Exploring Ethnomathematics: Understanding Lobachevsky Geometry through Traditional Fishing Tools of the Bengkulu People Abdurrobbil Falaq Dwi Anggoro, Wardono Wardono, Scolastika Mariani, Bambang Eko Susilo ASM Science Journal, 2026 This research bridges a gap in ethnomathematics by exploring non -Euclidean geometry through local culture. We demonstrate that the abstract concepts of Lobachevsky geometry can be intuitively understood using bubu, a traditional Bengkulu fishing trap. This study enriches Indonesian ethnomathematics and provides a pedagogical framework for teaching advanced math. Analysis of the bubu's internal structure reveals hyperbolic characteristics that embody the Lobachevsky Axiom of Parallelism. This axiom, which states that through a point outside a line there are at least two lines parallel to it, is visually reflected in the arrangement of the trap's blades. Our findings show that students grasp the Lobachevsky Parallelism Theorem not through formal proof, but as a conceptual discovery. They logically conclude that if the axiom allows for ‘at least two parallel lines’, then in hyperbolic space, the number must be ‘infinite’. This cognitive process proves how cultural contexts like the bubu can be a powerful learning medium for visualising and understanding complex mathematical principles.
Augmented Reality assisted by GeoGebra 3-D for geometry learning W. Widada, D. Herawaty, K. U. Z. Nugroho, A. Anggoro Journal of Physics Conference Series, 2021 Geometry becomes a difficult subject for students. The abstract object was one of the factors. Therefore, more concrete learning media are needed. One of them was augmented reality assisted by GeoGebra. The purpose of this study was to determine the ability to understand the geometrical concepts of high school students through augmented reality learning assisted by GeoGebra. Treatment was given to students through learning using GeoGebra-assisted augmented reality. This was a quasi-experimental study with a pre-test post-test control group design. This research instrument was a test of the ability to understand the concept of geometry. The test was used to measure students’ initial abilities, and this was referred to as a covariate. Also, to measure the ability to understand concepts after students follow augmented reality learning assisted by GeoGebra. Data were analyzed by covariate analysis (ANCOVA). The results of this study were F = Fo (A) = 9,150 with p-value = 0,000 <0,005. That means, there are differences in the ability to understand the concept of geometry between those taught with augmented reality which is assisted by GeoGebra and conventional learning. Other results show that t = 6.723 with p-value = 0.000 <0.05. This shows that the ability to understand the geometry concepts of students taught with augmented reality assisted by GeoGebra was higher than students who were taught conventionally after controlling for covariates. The conclusion was that the ability to understand the concepts of geometry through GeoGebra-assisted augmented reality learning was better than students taught with ordinary learning.
The ability to solve mathematical problems through realistic mathematics learning based on ethnomathematics A. Lubis, W. Widada, D. Herawaty, K. U. Z. Nugroho, A. Anggoro Journal of Physics Conference Series, 2021 Problem-solving is one of the goals of mathematics learning. Ethnomimetic-based realistic mathematics learning is learning with starting-point contextual problems that are close to students’ minds. This study aims to determine the effect of ethnomathematics-oriented realistic mathematics learning on problem-solving abilities. That is a type of quasi-experimental research. The study design was a non-equivalent control group. The population is SMA N 2 Kota Bengkulu in 2019. The sample of this study was 68 students from Class X MIPA A and X MIPA D. The research instrument was a test of problem-solving skills. Data were collected through tests and analysed by covariate analysis. The results of this study are that realistic mathematics learning oriented to ethnomathematics has a positive effect on the ability to solve. The conclusion is that realistic mathematics learning with ethnomathematics orientation can improve mathematical problem-solving skills for secondary school students. We suggest that mathematics teachers can develop realistic mathematics learning tools with ethnomathematics as a starting point for learning.
The cognitive process of students understanding quadratic equations D Herawaty, W Widada, W Gede, D Lusiana, Y Pusvita, Y Widiarti, A F D Anggoro Journal of Physics Conference Series, 2021 Algebra is mandatory learning in junior high school. That is a continuation of arithmetic with the bridge being variable. Students often have difficulty in understanding it, especially quadratic equations. The purpose of this study is how students’ cognitive processes in understanding the principles of quadratic equations. It was an exploratory study conducted on research subjects. The subjects were junior high school students selected based on their ability to understand concepts and principles about quadratic equations. That’s done through tests about understanding quadratic equations. There were 16 selected research subjects. They were interviewed in-depth by researchers using interview guides. Interview data were analyzed qualitatively based on genetic decomposition. The results of this study are that students can use square, rectangular and unit square cards to determine the principle of factorization of quadratic equations. Students can generalize until completing a perfect quadratic equation. The conclusion is that the cognitive process of students who learn to use learning media based on square and rectangular able to reach a high level (trans-level).
The abstraction ability about natural numbers through playing traditional music for elementary students D Herawaty, W Widada, H Ardy, R Furqany, Suharto, A F Dwi Anggoro Journal of Physics Conference Series, 2020 The ability of music has a positive impact on the balance of thinking. The purpose of this study is to determine whether the musical ability has a direct effect on the ability of abstraction of native numbers of elementary school students at a low level. This is survey research as an evaluation stage for the development of elementary thematic learning models in Kota Bengkulu, Indonesia. The research sample was 95 elementary school students in Kota Bengkulu. The instruments of this research were musical ability tests and abstraction ability test. Data were analyzed through the Lisrel 8.8 test. The results of this study is that musical ability has a direct positive effect on the ability of abstraction of native elementary students to a low level.
The cognitive process of students in understanding the parallels axiom through ethnomathematics learning D Herawaty, D Khrisnawati, W Widada, P Mundana, A F D Anggoro Journal of Physics Conference Series, 2020 The thinking process of students in understanding the parallels axiom through ethnomathematics learning was abstract activities of remembering, analyzing, understanding, judging, reasoning, imagining and speaking that was needed in learning geometry. This was the cognitive process of students based on culture. Lobachevsky’s axiom of parallelism was difficult to understand through low thinking. Ethnomathematics was one solution. The purpose of this study was to describe the cognitive process of students in understanding parallels through ethnomathematics learning. This research was the initial stage of development research. We conducted in-depth interviews with 8 high school students in Bengkulu, Indonesia. The research instrument was the researcher himself who was guided by an interview guide on understanding the Lobachevsky Axiom of Parallel Lines. Interviews were conducted during geometry through the ethnomathematics learning approach. Data were analyzed qualitatively through fixed comparison techniques. The results of this study were that students can encapsulate two or more traits in the Lobachevsky Parallel Lines axiom through ethnomathematics in the form of bubu. (Bubu was a traditional fishing gear in the village community in Bengkulu). The next cognitive process was that students can build an object about infinite lines that were parallel to certain line. The encapsulation activity produces a correct understanding based on the properties of woven mats. The conclusion of this study was that through the ethnomathematics approach students can achieve trans level cognitive processes.
The characteristics of relational students in understanding the concepts of normal subgroups Wahyu Widada, Dewi Herawaty, Selvin Ariska, Ririn Afifah, Abdurrobbil F D Anggoro Journal of Physics Conference Series, 2020 The quality of students’ responses in understanding the normal subgroup concept can be analyzed through SOLO Taxonomy. One level was relational. The purpose of this study was to describe the characteristics of relational students in understanding the concept of a normal subgroup. This was part of research development. This stage was a needs assessment. The research subjects were 29 undergraduate students of Mathematics Education at the University of Bengkulu. The instrument of this research was the researchers themselves with interview guides. Data collection was done through task-based interviews. Data were analyzed qualitatively through fixed comparison techniques. The results of this study are that the concept of normal subgroup was understood through the relationships between objects in a group. Like the right coset and left coset. The relationship between these objects becomes an integrated entity. The conclusion of this study was that relational students can represent all elements and conduct interdependence with one another, so that it becomes an integrated entity.
Students' obstacles in understanding the properties of the closed sets in terms of the APOS theory Dewi Herawaty, Wahyu Widada, Sri Handayani, Berindo, Rina Febrianti, Abdurrobbil F D Anggoro Journal of Physics Conference Series, 2020 An understanding of the concepts and principles of open sets can be done through activities in the form of mathematical actions, processes, objects organized in a scheme. This was the operationalization of the APOS theory (Action, Processes, Objects, and Schema). The purpose of this study was to describe students’ mistakes in understanding the properties of open sets in terms of the APOS Theory. This research was part of development research. It was the stage need assessment stage. We want to determine the characteristics of students to determine the right learning model. The subject of this study were 15 students of mathematics education at the University of Bengkulu. Students were selected based on the tasks that they do in learning Real Analysis. Data was collected from paper and pencil results and task-based interview results. Data were analyzed qualitatively using fixed comparison techniques. The results of this study were that students can only coordinate two or more sets, and the difficulty of proving a set theorem closes. One such theorem was “F was a subset of R, F closed sets if and only if F contains all the cluster points”. He can only take actions separately from the characteristics of the set given. The conclusion of this study was the difficulty of students in understanding the properties of the closed sets was the inability of students to carry out interiorization from actions to processes. Also, it was not able to encapsulate processes into objects. He was unable to reach the scheme of the properties of closed sets.
The cognitive process of extended trans students in understanding the real number system D. Herawaty, W. Widada, Iran Sairan, Fizi Herdian, K. U. Z. Nugroho, Abdurrobbil Falaq Dwi Anggoro Journal of Physics Conference Series, 2020 There were seven levels of student schema development in learning real analysis. Extended trans was the highest cognitive level. The purpose of this study was to describe the cognitive process of students in understanding the real number system. This was the initial part of development research. We want to know the highest initial ability students have about real number systems. The subjects of this study were 12 students of Real Analysis at the Bachelor of Mathematics Education Program. Students were interviewed based on assignments. Data were analyzed using fixed comparison techniques. The results of this study were that students can build linkages between actions, processes, objects, and other schemes (performing retrieval of the previous schema) by using and selecting procedures or operations in real number systems. He was able to apply the concept of the properties of bounded set to problem solving so that a mature scheme was formed. The scheme can be used to solve related problems. Also, can build new structures based on mature schemes that they already have. The conclusion of this study was that students can interiorize, encapsulate and thematize schemes that mature into a deductive structure.
Overcoming the difficulty of understanding systems of linear equations through learning ethnomathematics Wahyu Widada, Dewi Herawaty, Mohammad H Rahman, Dita Yustika, Elsa P Gusvarini, Abdurrobbil Falaq Dwi Anggoro Journal of Physics Conference Series, 2020 Middle school students have difficulty in understanding the system of linear equations. Ethnomathematics learning was one alternative to overcome it. The purpose of this study was to describe ethnomathematics learning techniques to overcome students’ difficulties in understanding systems of linear equations. This research was part of development research. This is part of student analysis. The subjects of this study were 38 junior high school students in the Kota Bengkulu. The application of ethnomathematics learning was given to the subject. The instrument of this study was the researchers themselves with interview guides and observation sheets. It was an interview about the ability of students to understand systems of linear equations. Data were analyzed qualitatively with fixed comparison techniques. The results of this study are the difficulty of students understanding the system of linear equations can be overcome through learning ethnomathematics. The horizontal mathematization used the culture of the fishermen of Bengkulu people “bundled fish, rice as small, relaxed”. This culture makes it easy for students to recall prerequisite concepts, making it easier for students to do interconnection between concepts. This makes it easy for students to achieve the principles of elimination, substitution and mixtures. The conclusion of this study is that learning ethnomatematics about Bengkulu fisherman culture can overcome the difficulties of students in understanding the system of linear equations.
Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra S Mariani, AFD Anggoro, W Wardono, BE Susilo European Journal of STEM Education 11 (1), 1-16 , 2026 2026
Hyperbolic geometry" lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra S Mariani, AFD Anggoro, W Wardono, BE Susilo European Journal of STEM Education 11 (1), 1-16 , 2026 2026
Beyond Straight Lines: Contextualizing Lobachevsky's Parallel Postulate Through the Geometry of the" Bubu" Fishing Gear AFD Anggoro, W Wardono, S Mariani, BE Susilo Journal of Honai Math 8 (3), 455-480 , 2025 2025
STRUCTURAL EQUATION MODELS: MATHEMATICAL REASONING ABILITIES AND GEOMETRIC PROBLEM-SOLVING ABILITIES AFD Anggoro, W Wardono, S Mariani, BE Susilo, R Hidayat, TT Wijaya Jurnal Math-UMB. EDU 12 (3), 260-274 , 2025 2025
Enhancing PISA-like mathematical literacy through deep learning assisted by mathos ai for junior high school students W Widada, KUZ Nugroho, M Masri, AFD Anggoro, D Herawaty, R Jumri, ... Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di … , 2025 2025 Citations: 3
Model Persamaan Struktural antara Kemampuan Koneksi Matematika dan Kemampuan Pemecahan Masalah Matematika Siswa SMP AFD Anggoro, W Wardono, S Mariani, BE Susilo PRISMA, Prosiding Seminar Nasional Matematika, 1-12 , 2025 2025
Problematika Dan Solusi Dalam Pembelajaran Geometri Non-Euclide KUZ Nugroho, W Widada, YL Sukestiyarno, SB Waluya, D Herawaty, ... Feniks Muda Sejahtera , 2025 2025 Citations: 2
KEMAMPUAN PEMAHAMAN MATEMATIKA MENGGUNAKAN KONTEKS BUDAYA LOKAL:(Pemecahan Masalah, Panalaran Matematis, dan Koneksi Matematika) AFD Anggoro, S Mariani, BE Susilo Feniks Muda Sejahtera , 2025 2025
INITIAL DESIGN FOR LEARNING THEORY INTRODUCTION TO RIEMANN GEOMETRY THROUGH AN ETHNOMATHEMATICS LEARNING APPROACH KUZ Nugroho, W Widada, AFD Anggoro, SDT Anggoro Jurnal Lebesgue: Jurnal Ilmiah Pendidikan Matematika, Matematika dan … , 2025 2025
KEMAMPUAN PENALARAN MATEMATIS, KONEKSI MATEMATIKA DAN PEMECAHAN MASALAH SISTEM PERSAMAAN LINIER MELALUI PENDEKATAN PEMBELAJARAN ETNOMATEMATIKA UNTUK SISWA SMP N 1 KOTA BENGKULU … AFD Anggoro IKIP Siliwangi , 2024 2024
Developing the skills for complex thinking research: a case study using social robotics to produce scientific papers EO Lopez-Caudana, CE George-Reyes, R Avello-Martínez Frontiers in Education 9, 1322727 , 2024 2024 Citations: 3
Mathematics study habits through an ethnomathematics approach and entrepreneurial behavior of mathematics education students AFD Anggoro, W Widada, KUZ Nugroho, D Herawaty, R Jumri, ... Wiyata Dharma: Jurnal Penelitian dan Evaluasi Pendidikan 11 (2), 144-152 , 2023 2023 Citations: 2
The Relationship among Self-Efficacy, Mathematical Concepts Understanding, Creative Thinking Skills, Mathematical Problem-Solving Skills, and Mathematics Learning Outcomes KUZ Nugroho, E Izwanto, W Widada, N Alias, AFD Anggoro, D Herawaty, ... Edumatika: Jurnal Riset Pendidikan Matematika 6 (2), 118-132 , 2023 2023 Citations: 1
Revisiting manipulatives in the learning of geometric figures R Ponte, F Viseu, TB Neto, AP Aires Frontiers in Education 8, 1217680 , 2023 2023 Citations: 29
Structural model between mathematical reasoning and mathematics problem-solving abilities of junior high school students AFD Anggoro, H Hendriana, A Yuliani Journal of Honai Math 6 (1), 71-75 , 2023 2023 Citations: 4
Studi Kasus: Efektivitas Latihan Batuk Efektif Terhadap Bersihan Jalan Nafas Pada Asma Bronkial Di IGD Rumah Sakit Umum Daerah Kraton Pekalongan PN DS, Z Amirudin Jurnal Lintas Keperawatan 4 (1), 272-280 , 2023 2023 Citations: 7
Kemampuan Pemecahan Matematika, Koneksi Matematika, dan Penalaran Matematis Siswa Sekolah Menengah AFD Anggoro, H Hendriana, A Yuliani Guepedia , 2023 2023 Citations: 15
Structural equation fit test of mathematical connection ability, mathematical reasoning, and mathematics problem-solving ability of junior high school students AFD Anggoro, S Haji, H Sumardi International Journal of Trends in Mathematics Education Research 5 (1), 82-93 , 2022 2022 Citations: 11
Students' cognitive processes in understanding the application of derivatives W Widada, D Herawaty, W Gede, KUZ Nugroho, AFD Anggoro, ... Annals of Mathematical Modeling 2 (1), 29-36 , 2022 2022 Citations: 5
Overcoming Difficulties in Understanding the Linear Equation System Through the Ethnomathematics Approach in the COVID-19 Pandemic D Herawaty, W Widada, AFD Anggoro, SDT Anggoro International Conference on Educational Sciences and Teacher Profession … , 2021 2021 Citations: 8
MOST CITED SCHOLAR PUBLICATIONS
Ethnomathematics and outdoor learning to improve problem solving ability W Widada, D Herawaty, AFD Anggoro, A Yudha, MK Hayati International Conference on Educational Sciences and Teacher Profession … , 2019 2019 Citations: 112
The improvement of the understanding of mathematical concepts through the implementation of realistic mathematics learning and ethnomathematics D Herawaty, W Widada, KUZ Nugroho, AFD Anggoro International Conference on Educational Sciences and Teacher Profession … , 2019 2019 Citations: 67
The tools of mathematics learning based on realistic mathematics education approach in elementary school to improve math abilities AFD Anggoro Universal Journal of Educational Research , 2019 2019 Citations: 63
Augmented Reality assisted by GeoGebra 3-D for geometry learning W Widada, D Herawaty, KUZ Nugroho, AFD Anggoro Journal of Physics: Conference Series 1731 (1), 012034 , 2021 2021 Citations: 54
Understanding the number concepts through learning Connected Mathematics (CM): A local cultural approach D Andriani, W Widada, D Herawaty, H Ardy, KUZ Nugroho, N Ma’rifah, ... Universal Journal of Educational Research 8 (3), 1055-1061 , 2020 2020 Citations: 54
The ability to solve mathematical problems through realistic mathematics learning based on ethnomathematics A Lubis, W Widada, D Herawaty, KUZ Nugroho, AFD Anggoro Journal of Physics: Conference Series 1731 (1), 012050 , 2021 2021 Citations: 52
Students’ ability to simplify the concept of function through realistic mathematics learning with the ethnomathematics approach D Herawaty, W Widada, A Adhitya, RDW Sari, L Novianita, ... Journal of Physics: Conference Series 1470 (1), 012031 , 2020 2020 Citations: 51
The ability to understanding of the concept of derivative functions for inter-level students during ethnomathematics learning W Widada, D Herawaty, KU Zaid Nugroho, AF Dwi Anggoro Journal of Physics: Conference Series 1179 (1), 012056 , 2019 2019 Citations: 43
The REACT strategy and discovery learning to improve mathematical problem solving ability W Widada, D Herawaty, P Mundana, M Agustina, FR Putri, AFD Anggoro Journal of Physics: Conference Series 1318 (1), 012081 , 2019 2019 Citations: 39
The thinking process of students in understanding the concept of graphs during ethnomathematics learning W Widada, D Herawaty, DS Andriyani, R Marantika, ID Yanti, ... Journal of Physics: Conference Series 1470 (1), 012072 , 2020 2020 Citations: 35
Overcoming the difficulty of understanding systems of linear equations through learning ethnomathematics W Widada, D Herawaty, MH Rahman, D Yustika, EP Gusvarini, ... Journal of Physics: Conference Series 1470 (1), 012074 , 2020 2020 Citations: 31
The scheme characteristics for students at the level of trans in understanding mathematics during etno-mathematics learning W Widada, D Herawaty, KUZ Nugroho, AFD Anggoro 3rd Asian Education Symposium (AES 2018), 417-421 , 2019 2019 Citations: 31
Revisiting manipulatives in the learning of geometric figures R Ponte, F Viseu, TB Neto, AP Aires Frontiers in Education 8, 1217680 , 2023 2023 Citations: 29
The cognitive process of students in understanding the parallels axiom through ethnomathematics learning D Herawaty, D Khrisnawati, W Widada, P Mundana, AFD Anggoro Journal of Physics: conference series 1470 (1), 012077 , 2020 2020 Citations: 27
The local culture-based learning model to improve teaching abilities for pre-service teachers S Julita, Sudarwan, AF Dwi Anggoro Journal of Physics: Conference Series 1179 (1), 012058 , 2019 2019 Citations: 23
Kemampuan Pemecahan Matematika, Koneksi Matematika, dan Penalaran Matematis Siswa Sekolah Menengah AFD Anggoro, H Hendriana, A Yuliani Guepedia , 2023 2023 Citations: 15
The cognitive process of students understanding quadratic equations D Herawaty, W Widada, W Gede, D Lusiana, Y Pusvita, Y Widiarti, ... Journal of Physics: Conference Series 1731 (1), 012053 , 2021 2021 Citations: 15
Structural equation fit test of mathematical connection ability, mathematical reasoning, and mathematics problem-solving ability of junior high school students AFD Anggoro, S Haji, H Sumardi International Journal of Trends in Mathematics Education Research 5 (1), 82-93 , 2022 2022 Citations: 11
Students of the extended abstract in proving Lobachevsky’s parallel lines theorem W Widada, D Herawaty, R Jumri, H Wulandari, F Aliza, AFD Anggoro Journal of Physics: Conference Series 1470 (1), 012098 , 2020 2020 Citations: 11
Students' obstacles in understanding the properties of the closed sets in terms of the APOS theory D Herawaty, W Widada, AFD Anggoro Journal of Physics: Conference Series 1470, 1-12 , 2020 2020 Citations: 10
