meldi, Nadya Ferah Ningtias Heni Pujiastuti Holyness Nurdin Singadimedja Hosnia Khairul Bariyyah Lestari Pasaribu, Revi Lestari, Revi Mahmuda Sumarno Mahmuda Sumarno Meldi, Nadya Febriana Meldi, Nadya Febriani Mohammad Rif&#039;at Muhammad Arjuna Munaldus Munaldus Nadya Febriani Meldi Nizarrahmadi Nizarrahmadi Nur Khotibah Nurdiana, Riyanti Nurfadilah Siregar Pasaribu, Revi Lestari Pelia Rif’at, Mohamad Riyanti Nurdiana Rustam Rustam Rustam Rustam Rustam Siti Nur Asma Siti Nur Asmah Siti Nur Asmah Siti Nur Asmah Suriyana Suriyana Suriyana Suriyana Suriyana Winarji, Agus Yassin, Muhammad Yuli Andriani Yulis Jamiah Zubaidah R, Zubaidah