FRAKTAL: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA

Eksplorasi Pengalaman Belajar Siswa Dalam Pembelajaran Bangun Ruang Berbantuan Perangkat Lunak Geogebra 3D

2026-05-30T03:54:57+00:00

Learning solid geometry requires strong visualization skills, while textbook illustrations often fail to help students fully understand the forms and elements of solid geometry. This study explores students’ learning experiences in solid geometry using GeoGebra 3D. Eighteen ninth-grade students at a junior high school in Samarinda participated in activities exploring and constructing solid geometry using GeoGebra 3D. Data were collected from students’ responses regarding their experiences during the learning process and analyzed qualitatively through data reduction, data display, and conclusion drawing. The results indicate that using GeoGebra 3D provided positive learning experiences for most students. Three-dimensional visualization helped students observe shapes more clearly and facilitated their understanding of the structures and elements. Through exploratory activities, students observed relationships among solids such as cubes, rectangular prisms, and prisms, and discovered various prism forms that had not been recognized when viewing textbook illustrations alone. In addition, the object manipulation feature enabled students to explore nets of solids and construct models more precisely than by drawing on paper. These findings suggest that GeoGebra 3D supports more exploratory and meaningful geometry learning and enriches students’ understanding of solid geometry concepts.

E-LKPD Statistika Berbasis Liveworksheets untuk Memfasilitasi Kemampuan Literasi Numerasi

2026-05-30T03:56:33+00:00

This study aims to develop a liveworksheets-based statistical e-LKPD to facilitate students' numeracy literacy skills that meet the criteria of being valid, practical, and effective. This type of research is Research and Development (R&D) with the ADDIE development model. The trial subjects in this study consisted of two experts in the field of mathematics education, mathematics educators, and students of class VIII B of SMP Diponegoro 7 Gumelar in the 2024/2025 academic year. Technical data analysis in this study includes data analysis of the validity, practicality, and effectiveness of the e-LKPD product. The results show that the developed e-LKPD meets the criteria of validity, practicality, and effectiveness. The validity of the e-LKPD was obtained from the results of the assessment of material experts at 26.98 out of 31.77 (fairly good category) and media experts at 14.79 out of 17.66 (fairly good category). The practicality of e-LKPD is demonstrated through the results of educator responses with a practicality percentage of 77.74% (good category) and a practicality percentage based on student responses of 71.11% (good category). The effectiveness of e-LKPD can be seen from the results of the posttest of numeracy literacy skills with a completion percentage reaching 78.26% (good category). Thus, the developed statistical e-LKPD is declared valid, practical, and effective in facilitating students' numeracy literacy skills.

Prediksi Curah Hujan Harian Dengan Metode K-Nearest Neighbor (KNN) Menggunakan Python

2026-05-30T04:26:25+00:00

Climate is the average weather conditions over a relatively long period of time over a large area that requires monitoring and projection. Rainfall is important information, particularly in agriculture. Rainfall information is useful for anticipating the possibility of extreme events that cause failure in agricultural production. Therefore, daily rainfall predictions are necessary. In this study, the K-Nearest Neighbor (KNN) method was used to predict daily rainfall. The K-Nearest Neighbor (KNN) method was chosen because it is able to handle unpredictable rainfall data. The K-Nearest Neighbor (KNN) method is a modern heuristic method based on algorithms from the field of soft computing (SC). This study utilized daily rainfall data, average air temperature, average humidity, average air pressure, wind speed, and sunshine duration from 2021 to 2025. The number of each data set was 1,826, with training data and sampling data comprising 80% and 20%, respectively. Based on the classification evaluation report, the results were 71% accuracy, 56% precision, 71% recall, and 61% f1-score. The classification performance criteria based on the accuracy produced in this study was 71%, so the value falls within the sufficient performance range.

Penerapan Model Problem Based Learning Berbantuan Geogebra Untuk Meningkatkan Kemampuan Pemecahan Masalah Siswa Kelas IX SMP Kristen 1 Amanuban Barat Pada Materi Transformasi

2026-05-30T03:21:41+00:00

Mathematics is one of the subjects studied at every level, starting from elementary, secondary, and vocational schools. Mathematics plays an active role in advancing students' thinking, enabling them to think logically, creatively, critically, and mathematically. This study aimed to improve students' problem-solving skills on Geometric Transformation material by using the Problem-Based Learning model assisted by GeoGebra Application. This type of research was a class action research conducted in two cycles, with each cycle consisting of four stages: planning, implementation, observation, and reflection. Data collection techniques in this study include observation, tests, and test questions. Data analysis techniques were descriptive, qualitative, and quantitative. The results of this study showed that the implementation value of teacher activity observation in cycle I was 92,11%, increasing to 100% in cycle II; the implementation value of student activity in cycle I was 78,57%, increasing to 96,43% in cycle II, and the percentage of classical student learning completeness in cycle I was 40.36%, increasing to 64.52% in cycle II. Thus, it could be concluded that the application of problem-based learning models assisted by GeoGebra could improve the problem-solving ability of students in grade IX of SMP Kristen 1 Amanuban Barat on geometry transformation material.

Eksplorasi Etnomatematika Pada Rumah Adat Sa’o Milo Wua Masyarakat Kelitey Dan Integrasinya Dalam Pembelajaran Matematika

2026-05-30T04:17:37+00:00

Culture is a community's habits that have been passed down from generation to generation and become the identity of an area. The unique culture of a particular region has the potential to contain mathematical concepts in it, one of which is traditional house culture. The thing that bridges education and culture, especially mathematics education, is ethnomathematics. This research aims to describe the philosophy of the Sa'o Milo Wua traditional house, describe ethnomathematics and mathematical concepts in the Sa'o Milo Wua traditional house and develop learning tools related to mathematical concepts found in the Sa'o Milo Wua traditional house. This research is qualitative research with an ethnographic approach, which was carried out in Kelitey Village, Inerie subdistrict, Ngada district. The subjects of this research were 2 people. The research instrument is a researcher as the main instrument and supporting instruments, namely observation, interviews and documentation. Data analysis was carried out using the Miles and Huberman model, namely through data reduction, data presentation and drawing conclusions. Testing the validity of the data was carried out using technical triangulation. The results of this research show that there is ethnomathematics in the structure of the Sa'o Milo Wua traditional house including counting, locating, measuring, designing, and explaining. From this ethnomathematics activity, mathematical concepts were identified which included the concept of numbering, plan and cardinal directions, non-standard measurements, and the geometric concept of flat shapes. The concepts of school mathematics in the Sa'o Milo Wua traditional house culture can be developed through designing learning tools that are appropriate to school mathematics.

Eksplorasi Etnomatematika Pada Permainan Tradisonal Masyarakat Timor Di Desa Oeteta Dan Integrasinya Dalam Pembelajaran Matematika

2026-05-30T04:19:41+00:00

Ethnomathematics exploration is an effort to identify and reveal mathematical concepts embedded in everyday cultural practices, one of which is traditional games. This study aims to explore ethnomathematics in the traditional games of the Timorese community in Oeteta Village and to integrate these findings into mathematics learning in schools. The research was conducted in Oeteta Village, Sulamu District, Kupang Regency, using an exploratory qualitative approach with the researcher as the main instrument. Data were collected through observation, interviews, and documentation. The results show that traditional games such as tatik fatu, piol, nakleti nise, and hau loti contain various ethnomathematical activities, including counting, measuring, designing, playing, and explaining. These activities are related to school mathematics concepts such as addition, multiplication, comparison, measurement, geometry, geometric transformations, probability, and mathematical logic. These findings indicate that traditional games have strong potential as contextual and meaningful learning resources. Therefore, this study can serve as a foundation for designing ethnomathematics-based instructional materials as an innovation to enhance the quality of mathematics learning in schools

Analisis Adversity Quotient Calon Guru Pendidikan Matematika

2026-05-30T03:21:43+00:00

This study aims to analyze the profile of the Adversity Quotient (AQ) of prospective mathematics education teachers, focusing on four core dimensions: control, origin and ownership, reach, and endurance. A descriptive qualitative approach was employed, involving 130 students from the Mathematics Education Study Program. Data were collected using a five-point Likert scale questionnaire and analyzed descriptively based on percentage categories. The findings indicate that three AQ dimensions—control (75%), reach (74%), and endurance (80%)—are in the strong category, while origin and ownership (52%) falls into the moderate category. These results suggest that students possess high levels of perseverance and optimism in facing challenges, but show lower levels of self-reflection and responsibility in addressing the causes of their academic difficulties. This highlights the need for teacher education curricula to incorporate reflective training and character-building strategies to prepare future educators who are not only academically competent but also resilient and mentally strong.

Penerapan Model Kooperatif Tipe Teams Games Tournament Berbantuan Powerpoint Interaktif Untuk Meningkatkan Hasil Belajar Siswa SMP Pada Materi Peluang

2026-05-30T03:21:44+00:00

This research was motivated by the low learning outcomes of class 8 at SMP Negeri 10 Kupang on opportunity material. The aim of this research is to describe the application of the Cooperative Teams Games Tournament (TGT) model assisted by Microsoft Powerpoint Interactive media to improve the learning outcomes of grade 8 students at SMP Negeri 10 Kupang on opportunity material. The research method used is Classroom Action Research (PTK), with qualitative and quantitative data types. Implementation of this Classroom Action Research has 4 stages, namely 1) Planning; 2) Implementation of action (action); 3) Observation; 4) Reflection. This research was carried out in class 8 at SMP Negeri 10 Kupang, totaling 24 students. Data collection techniques in this research were through observation and tests with the instruments used, namely teacher and student observation sheets as well as test questions on student learning outcomes. Data analysis in research is analysis of data from teacher observations, analysis of data from student observations and analysis of student learning achievement tests. The research results showed that the percentage of completeness of students' classical learning outcomes at the end of cycle I reached 66.67%, increasing to 83.33% at the end of cycle II. The implementation of teacher teaching activity score data at the end of cycle I reached 95%, increasing to 100% at the end of cycle II and was in the very good category. In addition, the implementation of student learning activity score data at the end of cycle I reached 88% and also increased to 100% at the end of cycle II and was in the very good category.

Strategi Guru Dalam Meningkatkan Motivasi Belajar Matematika Siswa: Studi Kasus Di MTs Negeri 4 Klaten

2026-05-30T04:02:03+00:00

Learning motivation is a crucial factor that shows students' academic success, especially in mathematics subjects often claimed to be difficult. This research aims to explore strategies applied by teachers in increasing student learning motivation at MTs Negeri 4 Klaten. The research method used is a case study with a qualitative approach. Data was collected through observation, semi-structured interviews, and document analysis. The results of the study showed that teachers applied various innovative learning strategies, such as the use of creative terms in explaining mathematical concepts, the use of singing to memorize formulas, giving real stories before lessons, and a personal approach to understanding the students' backgrounds. In addition, the attitude of teachers who respect each student without considering them as "stupid" students also contributes to increasing students' confidence and motivation. The main obstacle faced in implementing this strategy is the difference in the level of student understanding and the impact of the Covid-19 pandemic. This study is expected to provide insight for educators in designing more effective strategies to increase student's motivation to learn mathematics.

Analisis Kesalahan Menyelesaikan Soal Matematika dalam Materi Matriks pada Siswa Kelas XI MIIA MAN 1 Flores Timur

2026-05-30T04:15:47+00:00

This study aims to describe students’ errors in solving mathematics problems on matrix topics in class XI MIIA at MAN 1 Flores Timur. This research employed a qualitative approach with a descriptive research design. Data were collected through tests and interviews, involving 9 students categorized into three ability levels: high, medium, and low. The research instrument consisted of the researcher as the main instrument, supported by mathematics ability tests, matrix tests, and interview guidelines. Data analysis was conducted through the analysis of students’ written work and interview results, while data validity was ensured using the technique of triangulation. The findings indicate that high-ability students (T1, T2, and T3) tend to make errors in process skills and in writing final answers. Medium-ability students (D1, D2, and D3) make errors in understanding the problem, process skills, and writing final answers. Meanwhile, low-ability students (R1, R2, and R3) exhibit more complex errors, including difficulties in understanding the problem, process skills, and writing final answers. These findings suggest that process skill errors are the most dominant type of error across all levels of student ability

E-Modul Berbasis Pendekatan Contextual Teaching Learning (CTL) Berbantuan Geogebra Pada Materi Transformasi Geometri

2026-05-30T03:21:46+00:00

This study aims to develop a Geogebra-assisted e-module based on the Contextual Teaching Learning (CTL) approach on geometric transformation material that meets the criteria of validity, practicality, and effectiveness. This study employed a Research and Development (R&D) method using the ASSURE model. The research was conducted at SMPN 4 Mandau involving ninth-grade students. The object of this study was the developed e-module. Data were collected through questionnaires and tests using instrument validation sheets, learning material expert validation sheets, educational technology expert validation sheets, student response questionnaires, and learning outcome test items. The data were analyzed descriptively using qualitative and quantitative techniques. The results showed that the developed e-module met the criteria of being highly valid, with a validity level of 88.53%. The e-module was also categorized as highly practical, with percentages of 91.63% in the small-group trial and 87.71% in the limited-group trial. The effectiveness test using the Mann–Whitney test showed that (2.97906 ≥ 1.96), indicating differences in learning outcomes between the experimental and control groups. Therefore, the Geogebra-assisted CTL-based e-module on geometric transformation material is feasible to be used as an alternative teaching material.

Komputasi Chemical Topological Graph (CTG) Melalui Indeks Topologis Graf Aljabar Menggunakan Python

2026-05-30T03:53:44+00:00

Dalam kimia komputasi dan teori graf, struktur molekul kimia dimodelkan sebagai graf topologis untuk menganalisis sifat fisikokimia secara matematis dan komputasional. Chemical Topological Graph (CTG) menggabungkan teori graf dengan kimia organik, merepresentasikan atom sebagai titik (vertex) dan ikatan sebagai garis penghubung (edge). Ini memprediksi sifat seperti titik didih, kelarutan, dan aktivitas biologis tanpa percobaan mahal, meskipun struktur rumit memerlukan indeks topologis efisien. Indeks graf aljabar, menggunakan matriks adjasensi, spektrum graf, dan operasi grup, menangkap simetri dan konektivitas lebih baik, mendukung desain obat dan kimia komputasi. Penelitian ini mengimplementasikan komputasi CTG melalui indeks topologis graf aljabar, mengadaptasi dua teorema dari Ningrum et al. (2024). Teorema pertama: indeks Zagreb pertama pada grup dihedral D_n, M_1(G) = n(2n^2+5n+5) dan Teorema kedua: indeks Wiener pada grup modulo {Z}_n, W(G)=(n(n-1))/(4) . Menggunakan Python dengan NetworkX dan NumPy, diterapkan pada data PubChem, implementasi ini memverifikasi teorema dan menyediakan kerangka kerja untuk prediksi sifat molekul yang cepat, terintegrasi dengan machine learning.

Pengembangan Media Manipulatif Triguci (Trigonometri Unit Circle) Pada Materi Perbandingan Trigonometri

2026-05-30T04:10:55+00:00

Learning trigonometric ratios in schools still encounters challenges due to the abstract nature of the material and the limited availability of adequate visual media, causing students to struggle in understanding the relationship between angles and trigonometric function values. This study aims to develop the manipulative learning media TRIGUCI (Trigonometry Unit Circle) to help students understand trigonometric ratio concepts more concretely and visually. The type of research used is research and development (R&D) employing the ADDIE model, which consists of the stages of analysis, design, development, implementation, and evaluation. The research subjects were 30 tenth-grade students of class X-5 at MA Almaarif Singosari. The research instruments included interview guidelines, validation sheets (media expert and practitioner validation), and questionnaires. Data were collected through interviews and questionnaires. The results showed that the TRIGUCI media obtained a validity percentage of 97.2% from media experts in the highly valid category and a feasibility percentage of 97.2% from practitioners in the highly feasible category. Student responses reached 77.62%, falling into the very good category. Therefore, TRIGUCI is declared suitable as a trigonometry learning media because it can concretely visualize concepts, enhance student engagement, strengthen understanding, and foster positive responses toward the relationship between angles and trigonometric function values.

Desain Hypothetical Learning Trajectory Pada Materi Bangun Datar Dengan Konteks Anyaman Kipas di SD GMIT Manumuti

2026-05-30T04:08:30+00:00

Pendidikan Matematika Realistik Indonesia merupakan pendekatan pembelajaran matematika yang dekat dengan kehidupan real peserta didik, sehingga menuntut guru untuk membuat desain HLT yang sesuai dengan konteks yang dekat dengan siswa. Penelitian ini bertujuan untuk mendesain Hypothetical Learning Trajectory pada materi bangun datar dengan menggunakan pendekatan matematika realistik di kelas IV SD GMIT Manumuti. Metode yang digunakan dalam penelitian ini yaitu design research yang mana metode ini difokuskan pada pengembangan desain pembelajaran dalam bentuk hypothetical learning trajectory. Penelitian ini merupakan penelitian kualitatif yang melibatkan 5 orang siswa pada siklus pilot experiment dan 16 orang siswa pada siklus teaching experiment. Penelitian ini dilakukan di SD GMIT Manumuti. Teknik pengumpulan data yang digunakan adalah tes tertulis, lembar validasi, wawancara, dan analisis data tes tertulis.Penelitian ini menghasilkan suatu learning trajectory melalui pendekatan PMRI yang dapat digunakan untuk mendukung proses pembelajaran terkait materi keliling dan luas jajar genjang di kelas IV SD GMIT Manumuti. Learning Trajectory yang dihasilkan terdiri atas 5 aktivitas dimana pendekatan PMRI menjadi acuan utama dalam setiap aktivitas yang ada. Konteks yang digunakan adalah budaya menganyam yang berbentuk bangun datar jajar genjang yaitu gambar anyaman pada kipas. Siswa diminta mengamati dan menyebutkan bentuk bangun datar apa saja yang ada pada anyaman kipas, setelah mengamati siswa diminta menggambar kembali bentuk bangun datar jajar genjang yang mereka amati pada kipas, kemudian siswa diminta mengukur panjang keseluruhan sisi yang ada pada gambar yang dibuat menggunakan penggaris, hasil pengukuran panjang sisi-sisi diketahui menjadi acuan untuk menentukan rumus keliling jajar genjang dan memotong jajar genjang berdasarkan sisi-sisinya lalu memotong jajar genjang secara vertikal berdasarkan petunjuk pada LKPD dan menyusun menjadi sebuah persegi panjang selanjutnya dengan rumus luas persegi panjang menjadi acuan untuk menentukan rumus luas jajar genjang serta dapat menyelesaikan soal keliling dan luas jajar genjang.

Pengembangan Modul Pembelajaran Matematika Berbasis Etnomatematika Untuk Meningkatkan Kemampuan Matematis Siswa SMP: Systematic Literature Review

2026-05-30T03:38:01+00:00

The low mathematical ability of Indonesian students and the limitations of contextual learning are important backgrounds for the development of ethnomathematics-based learning modules. This study aims to analyze the development of ethnomathematics-based mathematics learning modules at the junior high school level through a Systematic Literature Review (SLR) approach. The study focuses on the local cultural context used, improved mathematical abilities, and the effectiveness of the modules based on empirical evidence. The SLR method follows the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) protocol with a literature search on Google Scholar for the period 2016–2025. From the 20 primary articles analyzed, the results show that the context of traditional houses or architecture is the most dominant local culture used. The most improved mathematical ability was problem-solving skills. In addition, all modules analyzed were proven to be effective with an average N-Gain of 0.64 accompanied by positive student responses. These findings indicate that ethnomathematics-based mathematics learning modules are effective in improving the mathematical abilities of junior high school students while strengthening the connection between mathematical concepts and local culture.