Imajiner: Jurnal Matematika dan Pendidikan Matematika
Imajiner: Jurnal Matematika dan Pendidikan Matematika , ISSN 2685-3892 (online) adalah jurnal yang diterbitkan oleh Program Studi Pendidikan Matematika Universitas PGRI Semarang. Jurnal ini merupakan wahana untuk mempublikasikan hasil-hasil penelitian dalam lingkup matematika dan pendidikan matematika yang dikelola oleh Program Studi Pendidikan Matematika Universitas PGRI Semarang. Jurnal ini terbit enam kali dalam satu tahun yaitu pada bulan Januari, Maret, Mei, Juli, September, dan November. Journal Title Imajiner: Jurnal Matematika dan Pendidikan Matematika Frequency Enam kali dalam setahun ISSN 2685-3892 (online) Editor-in-chief Lukman Harun Publisher Program Studi Pendidikan Matematika Universitas PGRI Semarang Citation Google Schoolar | Garuda email : imajiner@upgris.ac.id Article Processing Charges (APCs)/ Article Publication Fee: IDR. 500.000
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Analisis Kesulitan Siswa SMP dalam Memecahkan Masalah Statistika Berdasarkan Tahapan Polya
Mathematical problem-solving skills are essential competencies in 21st-century education, particularly in statistics, where students must interpret data, analyze variability, and make informed decisions. However, many students experience significant difficulties when solving statistical problems. This study aims to analyze students' difficulties in solving statistical problems based on Polya's four stages of problem-solving: understanding the problem, developing a plan, implementing the plan, and looking back. This study uses a descriptive qualitative approach with 70 junior high school students in Semarang as subjects selected using a purposive sampling technique. Data were collected through written tests and semi-structured interviews. The findings revealed that students experienced difficulties in solving statistical problems based on Polya's stages were 45% of students were unable to complete the understanding stage, especially in identifying known information and organizing important information needed; 55% of students had difficulties at the planning stage, especially in selecting appropriate statistical procedures; 61% of students still had difficulties at the implementing stage of the plan; and 66% of students still had difficulties at the re-examination stage. This study provides implications for the development of integrated learning designs with real-world contexts and technology that emphasize structured problem-solving processes, thereby improving students' problem-solving abilities.
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Pemodelan Faktor-Faktor Kemiskinan di Indonesia Menggunakan Pendekatan Regresi LASSO
In September 2024, the percentage of poor people in Indonesia reached 8.57 percent. This figure shows a decrease of 0.46 percentage points compared to March 2024. However, this poverty rate is still far from the national target. This study aims to analyze the factors that influence the percentage of poor people (P0) in order to provide a reference for the government to optimize policies on the dominant factors that have a strong impact on the percentage of poor people (P0). The research method uses LASSO regression due to the high multicollinearity problem in the data used. The analysis results show that the poverty depth variable (P1) and poverty severity variable (P2) have a dominant influence on the percentage of poor people (P0). The coefficient of determination value of 95% on the training data and 96% on the testing data indicates that the model has a very good ability to explain the percentage of poor people (P0).
Pemodelan Profil Siswa SMP Berdasarkan Mathematics Self-Regulated Learning Menggunakan Metode K-Means Clustering
Mathematics achievement at the junior high school level remains a significant challenge, with non-cognitive factors such as self-regulated learning (SRL) playing a critical role alongside cognitive ability. This study aims to develop a mathematical model for classifying Mathematics SRL profiles of junior high school students in Cirebon City using K-Means Clustering. A descriptive-exploratory quantitative design was employed with 68 students selected through stratified random sampling. Data were collected using a validated Mathematics SRL questionnaire (α = 0.823) encompassing four dimensions: Goal Setting, Self-Monitoring, Self-Efficacy, and Metacognition & Motivation. Prior to clustering, data were standardized using Z-score normalization and analyzed through Principal Component Analysis (PCA). The optimal number of clusters (K = 3) was determined via the Elbow Method and Silhouette Index (SI = 0.286). Results identified three distinct student profiles: High (32.4%), Moderate (45.6%), and Low (22.1%), with statistically significant differences across all SRL dimensions (p < 0.001). Self-Efficacy emerged as the most discriminating dimension (F = 70.349). The resulting classification model, C*(xᵢ) = , serves as a practical diagnostic tool for identifying student SRL profiles, enabling educators to design targeted, evidence-based pedagogical interventions.
Pengelompokan Pengguna Spotify Berdasarkan Data Tipe Campuran Menggunakan Algoritma K-Prototype
Competition in streaming music services requires a better understanding of user behavior and churn tendencies. This study aims to segment Spotify users and analyze churn patterns based on demographic characteristics and service usage behavior using the K-Prototypes method on mixed-type data. The optimal number of Cluster was determined using the Elbow method, while the churn variable was used to evaluate the clustering results. The analysis shows that three user cluster were formed with distinct characteristics. The first cluster represents younger premium users with relatively high usage intensity, the second cluster represents student users with the highest churn proportion, and the third cluster represents free users with high ad exposure but the lowest churn proportion. These findings indicate that the K-Prototypes method is effective in grouping Spotify users and provides useful information for understanding user behavior and churn tendencies.
Pemodelan Spasial Tingkat Pengangguran Terbuka Kabupaten/Kota di Pulau Sumatera Menggunakan Pendekatan Geographically Weighted Panel Regression
This study aims to analyze the factors affecting the Open Unemployment Rate (OUR) at the regency/city level in Sumatra Island during the 2022–2024 period by considering spatial and temporal variations. The study employs panel data obtained from Statistics Indonesia, with the Open Unemployment Rate as the dependent variable and the Human Development Index, Mean Years of Schooling, Labor Force Participation Rate, and Gross Regional Domestic Product as independent variables. Panel data regression and Geographically Weighted Panel Regression (GWPR) are applied as analytical methods. The best panel regression model is selected using the Chow and Hausman tests, which indicate that the Fixed Effect Model is the most appropriate. The Breusch–Pagan test confirms the presence of spatial heterogeneity, justifying the use of the GWPR approach. The GWPR model with an adaptive bisquare kernel weighting function and optimal bandwidth successfully captures local variations in the relationship between explanatory variables and unemployment. The results reveal that Mean Years of Schooling and Gross Regional Domestic Product have a positive effect on the Open Unemployment Rate, while the Labor Force Participation Rate has a negative effect, with varying magnitudes across regions. The GWPR model outperforms the global panel regression, achieving a coefficient of determination of 96.8%. These findings highlight the importance of incorporating spatial approaches in formulating region-specific employment policies in Sumatra Island.
Pengembangan Media Pembelajaran Interaktif Digital Berbasis Deep Learning Untuk Meningkatkan Kemampuan Berpikir Kritis Siswa SMA
Pembelajaran matematika di sekolah masih sering didominasi oleh metode konvensional yang menyebabkan keterlibatan siswa dalam proses belajar kurang optimal dan kemampuan berpikir kritis siswa belum berkembang secara maksimal. Salah satu upaya yang dapat dilakukan untuk mengatasi permasalahan tersebut adalah melalui pengembangan media pembelajaran interaktif yang mampu mendorong keterlibatan aktif siswa dalam proses belajar. Penelitian ini bertujuan untuk mengembangkan media pembelajaran interaktif digital berbasis deep learning yang valid, praktis, dan efektif untuk meningkatkan kemampuan berpikir kritis siswa SMA pada materi persamaan dan fungsi kuadrat. Penelitian ini merupakan penelitian pengembangan dengan menggunakan model ADDIE yang meliputi tahap analisis, desain, pengembangan, implementasi, dan evaluasi. Produk yang dikembangkan berupa e-modul interaktif menggunakan Flip PDF Professional yang dilengkapi dengan aktivitas interaktif berbasis GeoGebra dan Wordwall. Subjek penelitian terdiri dari siswa kelas X SMA yang terdiri dari kelas eksperimen dan kelas kontrol. Hasil penelitian menunjukkan bahwa media yang dikembangkan memenuhi kriteria valid berdasarkan validasi ahli dengan persentase sebesar 96,36% dari ahli media dan 90% dari ahli materi, praktis berdasarkan respon siswa dengan persentase sebesar 84,18%, serta efektif berdasarkan hasil uji coba hipotesis yang menunjukkan nilai signifikansi 0,000<0,05, nilai N-gain kelas eksperimen sebesar 0,6823 lebih tinggi dari kelas kontrol sebesar 0,5353, serta ketuntasan belajar klasikal pada kelas eksperimen mencapai 81,25%. Hasil penelitian ini menunjukkan bahwa e-modul interaktif berbasis deep learning dapat menjadi alternatif media pembelajaran yang mendukung peningkatan kemampuan berpikir kritis siswa dalam pembelajaran matematika.
Indeks Hyper Wiener pada Graf Nilpoten dari Gelanggang Bilangan Bulat Modulo
Graf merupakan struktur matematika yang digunakan untuk merepresentasikan hubungan antar objek. Salah satu jenis graf yang berkaitan dengan struktur aljabar adalah graf nilpoten. Untuk suatu gelanggang R, graf nilpoten adalah graf dengan himpunan simpul berupa seluruh unsur di R dan dua simpul berbeda x dan y bertetangga jika dan hanya jika hasil perkalian x dan y merupakan unsur nilpoten di R. Indeks Hyper-Wiener merupakan salah satu indeks topologi yang mengukur jarak dan kuadrat jarak antar pasangan simpul dalam graf. Penelitian ini bertujuan untuk menentukan rumus umum Indeks Hyper-Wiener pada graf nilpoten dari gelanggang bilangan bulat modulo, khususnya pada dua kasus, yaitu bilangan bulat modulo p pangkat k dan bilangan bulat modulo hasil kali p dan q, dengan p dan q merupakan bilangan prima serta k merupakan bilangan asli. Metode yang digunakan bersifat deduktif, dimulai dengan pengkajian struktur graf nilpoten dari bilangan bulat modulo n, klasifikasi pasangan simpul, serta perhitungan jarak antar simpul. Hasil yang diperoleh berupa rumus tertutup Indeks Hyper-Wiener untuk masing-masing kasus.
Penerapan Agglomerative Hierarchical Clustering Untuk Pengelompokan Kabupaten/Kota di Provinsi Sumatera Barat Berdasarkan Potensi Sambaran Petir
Lightning strike are an atmospheric phenomenon that pose significant risk to human safety and infrastucture, partuculary in topical regions sudh as Indonesia, inculding West Sumatra Province. Variations in geographical and environmental conditions contribute to differences in lightning strike potential across districts/municipalities. This study aims to classify districts/municipalities in West Sumatera Province based on their lightning strike potential in order to identify areas requiring higher mitigation priority. The classification was conducted using Agglomerative Hierarchical Clustering with Ward’s method based on three main variables including lightning density, rainfall, and population density. The result indicate that West Sumatera Province can be grouped into 4 cluster of lightning strike potential: low, moderate, high, and very high. The low-potential cluster consists of 6 districts/municipalities, the moderate-potential cluster consists 6 districts/municipalities, the gigh-potential cluster consisits 6 districts/municipalities, and the very high potential cluster contains only 1 municipality. These findings provide a systematic spatial overview of lightning strike potential levels and may serve as a basis for determining regional risk mitigation proirities and infrastructure protection strategies.
Analisis Pengaruh Model Pembelajaran Discovery Learning dengan Pendekatan Deep Learning Terhadap Kemampuan Pemahaman Konsep dan Penalaran Matematis Siswa Pada Materi SPLTV
This study aims to analyze the effect of the Discovery Learning model with a Deep Learning approach on students' conceptual understanding and mathematical reasoning abilities on the topic of Three Variable Linear Equation Systems (SPLTV) in grade X of SMA Negeri 17 Medan in the 2025/2026 academic year. This study used a quantitative approach with a quasi-experimental design. The sample consisted of class X-4 as the experimental class and class X-6 as the control class selected through cluster random sampling. Data were collected using tests, questionnaires, and observation sheets. The data were analyzed using descriptive and inferential analysis. The results showed that the Discovery Learning model with a Deep Learning approach had a significant effect on students' conceptual understanding and mathematical reasoning abilities with a significance value < 0.05. In addition, students taught using this model showed better conceptual understanding than those taught using conventional learning. The implementation of this model also increased students' active participation in mathematics learning.
Kemampuan Representasi Matematis Siswa SMP Ditinjau dari Self-Efficacy pada Model Pembelajaran CORE Berbantuan Liveworksheets
Penelitian ini bertujuan untuk menguji efektivitas model pembelajaran CORE berbantuan Liveworksheets terhadap kemampuan representasi matematis siswa ditinjau dari self-efficacy. Penelitian ini menggunakan metode gabungan atau mixed method desain True Experimental tipe Post-test Only Control Design. Penelitian dilakukan di SMP N 2 Semarang dengan populasi adalah seluruh siswa kelas VII. Sampel penelitian adalah kelas VII H (kontrol) dan kelas VIII I (eksperimen). Pengumpulan data kuantitatif dilakukan dengan pemberian tes kemampuan representasi matematis dan angket self-efficacy. Pengumpulan data kualitatif dilakukan dengan wawancara terhadap 6 siswa sebagai subjek penelitian berdasarkan kategori self-efficacy. Hasil penelitian diperoleh bahwa: (1) rata-rata hasil tes kemampuan representasi matematis pada kelas eksperimen mencapai ketuntasan individual, (2) proporsi siswa yang tuntas dalam hasil tes kemampuan representasi matematis pada kelas eksperimen mencapai 75%, (3) rata-rata hasil tes kemampuan representasi matematis siswa pada kelas eksperimen lebih tinggi dibandingkan kelas kontrol, dan (4) proporsi siswa yang tuntas pada hasil tes kemampuan representasi matematis di kelas eksperimen lebih besar dibandingkan kelas kontrol. Hal ini menunjukkan bahwa pembelajaran model CORE berbantuan Livewokrsheets efektif terhadap kemampuan representasi matematis siswa.
Model Matematis dan Analisis Statistik Indeks Efisiensi Investasi Pariwisata (T-CLEI)
This study develops a mathematical and statistical framework for analyzing tourism investment efficiency through the Tourism Capital–Leverage Efficiency Index (T-CLEI). The model is formulated as a fractional optimization problem using a Cobb-Douglas profit function and analyzed via differential calculus, Hessian matrix analysis, and logarithmic transformation. Existence and uniqueness of the optimal solution are rigorously proven using the Extreme Value Theorem and concavity analysis. A statistical framework applying the Delta Method provides first-order approximations for the expectation and variance of T-CLEI, enabling confidence interval construction. The central theorem establishes that the optimal solution is unique when the sum of output elasticities satisfies β + γ < 1. The model contributes for tourism investment efficiency analysis with potential for empirical validation on panel data.
Pengaruh Model Pembelajaran Problem Based Learning (PBL) Terhadap Kemampuan Pemecahan Masalah Matematis dan Motivasi Belajar Siswa pada Materi SPLTV di Kelas X
This study aims to analyze the effect of the Problem Based Learning (PBL) learning model on mathematical problem-solving ability and student learning motivation on the Three Variable Linear Equation System (SPLTV) material in class X of SMK Swasta Budi Setia Sunggal Academic Year 2025/2026. This study uses a quantitative approach with a quasi-experimental study design in the form of a posttest-only control group design. The population of this study was all students of class X of SMK Swasta Budi Setia Sunggal consisting of 5 classes. The sample was determined using a purposive sampling technique. The research instruments used were tests, questionnaires, and observation sheets which were tested for validity, reliability, difficulty level, and discriminating power first. Post-test data were analyzed using normality tests, homogeneity tests, t-tests, and effect size. The results showed that the average post-test problem-solving ability in the experimental class reached 51.53 higher than the control class which reached 44.07. Meanwhile, the average post-test results of learning motivation in the experimental class reached 56.53, higher than the control class which reached 50.37. The results of the study showed that there was a significant influence between students' mathematical problem-solving abilities between the experimental class and the control class with a significant value of 0.001 <0.05. In addition, there was no significant influence on students' learning motivation between the experimental class and the control class with a significant value of 0.191 > 0.05. Thus, it can be concluded that the use of the problem-based learning model has a significant effect on problem-solving abilities, while there is no significant influence on learning motivation.
Efektiitas Pembelajaran Dengan Media Pembelajaran Berbasis Budaya Batak Terhadap Peningkatan Pemahaman Konsep Siswa Kelas X SMA Swasta Free Methodist Medan Pada Materi Jarak Dalam Bangun Ruang 3 Dimensi
This study aims to determine the effectiveness of learning using Batak culture–based learning media in improving the mathematical conceptual understanding of Grade X students at Free Methodist Private Senior High School Medan on the topic of three-dimensional geometry. This study integrates Batak culture through the context of Jabu Bolon as a mathematics learning medium to support the visualization of distance concepts in three-dimensional geometry. In this study, local culture is not merely used as an illustrative context, but the structure and architectural form of Jabu Bolon are directly utilized as visual and contextual media in mathematics learning. The integration of local culture not only strengthens the connection between mathematical concepts and students’ real-life experiences, but also provides a more meaningful, contextual, and culturally relevant learning experience for students.This research used a quasi-experimental method with a population consisting of all Grade X students from three classes. The instruments used were tests and observations. The sample was determined through cluster random sampling, resulting in class X-C as the experimental class and class X-B as the control class. Data were collected using a conceptual understanding test. Data analysis was conducted using the Liliefors normality test, t-test, and N-Gain test. The results of the t-test showed a significance value of sig. (P(T≤t) two-tail) of 0.0074 < 0.05, indicating that there is a significant difference in conceptual understanding between the two sample classes. The average N-Gain score of the experimental class was 0.75 or 75%, which falls into the high category, while the control class obtained an N-Gain score of 0.39 or 39%, which falls into the medium category. When viewed from the indicators of effectiveness in the experimental class: (1) the quality of learning shows a sig. value (P(T≤t) two-tail) of 0.0074 < 0.05 and an N-Gain of 75%; (2) the appropriateness of the learning level is categorized as “very good” with a percentage value of 85.3%; and (3) learning time is categorized as “good” with an average score of 4.6. Therefore, it can be concluded that Batak culture–based learning is effective in improving the conceptual understanding of Grade X students on the topic of distance in three-dimensional geometry.
Efektivitas Pembelajaran Berbasis Masalah Terhadap Pemahaman Konsep dan Kemampuan Berpikir Tingkat Tinggi Siswa Pada Materi Fungsi Kuadrat di Kelas X SMK Swasta Parulian 1 Medan T.A 2025/2026
This study aims to determine the effectiveness of problem-based learning on students’ conceptual understanding and higher-order thinking skills regarding quadratic functions among 10th-grade students at Parulian 1 Private Vocational High School in Medan during the 2025/2026 academic year. This is a quantitative study using a descriptive approach. The population in this study consists of all 10th-grade students, while the sample comprises Class X-TKJ and X-AP, selected through purposive random sampling. The instruments used include essay tests, questionnaires, and observation sheets, all of which have been validated for validity and reliability. The results of the study indicate that problem-based learning is effective in improving students’ conceptual understanding of mathematics and higher-order thinking skills, with a level of effectiveness falling into the moderate category.
Efektivitas Pembelajaran Berbasis Masalah terhadap Kemampuan Berpikir Kritis dan Literasi Matematis pada Materi Barisan dan Deret Aritmatika kelas X SMK Telkom 1 Medan T.A 2025/2026.
This quantitative study, employing a one-shot case study design, evaluates the effectiveness of problem-based learning (PBL) on students’ critical thinking skills and mathematical literacy in the topic of arithmetic sequences and series for 10th-grade students at SMK Telkom 1 Medan during the 2025/2026 academic year. The sample was randomly selected from two classes (X RPL 1 and X RPL 2) out of a total population of five classes. Data were collected through tests, questionnaires, and observations that had been validated for validity and reliability, then analyzed descriptively using frequency distribution tables and criteria for the achievement of learning objectives. The results showed that all indicators of effectiveness namely, the systematic nature of instruction, teacher communication, student responses, student activities, and the achievement of learning objectives were met. Thus, the PBM was deemed effective in improving critical thinking skills and mathematical literacy in the subject matter, with the level of effectiveness falling into the high category.
Efektivitas Tipe Student Teams Achievement Devisions Terhadap Pemahaman Konsep dan Kemampuan Berpikir Tingkat Tinggi Dalam Pembelajaran Sistem Persamaan Linier Tiga Variabel Kelas X SMK Swasta Parulian 1 Medan T. A. 2025/2026
This study aims to determine the effectiveness of the Student Teams Achievement Divisions (STAD) method on conceptual understanding and higher-order thinking skills in the teaching of systems of linear equations with three variables for 10th-grade students at Parulian 1 Private Vocational High School, Medan, Academic Year 2025/2026. The study population consists of all 10th-grade students, and the sample comprises 60 10th-grade students. The sampling technique used was Purposive Random Sampling. The instruments used were tests, questionnaires, and observations. The research results, as seen from the indicators of learning effectiveness, were met: the learning structure was in the “good” category, teacher communication was in the “good” category, student response was in the “good” category, student activity was in the “good” category, and learning achievement was in the “achieved” category. The research results indicate that the Student Teams Achievement Divisions (STAD) learning method is effective in enhancing conceptual understanding and higher-order thinking skills.
Efektivitas Pembelajaran Berbasis Web Wolfram Alpha Terhadap Kemampuan Pemecahan Masalah Matematis Siswa Pada Materi Fungsi Kuadrat Di Kelas X SMK Swasta Imelda Medan T.A 2025/2026
This study aims to determine the effectiveness of Wolfram Alpha-based web learning on students’ mathematical problem-solving skills in quadratic functions in Grade X at Imelda Private Vocational High School, Medan, Academic Year 2025/2026. This is a pre-test post-test control groupdesign study with the research population consisting of students in Grade X at Imelda Private Vocational High School, Medan. The research sample was selected using simple random sampling, resulting in the experimental class MP1 and the control class X-TKJ4. After being subjected to different treatments, the data were analyzed using inferential and descriptive analysis. The results of the analysis showed that the data on conceptual understanding met the prerequisite tests and were normally distributed, homogeneous, and linear. The t-test (α = 0.05) revealed a significant difference between the experimental and control classes. The results of the study showed that students’ mathematical problem-solving skills met the effectiveness indicators, leading to the conclusion that web-based learning is effective in enhancing students’ mathematical problem-solving skills.
Efektivitas Pemanfaatan GeoGebra Dengan Tipe STAD Terhadap Pemahaman Konsep Matematis Siswa Pada Materi Matriks di Kelas XI SMA Negeri 14 Medan T.A 2025/2026
This study aims to examine the effectiveness of using GeoGebra based on the Student Teams Achievement Divisions (STAD) model in improving students’ understanding of mathematical concepts in the matrix curriculum for XI-grade students at State SMA Negeri 14 Medan T.A 2025/2026. The method used was quantitative research with a quasi-experimental design. The study population consisted of 11th-grade students, with a sample of 69 students from classes XI 4 and XI 5 selected through purposive sampling. The instruments used included an essay test, a questionnaire, and an observation sheet. The research results indicate that all five indicators of effectiveness were met: (1) the instructional structure was in the “good” category, based on evaluations by two out of three observers, who assigned scores of 86 and 87, respectively; (2) teacher communication was good, with two observers assigning a score of 34; (3) student response was good, as evidenced by 57 out of 69 students falling within the “good” frequency range; (4) student activity was good, with 62 students in the good category according to three observers; (5) learning achievement was complete without remedial instruction, with 58 students (91.3%) scoring in the 66–85% range. Thus, the use of the STAD method with GeoGebra is effective in enhancing students’ understanding of mathematical concepts.
Efektivitas Media Pembelajaran GeoGebra Terhadap Kemampuan Pemahaman Konsep dan Pemecahan Masalah Matematis Siswa Pada Materi Sistem Persamaan Linear Tiga Variabel Di Kelas X SMK Swasta Budi Setia Sunggal T.A 2025/2026
This study aims to determine the effectiveness of the GeoGebra learning medium on students’ conceptual understanding and mathematical problem-solving skills regarding the topic of systems of linear equations with three variables in the 10th grade at Budi Setia Private Vocational High School. This study employed a quantitative method using a quasi-experimental design in the form of a pretest-posttest-only control group design. The study population consisted of all Grade 10 students at Budi Setia Private Vocational High School, comprising 5 classes. The sample was determined using purposive sampling, resulting in Class X TKR as the experimental class (30 students) and Class X MP as the control class (30 students). The research instrument consisted of an essay test that had been validated for validity and reliability. Pre-test and post-test data were analyzed using normality tests, homogeneity tests, t-tests, N-Gain, and Effect Size. Calculations for the experimental class showed an average score of 77.80 for mathematical concept comprehension, while the control class had an average score of 68.07. Calculations for the experimental class showed an average score of 73.63 for mathematical problem-solving ability, while the control class had an average score of 66.73. Based on the t-test results, a significance value of 0.001 < 0.05 was obtained, so the null hypothesis was rejected. The GeoGebra learning tool was found to be effective because it was proven to significantly improve student learning outcomes, as evidenced by a comparison of average post-test scores between classes that used the tool and those that did not. In terms of mathematical concept comprehension, students in the experimental class taught using GeoGebra achieved an average score of 77.80, far surpassing the control class, which averaged only 68.07. This advantage was also consistently evident in the mathematical problem-solving ability indicator, where the experimental class recorded an average score of 73.63, while the control class lagged behind at 66.73. The conclusion of this study is that the GeoGebra learning medium is effective in enhancing students’ mathematical conceptual understanding and problem-solving abilities regarding the topic of systems of linear equations with three variables in Grade 10 at Budi Setia Private Vocational High School.
Efektivitas Pembelajaran Berbasis Masalah Terhadap Kemampuan Berpikir Tingkat Tinggi Siswa pada Materi SPLTV Kelas X SMA
This study was conducted to determine the effectiveness of implementing problem-based learning (PBL) on students’ higher-order thinking skills regarding SPLTV material in 10th grade at State High School 17 Medan during the 2025/2026 academic year. This study is a quantitative study using a one-shot case study design. The population in this study consists of all 10th-grade students at State High School 17 Medan, comprising 9 classes, and the sample consists of classes 10-8 and 10-9, selected using purposive sampling. The instruments used in this study include tests, questionnaires, and observation sheets, all of which were first tested for validity and reliability. The effectiveness of learning was assessed based on effectiveness indicators, namely the systematic structure of instruction, teacher communication, student response, student activity, and criteria for the achievement of learning objectives. Data from each indicator instrument in this study were analyzed using descriptive analysis with the aid of frequency distribution tables and tables of criteria for the achievement of learning objectives. The results of this study indicate that all five indicators—namely, the systematic nature of learning—met the “good” category; teacher communication met the “good” category; student responses and student activities met the “good” category; and learning objectives were achieved. Based on these five indicators, the effectiveness of learning also met the “good” criteria. Consequently, problem-based learning aimed at developing higher-order thinking skills in the SPLTV curriculum is effective and falls into the high category.
Pengaruh Pendekatan Deep Learning Terhadap Kemampuan Pemecahan Masalah Matematika di Kelas XI SMK
This study was motivated by the low level of mathematical problem-solving skills among students at the Jambi Medan Private Vocational High School, which is attributed to the use of conventional teaching methods that do not sufficiently encourage active engagement and deep understanding. The objective of this study is to determine the influence and magnitude of the impact of the Deep Learning approach on the mathematical problem-solving skills of 11th-grade students in matrix material. The research method used is a Quasi-Experiment with a Post-test Only Control Group Design. The research population includes all 11th-grade students, with a sample selected through Cluster Random Sampling consisting of class XI MPLB 2 as the experimental class and XI MPLB 1 as the control class. Data analysis results showed that the average post-test score of the experimental class (72.62) was higher than that of the control class (46.40). Based on the t-test, a significance value of 0.000 < 0.05 was obtained, indicating a significant effect. The Effect Size test using Cohen’s D yielded a value of 3.29, which falls under the “very large” criterion. Thus, the Deep Learning approach is effective in improving students’ mathematical problem-solving skills at the Jambi Medan Private Vocational High School.
Pengembangan Media Pembelajaran Berbasis Etnomatematika dalam Tradisi Nyadran pada Materi Bangun Ruang Sisi Lengkung untuk Meningkatkan Kemampuan Pemahaman Konsep
This study aims to develop ethnomathematics-based learning media in the Nyadran tradition on the material of curved sided solids to improve students' conceptual understanding. This research is a research and development (R&D) using the ADDIE model which includes the stages of Analysis, Design, Development, Implementation, and Evaluation. The limited trial subjects were 16 grade IX students. The research instruments included expert validation sheets to measure the validity of the media, student practicality questionnaires to measure the level of practicality of the media, and pre-test and post-test questions to measure the effectiveness of the media. The results showed that the developed learning media met the criteria of very valid with a percentage of 95% based on the assessment of media experts and 91% based on the assessment of material experts. The results of the practicality test obtained a percentage of 89% with a very practical category. Meanwhile, the results of the effectiveness test showed an N-Gain value of 0.5 which is in the medium category, this indicates an increase in students' conceptual understanding after using learning media. Based on these results, ethnomathematics-based learning media in the Nyadran tradition meets the criteria of being valid, practical, and effective in improving the ability to understand mathematical concepts.
Implementasi model kooperatif tipe STAD untuk meningkatkan hasil belajar matematika
This study is prompted by the low level of mathematics learning achievement in class IX.10 students at MTsN 1 Kota Padang, due to insufficient student activity and engagement within the teaching and learning process. This study is conducted to enhance students’ mathematics learning achievement through the application of the Student Teams Achievement Divisions (STAD) cooperative learning model. This study adopts a Classroom Action Research (CAR) design implemented in two cycles, each comprising planning, action, observation, and reflection stages. This study involved 30 students from class IX.10 in the odd semester of the 2025/2026 academic year. The data collection tools comprised observation sheets for monitoring teacher and student activities and learning outcome tests administered at the end of each cycle. The results demonstrated a meaningful improvement in students’ learning outcomes. In the pre-cycle, the average student score was only 74.06 with a low classical completeness percentage. After implementing the STAD model, the average learning outcome increased to 78.50 in Cycle I and reached a higher increase of 82.40 in Cycle II, with the classical completeness level meeting the success criteria. This improvement was also accompanied by changes in student behavior, becoming more active, enthusiastic, and responsible in group work. The findings suggest that the application of the STAD cooperative learning model is effective in improving mathematics learning outcomes for class IX.10 students at MTsN 1 Kota Padang.
Analisis Sistem Antrian Multi Chanel-Multi Phase pada Pelayanan Pembuatan Kartu Tanda Penduduk dengan Model Antrian (M/M/C):(GD/ ) di Disdukcapil Labuhanbatu Selatan
Public administrative services require speed, effectiveness, and efficiency to meet community expectations. At the Civil Registration Office of Labuhanbatu Selatan Regency, the issuance of identity cards (KTP) often experiences long queues, especially on specific days such as the beginning of the week and after major holidays. This study aims to analyze the performance of the current queuing system and determine the most appropriate model to improve service quality. A qualitative case study approach was used, supported by primary data obtained through direct observation of customer arrivals and service duration over five working days. Queueing theory was applied to test the distribution of arrivals and service times as well as evaluate system performance indicators. The results show that arrival patterns follow a Poisson distribution while service times follow an exponential distribution. The appropriate model for the system is the Multi Channel–Multi Phase (M/M/C):(GD/) queue. The highest utility rate occurred at entrance 2, reaching 30%, yet the average waiting time remained low at 0.18–0.24 minutes. Thus, the current queuing system is considered effective and capable of managing service demand without causing critical congestion.
Efektivitas Model Pembelajaran Creative Problem Solving Berbantuan Alat Peraga Manipulatif Terhadap Hasil Belajar Siswa SMP
The study was conducted to determine the effectiveness of the Creative Problem Solving learning model assisted by manipulative teaching aids on the learning outcomes of junior high school students. The research method used is quantitative with a research design in the form of a posttest-only control design. The study was conducted at SMP Negeri 1 Bangsri with sampling using the cluster random sampling technique on class VIII students. The sample consisted of two class, namely class VIII C as an experimental class tha would be given treatment in the form of the application of the Creative Problem Solving learning model assisted by manipulative teaching aids and class VIII D as a control class that would be given treatment in the form of the application of conventional learning models. Data collection techniques in the form of tests given after the treatment. Based on the effectiveness indicators, there are three assessments in this study, namely the difference in learning outcomes of the experimental class and the control class, a better comparative test, and the completeness of learning outcomes in the experimental class. The final data were analyzed using the Independent Sample T-test that there were difference in learning outcomes of students in the experimental class and the control class. Then for the comparative test of the experimental class and the control class, the One-Party T-test formula was used by showing that the experimental class was better than the control class. The learning outcomes of the experimental class reached an average value of 78 with 25 students achieving individual completeness and 5 students who did not complete it. So it can be said that the completeness of student learning in the experimental class classically can be said to be complete because it achieved completeness of 83%.
Peramalan Pertambahan Pasien Rawat Inap dengan Menggunakan Model Support Vector Regression (SVR)
This research aims to see the prediction of the number of patients at the Medan Haji General Hospital in 2022-2023. A hospital is a health service institution that provides complete individual health services, providing inpatient, outpatient and emergency services. In implementing health services, hospitals must maintain medical records to support services and process patient information. This hospital serves all types of groups around North Sumatra. Prediction is the process of forecasting future demand which will include demand in terms of quantity, quality, time and location to meet demand for goods, services or the environment. This research uses the Support Vector Regression (SVR) method. Support Vector Regression (SVR) is a learning system that applies linear functions to a hypothetical feature space with high dimensions. The SVR algorithm concept can produce good forecasting values because SVR has the ability to solve overfitting problems. Overfitting is data behavior during the training phase that results in almost perfect prediction accuracy. Based on the results of data processing using the Support Vector Regression (SVR) method, it can be concluded that the application of the forecasting method in predicting the number of inpatient visits at RSU Haji Medan using the SVR method is carried out by determining predictions using three kernels, namely the RBF, linear and polynomial, then determine the best MSE and RMSE values to then be used as the best kernel. The results of forecasting inpatient visits using the SVR method show that the predicted results have decreased from the previous actual data which is not much different, but the predicted number of inpatients is almost the same every month and experiences insignificant decreases and increases. Keywords: Prediction; Support Vector Regression (SVR).
Efektivitas Model Pembelajaran Discovery Learning dan Problem Based Learning (PBL) Berbantuan GeoGebra Terhadap Kemampuan Pemecahan Masalah Siswa
This study aims to determine the effectiveness of Discovery Learning and Problem Based Learning (PBL) learning models assisted by Geogebra on students' problem solving skills. The research design used is True Experimental Design with the form of Posttest Only Control Design. The research population consisted of all eighth-grade students at MTs Matholiul Anwar Sarimulyo. The sample was taken using cluster random sampling, with three classes selected: experiment class I using GeoGebra-assisted discovery learning, experiment class II using GeoGebra-assisted problem-based learning, and the control class using conventional learning. Data analysis was conducted in several stages, including a prerequisite test covering normality and homogeneity tests, hypothesis testing using one-way analysis of variance (One Way ANOVA) to compare the average problem-solving abilities between groups, post-hoc testing using the Scheffe method if significant differences were found, simple linear regression testing to examine the effect of activity on problem-solving abilities, and analysis of student learning completeness individually and classically. The results showed that: (1) There is a difference in the average problem solving ability of students with Geogebra-assisted Discovery Learning model, Geogebra-assisted Problem Based Learning model and Conventional model. (2) The problem solving ability of students using the Geogebra-assisted Discovery Learning model is better than the problem solving ability of students using the conventional model. (3) The problem solving ability of students using the Geogebra-assisted Problem Based Learning model is better than the problem solving ability of students using the conventional model. (4) There is no difference in the average problem solving ability of students using the Discovery Learning model and Geogebra-assisted Problem Based Learning. (5) There is an effect of activeness on the problem solving ability of students using the Discovery Learning and Problem Based Learning models assisted by Geogebra. (6) Students with Geogebra-assisted Discovery Learning and Geogebra-assisted Problem Based Learning learning models have been completed individually and have not been completed classically.