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Didactic Obstacles in Trigonometric Ratios: Insights into Students’ Mathematical Understanding Silfia Hayuningrat; Didi Suryadi; Imam Rofiki
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.166

Abstract

This study examines the relationship between the knowledge prescribed in the school curriculum, the knowledge enacted by mathematics teachers, and the knowledge constructed by students in learning trigonometric ratios through the perspective of Didactic Transposition Theory. A qualitative intrinsic case study was conducted with one mathematics teacher and 22 tenth-grade students in an Indonesian senior high school. Data were collected from curriculum documents, teaching notes, classroom observations, interviews, and two tests designed to capture students’ conceptual understanding. The data were analyzed using document analysis, content analysis, and descriptive analysis. The findings show that although students’ understanding of trigonometric ratios improved during instruction, the enacted classroom practices mainly emphasized trigonometric ratios as fixed relationships among the sides of right triangles. Consequently, students tended to interpret sine, cosine, and tangent primarily as geometric ratios rather than as functions of angles. This emphasis limited students’ ability to connect geometric reasoning with functional interpretations of trigonometric relationships. These results highlight the importance of strengthening instructional coherence in curriculum implementation so that classroom teaching better supports the development of both geometric and functional understanding of trigonometry.
LEARNING OBSTACLES IN DESCRIPTIVE STATISTICS: CHALLENGES IN STATISTICAL THINKING FOR PROSPECTIVE MATHEMATICS TEACHERS Eliva Sukma Cipta; Didi Suryadi; Tatang Herman; Al Jupri
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol. 15 No. 2 (2026)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v15i2.14702

Abstract

Statistical thinking is an essential competency for prospective mathematics teachers, as it enables them to understand, organize, represent, analyze, and interpret data effectively. However, many students still experience difficulties in understanding and applying descriptive statistics concepts, which may hinder the development of their statistical thinking skills. Therefore, identifying learning obstacles is necessary as a basis for designing more effective learning experiences. This study aims to identify the learning obstacles encountered by prospective mathematics teachers in descriptive statistics courses. The study employed Didactical Design Research (DDR) using a qualitative methodology within an interpretive paradigm. The participants were 38 prospective mathematics teachers enrolled at a private university in Bandung, Indonesia. The research instruments consisted of a statistical thinking test, semi-structured interview guidelines, and document analysis. Data were collected through tests, interviews, and document analysis and were analyzed through the processes of identification, classification, reduction, and verification. Data trustworthiness was established through methodological and source triangulation. The findings revealed that students experienced difficulties across all indicators of statistical thinking, including describing, organizing, representing, analyzing, and interpreting data. These difficulties were reflected in misconceptions regarding the relationship between mean, median, mode, and distribution skewness, the application of measures of position, the interpretation of data variability, and the analysis of relative performance. The study identified ontogenic, epistemological, and didactical obstacles that hindered the development of students’ statistical thinking. These findings provide an empirical basis for developing a hypothetical learning trajectory to enhance statistical thinking in descriptive statistics courses.
Epistemological obstacles in combinatorics as praxeological gaps among pre-service mathematics teachers Marhami Marhami; Dadan Dasari; Didi Suryadi; Dadang Juandi
Jurnal Elemen Vol 12 No 3 (2026): July
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/jel.v12i3.35192

Abstract

Combinatorics is widely regarded as difficult, yet most studies stop at classifying student errors without explaining their internal structures. This study reframed epistemological obstacles in combinatorial counting principles as praxeological gaps. Drawing on Brousseau's notion of obstacle and Chevallard's four-component praxeology (task, technique, technology, theory), it asks not where a difficulty comes from but which part of a learner's knowledge has failed to develop. Within the prospective phase of Didactical Design Research, we collected written responses to two counting problems from 83 pre-service mathematics teachers who had completed a Discrete Mathematics course, interviewed 17 of them, and read their textbooks praxeologically. Triangulating these sources, we identified three recurring gaps: a technique whose justification had collapsed into a surface keyword rule ("and" means multiply, "or" means add); a technique fitted only to familiar problems; and a technique applied with no justification at all. Across all, the practical block was secure while the theoretical block remained thin, an asymmetry mirrored in the textbook, which defined the rules through keywords rather than independence and disjointness. Reading obstacles this way turns a general diagnosis into a specific one, giving teacher educators a tool for designing instruction that targets the precise failed component of reading.
Learning Obstacles in Understanding the Pythagorean Theorem among Ninth-Grade Students Yuce Sandra; Didi Suryadi; Dadan Dasari
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.v8i2.183

Abstract

The Pythagorean Theorem is a fundamental concept in geometry and serves as a foundation for various mathematical topics. Despite its fundamental importance in mathematics, students still have difficulty understanding and applying this theorem correctly, indicating limited conceptual understanding. This study aimed to examine the learning obstacles encountered by ninth-grade students. This qualitative descriptive study involved 32 ninth-grade students in a junior high school in Bandung. Subjects covered in this research are considered with students who have studied the Pythagorean Theorem. Data collection using tests with eight questions, interviews with questions that make clear of the answers given by students on tests, and documentation. The result found that students had obstacles in learning the Pythagorean Theorem with three main points, namely: inadequate understanding of prerequisite material; limited conceptual understanding of the Pythagorean Theorem; and difficulty in solving contextual problems. These obstacles were further classified into ontological, epistemological, and didactical obstacles based on Brousseau’s framework. This study contributes to mathematics education by showing that learning obstacles remain evident even after students have completed formal instruction on the Pythagorean Theorem. By identifying the underlying conceptual and contextual characteristics of these obstacles, the study extends current understanding of students’ post-instruction learning obstacles and offers empirical evidence to inform future instructional planning and related research
Validity of Flip PDF Based E-Modules as Learning Media on Cube and Cuboid Materials Lucky Heriyanti Jufri; Didi Suryadi; Kusnandi Kusnandi; Turmudi Turmudi
Mosharafa: Jurnal Pendidikan Matematika Vol. 13 No. 4 (2024): October
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/mosharafa.v13i4.965

Abstract

Abstrak Penelitian ini bertujuan untuk mengetahui validitas e-modul Berbasis Flip PDF sebagai Media Pembelajaran Untuk Melatih Kemampuan Literasi Matematis Siswa Pada Materi Kubus dan Balok dilihat dari validitas sistem operasi, validitas isi, validitas bahasa dan desain. Penelitian ini menggunakan jenis penelitian Research and Development (R&D) yang mengacu pada model pengembangan Plomp yang terdiri atas 3 (tiga) tahapan, yaitu tahap preliminary research (fase investigasi awal), tahap prototyping phase (pembuatan dan pengembangan prototipe) dan tahap assesment phase (fase penilaian). Namun artikel ini hanya membahas sampai tahapan prototyping phase. Instrumen yang digunakan adalah lembar validasi, angket dan wawancara. Berdasarkan hasil validasi menunjukkan bahwa E-modul Interaktif yang dikembangkan memperoleh persentase rata-rata 87,5% untuk validitas sistem operasi termasuk kategori sangat valid, 80% untuk validitas isi termasuk kategori sangat valid, 90% untuk validitas bahasa termasuk kategori sangat valid dan 85,9 % untuk validitas desain termasuk kategori sangat valid untuk digunakan sebagai media pembelajaran untuk melatih kemampuan literasi matematis siswa. Abstract This research aims to determine the validity of the Flip PDF-based e-module as a learning medium for training students' mathematical literacy skills in cube and block material in terms of operating system validity, content validity, language validity and design. This research uses the Research and Development (R&D) type of research which refers to the Plomp development model which consists of 3 (three) stages, namely the preliminary research stage (initial investigation phase), the prototyping phase (prototype creation and development) and the assessment phase (assessment phase). However, this article only discusses the prototyping phase. The instruments used were validation sheets, questionnaires and interviews. Based on the validation results, it shows that the Interactive E-module developed obtained an average percentage of 87.5% for operating system validity including the very valid category, 80% for content validity including the very valid category, 90% for language validity including the very valid category and 85 .9% for design validity is in the very valid category for use as a learning medium to train students' mathematical literacy skills.
Limit of Function Understanding by Student of National Mathematics Olimpiad ON MIPA in University Wilda Syam Tonra; Didi Suryadi; Kusnadi; Endah Cahya Mulyaning
SAINSMAT: Jurnal Ilmiah Ilmu Pengetahuan Alam Vol. 13 No. 2 (2024): Volume 13 Nomor 2 (September 2024)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar

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

Abstract

Limits of function is one of sub-topic of Calculus that is complex and difficult to understand. Several studies, both examining misconception and understanding related to function limits, aim to improve teaching and learning. This research is single Subject Research with a single subject, namely by Student of National Mathematics Olimpiad ON MIPA in University. Data was collected through a test instrument consisting of 7 questions on understanding function limits and interviews were conducted to confirm the subject's answers. Data analysis is qualitative. The research results show that 1) Subject can determine the limit value of the function. However, the subject still has a partial understanding. 2) Subject does not understand the meaning of function limits. The subject believes that if there are 2 functions with the same function limit value, then both functions will be the same. 3) Subject can determine the value of the left limit and the right limit from the graph of the given function. 4) Subject cannot formally prove (epsilon-delta) the limit value of the function, the subject does not yet understand what information is given, what information will be sought. The subject is also not able to determine the delta limit in proof problems that have factors 5) Subject can determine the limit value at infinity 6) Subject can determine the value of infinite limit 7) Subject can investigate whether a function is continuous or not continuous. The conclusion of the research is that from 7 understandings of function limits, the subject has 4 perfect understandings regarding left and right limits, limits at infinity and infinity and function continuity. However, the subject was not yet able to prove the limit (epsilon-delta).
Exploring the Thinking Experiences of Preservice Mathematics Teachers in Learning Geometric Transformation Proofs Talisadika Serrisanti Maifa; Didi Suryadi; Siti Fatimah; Suhendra
RANGE: Jurnal Pendidikan Matematika Vol. 7 No. 1 (2025): Range Juli 2025
Publisher : Pendidikan Matematika UNIMOR

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/jpm.v7i1.9662

Abstract

This study aimed to explore the thinking experiences of preservice mathematics teachers in learning geometric transformation proofs, focusing on four categories of thinking: personalization, contextualization, depersonalization, and decontextualization. Employing a qualitative approach with a phenomenological design, the study involved 24 preservice mathematics teachers in a mathematics education program who had completed a course on Geometric Transformations. Data were collected through written test tasks and in-depth interviews and analyzed thematically. The data analysis followed a four-stage phenomenological procedure: bracketing, to suspend researcher assumptions; intuiting, to immerse in participants’ experiences; thematizing, to identify recurring patterns; and describing, to construct a comprehensive understanding of the phenomenon. The findings identified seven key themes that reflect the thinking experiences of preservice mathematics teachers. Through an in-depth analysis of these themes, it was revealed that the participants’ reasoning predominantly remained at the stages of personalization and contextualization. Depersonalized and decontextualized thinking was not identified, suggesting that the transition toward formal and abstract mathematical reasoning had not yet occurred. The findings suggest possible cognitive obstacles experienced by preservice teachers in transitioning toward formal reasoning, based on interview responses. However, the exploration of these challenges was limited to data gathered through interviews. Future studies are recommended to conduct deeper investigations through classroom observations and analysis of instructional materials to better understand how these thinking difficulties emerge.
Kemampuan Pemecahan Masalah Matematis: Sebuah Tinjauan Literatur Sistematis Siti Zakiyah; Dadang Juandi; Didi Suryadi
Jambura Journal of Mathematics Education Vol 7, No 1: Maret 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jmathedu.v7i1.23960

Abstract

Mathematical problem-solving ability is a core 21st-century competency that constitutes a major focus of mathematics learning. Research on this topic has grown rapidly but remains scattered across diverse contexts, necessitating a systematic synthesis. This study aims to map publication trends, the distribution of countries, the educational levels of research subjects, and the learning approaches employed. The method used is a Systematic Literature Review (SLR) following the PRISMA 2020 guidelines applied to Scopus-indexed articles published between 2016 and 2026. From the 144 articles identified, 35 articles that positioned problem-solving as the main variable were obtained. The results indicate an increasing publication trend, peaking in 2024, a predominant contribution from Indonesia, a coverage of educational levels ranging from early childhood education to higher education with the largest concentration at the higher education and primary school levels as well as a diversity of approaches such as PBL, RME, STEM/STEAM, ethnomathematics, and technology integration. These findings can serve as a reference for the development of problem-solving-oriented mathematics learning and for further research.
Examining Mathematics Learning Problems in Elementary Schools Using Nvivo 12 Software Aplication: A Case Study in Metro Nia Fatmawati; Tatang Herman; Didi Suryadi; Cepi Riyana; Kisno Kisno
EduBase : Journal of Basic Education Vol. 7 No. 2 (2026): EduBase : Journal of Basic Education
Publisher : LJPI UI Bunga Bangsa Cirebon

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47453/edubase.v7i2.3764

Abstract

Objective: This study aims to examine and systematically map mathematics learning problems in elementary schools from students’ perspectives using NVivo 12. Novelty: The study contributes an integrated, student-perspective mapping of mathematics learning problems by analyzing four dimensions simultaneously through qualitative data processing using NVivo 12. Methods: A qualitative case study was conducted with 74 fourth-grade elementary school students in Metro City, Lampung, Indonesia. Data were collected through an open-ended questionnaire and analyzed using coding and categorization in NVivo 12 across four dimensions: cognitive, affective, psychomotor, and learning-environment factors. Results: The findings show that cognitive problems were the most prominent (87% negative responses), followed by affective problems (71%), psychomotor problems (42%), and learning-environment problems (9%). Cognitive difficulties mainly involved understanding mathematical concepts, completing mathematical tasks, and developing thinking skills, while affective difficulties included low interest, lack of self-confidence, and negative perceptions of mathematics. Conclusion: The findings provide a diagnostic basis for teachers to identify students’ difficulties and design more responsive and comprehensive mathematics learning strategies.
The Misconceptions of Students on Equations based on Their Arithmetic Knowledge Ardiansari, Lia; Suryadi, Didi; Dasari, Dadan
Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan Vol. 8, No. 6
Publisher : citeus

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

Abstract

Many students have an operational view of the equals sign. This conception is seen as a misconceptions. This study aims to investigate the extent to which students have misconceptions about equality, where the equal sign is the focus. This research is a descriptive qualitative research with a case study approach. A total of 35 students in the city of Bandung became participants in this study. The results of the study reported that there were several misconceptions such as closing, using all numbers in the equation, string operations, and “pindah ruas”.
Co-Authors Aan Hasanah Abdul Fatah Abdul Mujib Abidin, Muhamad Zainal Addilah, Aulia Ade Sunawan Adillah, Aulia adisti, yulia Aditya Prihandhika Adnan, Mazlini Ady Akbar Agung Wicaksono Agustia, Devi AHMAD LUTFI Ahmad Mukhibin, Ahmad Ahwan, M. Tami Rosadi Aiyub Aiyub Akbar, Ady Akhmad Ridlo Al Jupri Amelia, Tia Amrita Kaur Andi Auliya Ramadhany Andi Hidayatul Fadlilah Andika Putra R Anggraini, Yulia Annisa Fitri Aqidatul Izzah Ardo, Okilanda Asmara, Putri Meilia Asri, Rian Puji Ayunda Sri Wahyuningrum Bernadeta Suhartini Brata, Syahrizal Kurniawan Cecep Anwar Hadi Firdos Santosa Cecep Anwar Santosa Cepi Riyana Cipta, Eliva Sukma Cris Kuntadi d, delrefi Dadan Dasari Dadang Juandi Darhim Darhim Devi Rahayu Dian Usdiyana Diding Ruchaedi, Diding Dwi Endah Lestari Dwi Fitriani Rosali Dwi Warli E. Elvis Napitupulu E. Elvis Napitupulu, E. Elvis Edi Supriyadi Edya Kresna Annizar, Edya Kresna Eka Supriatna Eka Swasta Budayati Eko Risdianto Eko Saputra Elah Nurlaelah Elah Nurlaelah Eli Nugraha, Eli Elsa Komala Elsa Komala, Elsa Endah Cahya Mulyaning Endang Cahya Mulyaning Endang Cahya Mulyaning A. Entit puspita Erika Yohanna Seventina Siahaan Eva Musyrifah, Eva Farah Salsabila Fardian, Dilham Fasya, Robby Ismail Fathiyah, Ifa Fatimah, Neneng Fatimah, Siti Fauziah, Ella Febrilia, Baiq Rika Ayu Firda, Nadiatun Firsta Yosika, Ghana Fitri April Yanti, Fitri April Fitriana Eka Chandra Fuadiah, Nyiayu Fahriza Galih Anggriawan Gulvara, M Akbar Gumpita, Melly Terry Haïdara, Youssouf Haidara, Youssouf Hantari, Dimar Hardian Ningsih, Hardian Hardinata, Riyan Harsela, Febey Haruna, Nana Harlina Hayuningrat, Silfia Hendriyanto, Agus Hengki Kumbara Heni Pujiastuti Hernani Kilkoda Hidayati, Febry Nur Husnul Khatimah Rusyid Hutkemri Zulnaidi I Made Suarsana I Made Suarsana Idiatul Fitri Danasari Ika Meika Imam Rofiki Inayah, Sarah Indah Puspita Sari Indah Puspita Sari, Indah Puspita Indrawati Indrawati Indriyani, Mona Irfan Fauzi Irfan Fauzi Irfan Fauzi Islamiyah, Wafa Isnarto Isnawan, Muhamad Galang Istikomah, Endang Itoh, Takashi Ivanov, Danail Jamhari Jamhari Jarnawi Afgani Dahlan Jaya Dwi Putra, Jaya Dwi Jihe Chen Joni Joni Jozua Sabandar Jozua Sabandar Juita, Krisna Jusniani, Nia Khoerunisa, Adlina Kisno Kisno Komang Sujendra Diputra KOMARIAH, NURUL Krida Singgih Kuncoro Kusnadi Kusnandi Kusnandi ,- Kusnandi Kusnandi Kusnandi Kusnandi, Kusnandi Laila, Alya Nur Najmi Lia Ardiansari Lorenza, Ade Novia Lucky Heriyanti Jufri Lucky Heriyanti Jufri, Lucky Heriyanti Lukman Lukman Lyna Sari, Dwi M Akbar Gulvara Maifa, Talisadika Serrisanti Maifianti, Khori Suci Marhami Marhami Martinez Edison Putra Mashud Maula, Nyla Farhatul Maulana, Dick Dick Maya L Hutapea, Maya L Melia Eka Daryati Mikkey Anggara Suganda Mimi Hariyani Mimin Ninawati Mirza Aulia Mohamad Gilar Jatisunda Mohamad Zaka Al-Farisi Mohammad Fauziddin Mu'afi, Yusniar Najmah Muhaimin, Lukman Hakim Muhammad Hatta Muhammad Kristiawan Muhammad Rayana Kusumanegara Muhammad Win Afgani Mulyaning. A, Endang Cahya Mulyawati, Sri N. Nurjanah nadia, elen falen Nadiva Dwi Anggani Nanang Priatna Nasir, Norma Nasir, Nurihan Nelly Fitriani Nia Fatmawati Nina Anindyawati Nina Novi Yanti Nur Eva Zakiah, Nur Eva Nur Qamariah Nurhayati, Lina Nurhidayati, Febry Nurjanah Nurjanah Nurjanah, Nurjanah3 P, Anditya Gilang Rizky Pacis, Estrella R. Pahmi, Samsul Palupi Sri Wijayanti Pandu Pratama Paryanto, Edi Pauji, Ikbal Pradana, Anditya Gilang Rizky Pranata, Muhammad Fariz Yoga Priatna M, Bambang Avip Puspasari, Eka Putra R, Andika Putra Sastaman B Putri Fitriasari, Putri Putri, Amelia Defrianti Putri, Jazila Anaka Putri, Santika Putri, Tanaya Eka Rahmadi Rahman, Zahra Fadhila Rahmat Putra Perdana Rahmi Nur'aini Azzahra Raisatunnisa Raisatunnisa Raisatunnisa, Raisatunnisa Ramli Rani Martalisa Taorina Rani Sugiarni Raudiyah Rizki R Rayhan, Nabila Cynthia Reny Andriyanty Repormasi, Amanah Rezza Dewintha, Rezza Rianto, Louis Riastuti, Ade Riyanti , Dwi Riyanto Riyanto Riyoko, Endie Rizki Rosjanuardi Rizky Rosjanuardi Rizky, Anditya Gilang Rosmayasari Rosmayasari Rosmayasari, Rosmayasari RR. Ella Evrita Hestiandari Rubiyatno Rubiyatno Rubiyatno Rudi Rudi Rudi Rudi Rusyid, Husnul Khatimah S. Maifa, Talisadika Sacko, Makan Sahid Agus Nurhamid, Sahid Agus Salsabila, Alya Salsabila Sani Sahara Saputri, Aulia Nabilla Sari, Atika Defita Sari, Desi Vita Sari, Dwi Maulida Sari, Liza Permata Sendi Ramdhani Sesilia Seli Setambah, Mohd Afifi Bin Bahurudin Seto, Rehino Yanu Setyaningrum, Desy Siahaan, Erika Yohanna Seventina Silfia Hayuningrat Sirait, Sudirman Siregar, Rama Nida Siti Fatimah Siti Noor Binti Ismail Siti Zakiyah Sri Yulianti Sufyani Prabawanto, Sufyani Suhendra Suhendra Suhendra Suhendra Suhendra, S Suhita, Cahyaningtyas Putri Sukma Murni Sukma Murni Sulistiawati Sulistiawati Sumaryanti Sumaryanti Suprihatin, Dewi Nawang Surya Kurniawan Sutawanir Darwis Suwito, Hanifah Wahyu Syafdi Maizora Syamsul Arifin Syamsuri Syamsuri Syarifah, Mufarrahatus Syarifah, Mufarrahatus Syisva, Syisva Talisadika Serrisanti Maifa Tarmudi, Tarmudi Tatang Herman, Tatang Theodore Dwivaland Fophin Tin Lam, Toh Tjahyanto, Teddy Tonra, Wilda Syam Toto Subroto Tri Nova Hasti Yunianta Turmudi Umbara, Uba Umbara, Uba Unaenah, Een Uray Gustian, Uray Wafa Islamiyah Wahyudi, Ibnu Wardah, Saidah Nabila Wardat, Yousef Warli, Dwi Warsitarumanti, Syahrani Wembrayarli, Wembrayarli Wijayanti, Bela Tri Wilda Syam Tonra Wina Romdhani, Wina Windia Hadi, Windia Y. Touvan Juni Samodra Yaya S. Kusumah Yaya S. Kusumah Yenda Puspita Yenni ,- Yoppy Wahyu Purnomo Yuce Sandra Yulidesni Yulidesni, Yulidesni Yuni Hajar Zainal Arifin zulnadila, zulnadila