Interval: Indonesian Journal of Mathematical Education
The Interval: Indonesian Journal of Mathematical Education accepts high-quality manuscripts resulting from research projects within the scope of mathematics education, which include Mathematics Ability, Mathematics Education, and Design/Development Research in Mathematics Education. Frequency: 3/year (April, August and December)
Authors who publish with this journal agree to the following terms: Authors retain copyright and acknowledge that the Interval: Indonesian Journal of Mathematical Education is the first publisher licensed under a Creative Commons Attribution 4.0 International License. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges and earlier and greater citation of published work.
Mathematical Conceptual Understanding in Inside-Outside Circle Learning: A Quasi-Experimental Study
Purpose of the study: This study aimed to investigate the effect of the Inside-Outside Circle (IOC) cooperative learning method on students' mathematical conceptual understanding and to determine whether the method provides better learning outcomes than conventional instruction among junior high school students. Methodology: This study employed a quantitative approach using a quasi-experimental method with a randomized posttest-only control group design. The participants consisted of seventh-grade students of SMP IT Al-Qur'aniyyah. Data were collected using an essay test of mathematical conceptual understanding. Descriptive statistics, normality tests, homogeneity tests, and independent samples t-tests were performed using IBM SPSS Statistics software. Main Findings: The findings revealed that students taught through the Inside-Outside Circle cooperative learning method achieved higher mathematical conceptual understanding scores than those receiving conventional instruction. Statistical analysis indicated a significant difference between the experimental and control groups, demonstrating that the IOC method effectively improved students' mathematical conceptual understanding and promoted more meaningful mathematics learning experiences. Novelty/Originality of this study: This study specifically emphasizes mathematical conceptual understanding as the primary outcome variable within the implementation of the Inside-Outside Circle method. Unlike previous studies that mainly focused on learning achievement or communication skills, this research provides empirical evidence from an Islamic junior high school context, thereby enriching current knowledge regarding cooperative learning in mathematics education.
Copyright (c) 2026 Wiwi Lasmanah, Yuli Hermawati https://creativecommons.org/licenses/by/4.0
The Effectiveness of Monopoly Mathematics Games in Improving Fifth-Grade Students' Learning Outcomes: A Quasi-Experimental Study
Purpose of the study: This study aimed to investigate the effectiveness of Monopoly Mathematics Games in improving fifth-grade students' mathematics learning outcomes. It also sought to determine whether students taught using the game achieved better performance than those receiving conventional instruction. Methodology: This study employed a quasi-experimental design involving experimental and control groups at SD Islam Darul Mu'minin. The sample consisted of 50 fifth-grade students selected through simple random sampling. Data were collected using essay tests, while instrument validity and reliability were examined. Statistical analyses, including normality, homogeneity, and independent samples t-tests, were conducted using IBM SPSS Statistics version 22.0. Main Findings: The findings indicated that students taught through Monopoly Mathematics Games achieved higher mathematics learning outcomes than those receiving conventional instruction. The experimental group obtained a mean score of 75.64, whereas the control group achieved 67.00. Statistical testing revealed a significant difference between the two groups with a significance value of 0.008. Cognitive achievement in the experimental group was also higher across Bloom’s taxonomy levels. Novelty/Originality of this study: The originality of this study lies in the development of a modified Monopoly Mathematics Game designed specifically for elementary mathematics learning. The game integrates knowledge cards, opportunity cards, help cards, and mathematical problem-solving activities. Additionally, this study evaluates students’ cognitive achievement based on Bloom’s taxonomy, thereby providing broader evidence regarding the effectiveness of game-based learning in mathematics education.
Copyright (c) 2026 Simbolon Lamhot, Muhammad Budi Wijaya https://creativecommons.org/licenses/by/4.0
Cultivating Mathematics Learning Autonomy through Resource-Based Learning: Insights from Classroom Action Research
Purpose of the study: This study aimed to examine the effectiveness of Resource-Based Learning in cultivating mathematics learning autonomy among junior high school students and to identify its contribution to improving students’ mathematics learning outcomes through classroom action research. Methodology: This study employed Classroom Action Research based on the Kemmis and McTaggart model involving planning, acting, observing, and reflecting stages. Participants were 18 seventh-grade students. Data were collected using observation sheets, interview guides, documentation, mathematics achievement tests, and a mathematics learning autonomy questionnaire validated through content validity and Cronbach’s Alpha reliability. Descriptive quantitative and qualitative analyses were applied. Main Findings: The implementation of Resource-Based Learning increased students’ mathematics learning autonomy in terms of initiative, self-confidence, and responsibility. Students’ mathematics achievement also improved across cycles. Learning activities became more active through the utilization of worksheets, peer tutors, manipulative media, and library resources. Limited learning resources were identified as a factor affecting instructional effectiveness. Novelty/Originality of this study: This study presents a comprehensive integration of Resource-Based Learning with multiple learning resources, including peer tutors, worksheets, manipulative media, and library utilization, to foster mathematics learning autonomy. The findings provide empirical evidence regarding the role of diverse learning resources in developing autonomous learning habits and enhancing mathematics achievement in classroom action research settings.
Copyright (c) 2026 Siti Fadiyatun Nikmah, Edo Prancis Kuno https://creativecommons.org/licenses/by/4.0
Fostering Mathematics Learning Engagement through Differentiated Teaching: Evidence from Classroom Action Research
Purpose of the study: This study aimed to examine the effectiveness of differentiated teaching in fostering mathematics learning engagement and improving mathematics achievement among secondary school students with diverse academic abilities through the implementation of classroom action research in a collaborative learning environment. Methodology: This study employed a classroom action research design conducted in two cycles involving 35 tenth-grade students of Madrasah Aliyah Pembangunan UIN Jakarta. Data were collected using mathematics learning engagement observation sheets, formative tests, interview guidelines, field notes, and documentation. Descriptive statistics and qualitative coding techniques were used, while data trustworthiness was established through triangulation procedures. Main Findings: The findings showed that students' mathematics learning engagement increased from 67.61% in Cycle I to 81.11% in Cycle II. The mean score improved from 5.39 to 6.76, while learning mastery increased from 34.3% to 63.0%. Standard deviation decreased from 2.57 to 1.50. Peer tutoring, handouts, quizzes, challenge tasks, and reward systems supported active participation and improved mathematics achievement. Novelty/Originality of this study: The novelty of this study lies in integrating differentiated teaching with cooperative learning mechanisms supported by peer tutoring, handouts, challenge tasks, quizzes, and reward systems to foster mathematics learning engagement. Unlike previous studies emphasizing achievement outcomes, this study highlights learning engagement as the primary focus while addressing students with diverse academic abilities.
Copyright (c) 2026 Wandari Kameilia, Rani Sundari https://creativecommons.org/licenses/by/4.0
Development of Learning Media Using PMRI-Based Scratch Applications for Statistics Material for Class VIII Junior High School
Purpose of the study: This study aims to develop interactive learning media using the Scratch application based on the Indonesian Realistic Mathematics Approach (PMRI) for Statistics material for eighth-grade junior high schools. It also examines the validity, practicality, and effectiveness of the developed media in mathematics learning.. Methodology:This study used the ADDIE (Analysis, Design, Development, Implementation, and Evaluation) model to develop Scratch-based learning media based on the Indonesian Realistic Mathematics Education (PMRI) approach for Statistics. The instruments used consisted of expert validation sheets, teacher and student response questionnaires, and pretest-posttest learning achievement tests. Data were analyzed using descriptive quantitative methods with a five-point Likert scale. Main Findings: The developed Scratch-based PMRI learning media on Statistics achieved a material expert validity score of 0.88, a media expert score of 0.90, and a language expert score of 0.83. Teacher and student responses indicated the media was highly practical. Pretest and posttest results showed improved student learning outcomes, indicating that the media was valid, practical, and potentially effective for mathematics learning. Novelty/Originality of this study: The novelty of this research lies in the integration of the Scratch application with the PMRI approach in developing interactive learning media for Statistics. The developed media incorporates real-life contexts and student-centered learning activities, thereby supporting more meaningful and engaging mathematics learning and enhancing student engagement.
Copyright (c) 2026 Shelly Gustia Putri, Dona Ningrum Mawardi, Maria Luthfiana https://creativecommons.org/licenses/by/4.0
An Analysis of Students' Mathematical Connections from an Ethnomathematical Perspective
Purpose of the study: This study aimed to analyze students' mathematical connection ability from an ethnomathematical perspective. The study focused on identifying students' ability to connect mathematical concepts with daily life and cultural contexts embedded in Sundanese culture. Methodology: This study employed a survey research design. Data were collected using an ethnomathematics-based mathematical connection test and teacher interviews. Cluster random sampling was used to select 120 eighth-grade students from three junior high schools in Cibeunying Kidul, Bandung, Indonesia. Descriptive statistical analysis was applied to analyze the collected data. Main Findings: Findings revealed that students' mathematical connection ability from an ethnomathematical perspective was generally categorized as low. Connections with daily life achieved a higher percentage than connections among mathematical topics, although both indicators remained low. Ethnomathematical contexts derived from Sundanese culture provided meaningful situations for identifying students' mathematical connections. Novelty/Originality of this study: Novelty of this study lies in examining students' mathematical connection ability from an ethnomathematical perspective rather than merely implementing ethnomathematics in learning. Cultural elements were used as analytical perspectives to reveal mathematical connections, contributing to the development of culturally responsive mathematics education and extending existing knowledge regarding mathematical connections.
Copyright (c) 2026 Dian Lestari, Sri Sukwantini https://creativecommons.org/licenses/by/4.0
Adaptation of Mathematics Learning Models for Deaf Students through a Visual Communication Approach: A Case Study
Purpose of the study: This study aimed to explore the adaptation of mathematics learning models for deaf students through a visual communication approach. Particular attention was given to instructional planning, classroom implementation, communication practices, learning media, and students’ learning experiences within the context of mathematics education for students with hearing impairments. Methodology: A qualitative approach with a case study design was employed. Participants consisted of one mathematics teacher and six eleventh-grade deaf students selected through purposive sampling. Data were collected using classroom observations, semi-structured interviews, and documentation. Data analysis followed the Miles and Huberman interactive model involving data reduction, data display, and conclusion drawing. Main Findings: Results indicated that mathematics learning adaptation was supported by visual communication strategies, including lip movements, hand gestures, facial expressions, repeated explanations, and the Maternal Reflective Method. Various concrete learning media facilitated students’ understanding of mathematical concepts. Positive student responses and active participation were observed during classroom activities. Learning outcomes demonstrated satisfactory achievement despite differences in communication abilities and mathematical competencies among students. Novelty/Originality of this study: Novelty of this study lies in emphasizing visual communication as an integral component of mathematics learning adaptation for deaf students. Unlike previous studies focusing mainly on learning outcomes, the present study highlights how communication strategies are embedded within instructional planning, classroom interaction, and the use of learning media to support meaningful mathematics learning experiences.
Copyright (c) 2026 Nining Sumarni, Radika Situmorang https://creativecommons.org/licenses/by/4.0
An Exploratory Study of Students’ Mathematical Problem-Solving Ability Based on Wankat and Oreovocz Theory
Purpose of the study: This study aims to explore students’ mathematical problem-solving ability based on the Wankat and Oreovocz theory by identifying how students perform across each stage of the problem-solving process in order to provide a comprehensive description of their abilities. Methodology: This study employed a qualitative descriptive approach using purposive sampling, involving six students from class VII E at SMP Negeri 19 Bandar Lampung. Data were systematically collected through observation, written essay tests, and semi-structured interviews, and analyzed using data reduction, data display, and conclusion drawing with triangulation techniques for validation purposes. Main Findings: The results show that most students achieved high problem-solving ability, with 59.26% in the excellent category and 25.93% in the good category. Students performed best at the motivation stage (“I Can”) but showed lower performance in planning, evaluation, and generalization stages. High-performing students completed all stages systematically, while lower-performing students experienced difficulties beyond initial stages, especially in selecting appropriate strategies and verifying solutions. Novelty/Originality of this study: This study offers a detailed stage-based analysis of students’ mathematical problem-solving ability using the Wankat and Oreovocz framework, focusing on students’ actual performance rather than instructional strategies. It provides new insights into specific difficulties at each stage, particularly in planning, and contributes to advancing knowledge on how structured problem-solving frameworks can be applied to analyze students’ cognitive processes.
Copyright (c) 2026 Dini Rahayu, Tan Wen Hsien
Development of a Didactical Design Based on Research and Development for Teaching Cones and Cylinders to Improve Junior High School Students’ Conceptual Understanding
Purpose of the study: This study aims to develop a didactical design based on Research and Development to improve junior high school students’ conceptual understanding of cones and cylinders by addressing their learning obstacles through structured instructional materials. Methodology: This study employed a Research and Development approach adapted from Borg and Gall and Sugiyono models. The research involved eighth-grade students, using interviews, observation sheets, validation instruments, and questionnaires. Data were analyzed using descriptive qualitative and quantitative methods with Likert scale scoring. Expert validation involved mathematics education lecturers and teachers. Small-scale and large-scale trials were conducted to evaluate the developed module’s feasibility and effectiveness in mathematics learning on cones and cylinders. Main Findings: The developed didactical design module showed significant improvement after expert validation and revision. The results indicated very good criteria in content quality, language clarity, and media design. Student responses in small-scale and large-scale trials reached 90–94%, categorized as very good. The module effectively reduced learning obstacles and improved students’ conceptual understanding of cones and cylinders. The findings confirm that the instructional material is valid, practical, and effective for classroom implementation. Novelty/Originality of this study: This study develops a didactical design module integrating learning obstacle analysis specifically for cones and cylinders using an R&D approach. The innovation lies in its structured adaptation of students’ cognitive difficulties into instructional design. It contributes a context-specific mathematics learning module that enhances conceptual understanding and provides a practical model for developing geometry-based teaching materials.
Copyright (c) 2026 Nurul Husna, Nurhasanah Nurhasanah
Examining the Effectiveness of Multiple Representation (SiMaYang) Learning Model on Students’ Mathematical Conceptual Understanding: The Role of Self-Efficacy
Purpose of the study: This study aims to examine the effectiveness of the Multiple Representation (SiMaYang) learning model on students’ mathematical conceptual understanding and to determine the role of students’ self-efficacy in influencing differences in conceptual understanding outcomes. Methodology: This study employed a quantitative approach with a quasi-experimental method using a 2×3 factorial design. Data were collected using essay tests and Likert-scale questionnaires. Statistical analysis included Liliefors normality test, Bartlett homogeneity test, independent t-test, and two-way ANOVA with unequal cells, followed by Scheffé test using statistical software. Main Findings: Results showed that the SiMaYang learning model produced higher mathematical conceptual understanding than conventional learning. Self-efficacy significantly affected students’ conceptual understanding, where high self-efficacy students performed better than others. No interaction effect was found between learning model and self-efficacy. SiMaYang model consistently improved understanding across all self-efficacy levels, indicating independent contributions of instructional model and affective factors. Novelty/Originality of this study: This study integrates cognitive and affective aspects by simultaneously examining the effect of the SiMaYang learning model and self-efficacy within a single analytical framework. It provides a more comprehensive understanding of learning effectiveness by using factorial design analysis, offering new insights into how instructional strategies and internal beliefs independently influence mathematical conceptual understanding.
Copyright (c) 2026 CJ Scholts, Wulan Agus Setyaningrum
Comparative Effectiveness of AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education Approaches on Students’ Mathematical Reasoning Ability
Purpose of the study: This study aims to compare the effectiveness of the AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education (RME) approaches in improving students’ mathematical reasoning ability at the senior high school level. Methodology: This study employed a quantitative quasi-experimental method with a posttest-only design, using essay-based test instruments, interviews, observations, and documentation; data were analyzed using descriptive statistics, Liliefors normality test, F-test homogeneity, and independent sample t-test with statistical calculation procedures. Main Findings: The results showed a significant difference between the two approaches, where the AIR approach produced higher mean scores than the RME approach in students’ mathematical reasoning ability. Statistical testing indicated tvalue > ttable, confirming that AIR is more effective in enhancing students’ reasoning skills compared to RME. Novelty/Originality of this study: This study provides a direct comparative analysis between AIR and RME approaches within a single quasi-experimental framework, focusing specifically on mathematical reasoning ability and offering empirical evidence to support instructional decision-making in mathematics education.
Copyright (c) 2026 Sudadio Sudadio, Dave Kalberg
Exploring Sociomathematical Norms Based on Students’ Interest in Mathematics Learning: A Qualitative Study at the Junior High School Level
Purpose of the study: This study aims to explore sociomathematical norms based on students’ interest in mathematics learning at the junior high school level, and to identify how different levels of learning interest influence students’ interaction, participation, and communication during mathematics learning activities. Methodology: This study used a descriptive qualitative approach with purposive sampling involving six students. Instruments included Likert-scale questionnaires, observation sheets, and semi-structured interview guidelines. Data were collected through observation, interviews, and questionnaires, and analyzed using the Miles and Huberman model with triangulation techniques. Main Findings: Students mostly show good sociomathematical norms, with the majority categorized at a moderate level of learning interest. Students with high interest demonstrate very good participation and communication, while those with moderate interest show consistent but less optimal interaction. Students with low interest tend to be passive and have difficulty expressing mathematical ideas clearly. Novelty/Originality of this study: This study integrates sociomathematical norms and learning interest in a single qualitative analysis, focusing on students’ real classroom behavior. It provides a deeper understanding of how different levels of interest shape interaction and communication, offering a more comprehensive perspective compared to previous studies that examined these aspects separately.
Copyright (c) 2026 Afifah Fitria, Elijah Wilsher
Design and Evaluation of a Guided Discovery-Based Calculus Module on Derivatives with Islamic Values Integration
Purpose of the study: This study aims to develop and evaluate a guided discovery-based calculus module on derivatives integrated with Islamic values to support students’ conceptual understanding, independent learning, and spiritual awareness in higher education mathematics learning. Methodology: This study employed a Research and Development (R&D) method using the 4D model (define, design, develop, disseminate). Data were collected through questionnaires, validation sheets, and documentation. Instruments included expert validation sheets and student response questionnaires. Data were analyzed using descriptive quantitative and qualitative techniques with a Likert scale (1–4). Main Findings: Results show that the module achieved valid criteria across material, media, and Islamic values aspects after revision. Material validation increased to 3.75, media design to 3.8, and Islamic values to 4.0. Limited trial results indicated an average score of 3.56, categorized as very attractive. These findings confirm that the module is feasible and well-received by students. Novelty/Originality of this study: This study presents an integrative calculus module combining guided discovery learning with Islamic values on derivative topics. It simultaneously addresses cognitive and spiritual aspects within a single instructional design. This approach provides a holistic learning resource and contributes to advancing mathematics education by integrating pedagogical strategy and value-based learning.
Copyright (c) 2026 Birgita Tyas Suryandari, Susan No Kim
Comparative Effectiveness of Learning Starts with a Question and Question Students Have Strategies on Junior Secondary Students’ Mathematics Achievement
Purpose of the study: This study examined the comparative effectiveness of two question-based active learning strategies, namely Learning Starts with a Question and Question Students Have, on junior secondary students’ mathematics achievement. Methodology: A quasi-experimental non-equivalent control group design was employed involving two Grade Eight classes. One class was taught using the Learning Starts with a Question strategy and the other using the Question Students Have strategy. Mathematics achievement was measured using validated essay tests administered as pretest and posttest. Data were analysed using descriptive statistics and independent samples t-test after normality and homogeneity assumptions were met. Main Findings: Both strategies improved students’ mathematics achievement. The class taught using the Learning Starts with a Question strategy obtained a higher posttest mean score of 84.16 compared to the class taught using the Question Students Have strategy with a mean score of 79.72. Independent samples t-test indicated a significant difference between the two classes with a probability value of 0.009. The increase in scores from pretest to posttest was also higher in the Learning Starts with a Question class, indicating greater improvement in mathematics learning outcomes. Novelty/Originality of this study: The Learning Starts with a Question strategy is more effective than the Question Students Have strategy in improving junior secondary students’ mathematics achievement. Initiating mathematics instruction with student-generated questions enhances cognitive readiness and supports conceptual understanding.
Copyright (c) 2025 Nur Akbar M, Abnaul Amir Moncobalang, Norma Norma
A Numerical Study of Bracketing Root-Finding Methods for Nonlinear Equations: Applications to Break-Even Point Determination
Purpose of the study: The purpose of this study is to compare the results of the Bisection Method, the Regula Falsi Method and the Secant Method in completing Break Even analysis. Methodology: The research method used is an applied method. The research location is the library of Alauddin State Islamic University, Makassar. The research procedure used by the researcher is to compare the results of the Bisection Method, the Regula Falsi Method, and the Secant Method in solving Break-Even Analysis. Main Findings: The results show that the secant method is an efficient method for conducting break-even analysis. This is demonstrated by the error value obtained at the end of the iteration process, which shows the smallest error value. In other experiments, the secant method also showed fewer iterations than other methods. Novelty/Originality of this study: This research can be used as reference material for readers who want to compare the bisection method and the falsi-regularization method. Furthermore, the researchers use the results as a means of evaluating the ability to apply theories in numerical courses.
Copyright (c) 2025 Ismuniyarto Ismuniyarto, David Pinheiro, El Hadji Lamine Sokhna
Exploring Ethnomathematics in Traditional Dance Movements: A Study of the Sigeh Penguten Dance of Lampung, Indonesia
Purpose of the study: This study aims to determine ethnomathematics activities and mathematical concepts applied in various Sigeh Pengeten dance movements. Methodology: The type of research used in this study is qualitative research with an ethnographic approach. Data were obtained through interviews, observation, and documentation. The research instruments consisted of the primary instrument, the researcher herself, and supporting instruments in the form of interview guidelines, observation sheets, and documentation tools. Method and source triangulation were used to validate the data. Main Findings: The results of this study indicate that in each sigeh penguten dance movement, counting activities are implemented by adjusting the fast or slow music beat in the form of a repetition of 1 x 8 counts. Some sigeh penguten dance movements implement measuring activities when the movement moves to adjust to the next floor pattern change. The concept of one-dimensional geometry is depicted from the movement that forms a straight line floor pattern. The concept of two-dimensional geometry is depicted from the shape of the floor pattern in the form of triangles, rectangles, squares, trapezoids, and circles. Reflection and rotation geometric transformations. The conclusion of this study is that in the sigeh penguten dance movements there are mathematical activities and mathematical concepts. Novelty/Originality of this study: This research can be used as input for educators to make ethnomathematics an alternative in the mathematics learning process, so that it can help improve learning outcomes and students' interest in mathematics learning.
Copyright (c) 2025 Riana Desmawati, Titik Nurhayati, Fatimatuz Zahro Ulbana, Raden Hari W Jayaningrat
Exploring Mathematical Concepts in Rebana Art: An Ethnomathematical Approach for Junior High School Learning
Purpose of the study: This study aims to identify ethnomathematical concepts in rebana art related to one-dimensional, two-dimensional, and three-dimensional geometry, arithmetic sequences, and integer operations. Furthermore, this study also seeks to test the potential of rebana art as a source of mathematics learning for junior high school students. Methodology: The data obtained were qualitative, while the sources were obtained from observations, interviews, and documentation related to the Rebana Art. The instrument in this study was the researcher herself. The tools used were interview guidelines, observations, and documentation. Data validity techniques were carried out through triangulation through checking method triangulation, source triangulation, and time triangulation, with the data analyzed descriptively qualitatively. Main Findings: The findings show that rebana art contains ethnomathematic concepts related to one-dimensional, two-dimensional, and three-dimensional geometry through measurement activities, including angles, circles, rectangles, cylinders, and cones. The concept of arithmetic sequences is identified in Qasidah rebana, while integer operations appear in Hadrah rebana performances. Furthermore, rebana art can be aligned with the curriculum as a source of mathematics learning for Grades VII, VIII, and IX. Novelty/Originality of this study: This study offers a new contribution by systematically mapping specific mathematical topics across different types of tambourine arts and explicitly aligning them with lower secondary school curriculum levels. This study advances ethnomathematics research by showing how local musical traditions can be transformed into structured mathematical learning resources grounded in formal curriculum standards.
Copyright (c) 2025 Putri Ramadhani, Muhammad Subchi, Ana Mega Silviani
Enhancing Mathematics Learning Outcomes through Realistic Mathematics Education: Evidence from Classroom Implementation
Purpose of the study: The aim of this study was to determine whether or not the Realistic Mathematics Education approach had an influence on students' mathematics learning outcomes. Methodology: This study is a quasi-experimental study using a nonequivalent control group design consisting of 38 students in the experimental class and 35 students in the control class with a purposive sampling technique. The data collection technique used was a pretest and posttest. Main Findings: The student learning outcomes test after being given treatment was analyzed using descriptive statistical analysis and inferential statistical analysis. The results showed a difference between the mathematics learning outcomes of students in the experimental class and students in the control class with tcount > ttable (tcount = 1.91; ttable = 1.666). Based on this, it can be concluded that there is an influence of the Realistic Mathematics Education approach on student learning outcomes. Novelty/Originality of this study: This study provides empirical evidence on the effectiveness of the Realistic Mathematics Education approach through a quasi-experimental, non-equivalent control group design at the classroom level. This study expands existing knowledge by demonstrating measurable differences in learning outcomes using pre-test and post-test analyses, thus strengthening the practical evidence base for implementing Realistic Mathematics Education in real-world learning environments.
Copyright (c) 2025 Nuriana Br Siregar, Ernidalisma Ernidalisma, Sumirah Sumirah
Effectiveness of Realistic Mathematics Education in Improving Grade 7 Students’ Learning Outcomes in a Rural Zambian Secondary School
Purpose of the study: This study aims to examine the effectiveness of the Realistic Mathematics Education approach in improving mathematics learning outcomes of Grade 7 students in a rural Zambian secondary school. Methodology: A quasi-experimental design with a one-group pretest–posttest model was employed. The participants consisted of 26 Grade 7 students selected from a rural public secondary school in Zambia. Data were collected through mathematics achievement tests, classroom observation sheets, and student response questionnaires. Descriptive statistical analysis was used to evaluate learning effectiveness based on learning outcomes, student activities, and student responses. Main Findings: The results indicate that the implementation of Realistic Mathematics Education led to a significant improvement in students’ mathematics achievement, with most students achieving the minimum mastery criterion and demonstrating a high normalized gain score. In addition, students showed active participation during learning activities and expressed positive responses toward the Realistic Mathematics Education -based instruction. Novelty/Originality of this study: These findings suggest that Realistic Mathematics Education is an effective instructional approach for enhancing mathematics learning in rural secondary school contexts in Zambia.
Copyright (c) 2025 Allan Musonda, Leonard Mubila, Justina Mulenga
From Problems to Progress: Improving Mathematics Learning Outcomes through Problem-Solving Instruction
Purpose of the study: The aim of this research is to improve students' learning outcomes in Mathematics by using the Problem Solving method. Methodology: The research conducted used Classroom Action Research. Data were obtained from qualitative and quantitative data. Data collection techniques included observation, testing, documentation, and interviews. The data analysis method used both qualitative and quantitative data. Main Findings: Based on the results of data analysis, it is known that, after using the Problem Solving method, student learning outcomes have increased. This can be seen from the results of the pre-test and post-test given to students, which always increased in each cycle. The increase in student learning outcomes in cycle 1 was 71.88% and in cycle II 87.10%. There was an increase in the completeness of student learning outcomes by 5.31%. Novelty/Originality of this study: This study introduces a structured problem-solving instructional model implemented through classroom action research to regularly improve students' mathematics learning outcomes. Unlike previous studies, it integrates iterative reflection cycles with authentic classroom problems, providing practical evidence on how problem-solving instruction directly enhances students' engagement, conceptual understanding, and achievement.
Copyright (c) 2025 Minh Tuấn Nguyễn, Bernard Alorgbey
Understanding Elementary Students’ Mathematics Learning Difficulties: A Qualitative Analysis of Internal and External Factors
Purpose of the study: This study aims to describe the factors causing mathematical difficulties. Methodology: This qualitative study involved 25 students who indicated they were having difficulty learning mathematics. Data collection techniques included observation, interviews, questionnaires, documentation, and field notes. Data analysis involved data reduction, data presentation, and drawing conclusions. Main Findings: The types of learning difficulties experienced by students include difficulty understanding the concept of fractional comparison, difficulty calculating whole numbers, and difficulty solving word problems. Factors contributing to students' learning difficulties include internal and external factors. Internal factors include negative attitudes toward learning mathematics, low motivation to learn, suboptimal physical health, and sensory impairment. External factors include a lack of variety in teaching methods, suboptimal use of learning media, school infrastructure, and family environment. Novelty/Originality of this study: Providing information about the causes of difficulties in learning mathematics that are often experienced by students, so that efforts can be made to reduce difficulties in learning mathematics.
Copyright (c) 2025 Ni’mah Mulyaning Tyas, Tyas Puji Rahayu, Sutrisno Sutrisno, Sri Muati
Picture Media as a Solution for Mathematics Learning: A Classroom Action Study on Fourth Grade Elementary School Students
Purpose of the study: The aim of this research is to improve mathematics learning outcomes by using image media for angle measurement material for fourth grade elementary school students. Methodology: This classroom action research used observation sheets, essay-type achievement tests, lesson plans, and image-based learning media. The method used followed two cycles of Classroom Action Research (planning, action, observation, and reflection). Data were collected through student achievement tests and then analyzed descriptively using percentage calculations without special software. Main Findings: The use of image-based learning media improved mathematics learning outcomes of fourth-grade students. Classical mastery increased from 25% in the pre-action stage to 50% in Cycle I, showing a 25% improvement. In Cycle II, classical mastery reached 83.3%, indicating a further increase of 33.3% and exceeding the minimum mastery criterion of 75%. Novelty/Originality of this study: This study offers novelty by systematically applying image-based learning media within a classroom action research framework to improve elementary students’ understanding of angle measurement. It provides practical evidence of step-by-step improvement across cycles, enriching empirical knowledge on effective visual media integration in primary mathematics learning.
Copyright (c) 2025 Arlisa Tri Winarni, Kisyanto Kisyanto
Trends in International Mathematics and Science Study (TIMSS): A Comparative Analysis of Mathematics Achievement
Purpose of the study: This study investigates global trends in mathematics education using TIMSS data to understand factors influencing student achievement. Methodology: Quantitative analysis of TIMSS datasets from the latest cycles was conducted using statistical tools such as SPSS and R for trend analysis, regression models, and comparative performance evaluations. Main Findings: Socioeconomic factors, teacher qualification, and curricular alignment were strongly associated with variations in student performance across countries. Novelty/Originality of this study: The study offers a detailed comparative analysis of the latest TIMSS results, emphasizing underrepresented countries, thereby contributing to strategies for improving global mathematics education.
Copyright (c) 2025 Marilyn T. Rubio, John Mensah, Benjamin Sokpe
Fun Strategies for Learning Mathematics: Exploring the Potential of Combinatorial Game Theory in Discrete Mathematics
Purpose of the study: This study aims to examine the effectiveness of using combinatorial game theory in discrete mathematics learning to improve students' understanding and interest in learning. Methodology: Using the Mixed Methods approach, quantitative data were collected through a quasi-experimental design with a pretest-posttest control group, while qualitative data were obtained through interviews and observations. The sample consisted of 60 grade XI students divided into experimental and control classes. Main Findings: The results of the analysis showed that the average gain score of students' conceptual understanding in the experimental class (0.68) was significantly higher than the control class (0.32) with a t-test significance value of 0.001 (p < 0.05). In addition, the motivation questionnaire showed an increase in the average score from 2.9 to 4.1 on a Likert scale of 1–5. Novelty/Originality of this study: Qualitative findings reinforce that game-based strategies encourage active participation, collaboration, and positive perceptions toward discrete mathematical theory.
Copyright (c) 2025 Leutrim Klinaku, Ledy J Elumba, Nada Mohammed Abbas
Critical Thinking as a Key to Solving Mathematical Problems: Findings from the TIMSS Framework in Middle Schools
Purpose of the study: The purpose of this study was to analyze the influence of critical thinking skills on students' mathematical problem solving based on the TIMSS framework. Methodology: This study uses a quantitative approach with a correlational survey design. The population of the study was junior high school students with a sample of 200 students selected by random sampling. Data collection used the Critical Thinking Ability Test and the Mathematics Problem Solving Test based on TIMSS. Data analysis was carried out using descriptive statistics, Pearson correlation tests, and simple linear regression using SPSS. Validity tests used content and construction tests, and reliability was tested with Cronbach's Alpha (0.745). Main Findings: The results of this study indicate a significant positive relationship between students' critical thinking skills and mathematical problem solving. The average score of critical thinking skills and mathematical problem solving is in the moderate category. The evaluation indicator has the highest score, while inference and synthesis have the lowest scores. The results of the Pearson correlation test showed a moderate relationship (r = 0.550), and the simple linear regression test showed that critical thinking skills significantly affect mathematical problem solving (R² = 0.303, p < 0.05). Novelty/Originality of this study: This study offers a fresh perspective by examining students’ critical thinking skills within the context of mathematical problem-solving using the TIMSS framework. The results enhance existing literature by demonstrating a strong link between critical thinking and effective problem-solving.
Copyright (c) 2025 Chan Roath, Zhyan Rafaat Ali Alkaki , Julie S James
Mathematics and Combinatorial Thinking: How Computational Ability Influences Problem-Solving in Number Patterns?
Purpose of the study: This study aims to analyze students' computational thinking abilities in solving combinatorial problems based on high, medium, and low ability categories. Methodology: This study uses a descriptive qualitative approach with subjects of 33 students of class VIII I State Islamic Junior High School 2 Bondowoso. Data were collected through written tests, semi-structured interviews, and documentation. Data analysis used the Miles and Huberman model (reduction, presentation, conclusion) with triangulation techniques for validation, comparing test results, interviews, and documentation. Main Findings: Students with high and medium computational abilities are able to meet all indicators of computational thinking, including identifying and understanding problems, and converting them into combinatorics. Meanwhile, students with low abilities have difficulty in re-understanding the problems found. Novelty/Originality of this study: This study provides new insights into how students' level of computational thinking ability influences their success in solving combinatorial problems, as well as offers perspectives in developing more effective learning strategies to enhance students' computational thinking ability.
Copyright (c) 2025 Khatriya Tiffani, Mohammed Rizzman Manaf, Riswan Efendi
Numerical Analysis of Flow Through Venturimeter with Variation of Neck Size to Determine Velocity Coefficient and Pressure Drop
Purpose of the study: This study aims to analyze the effect of variations in the size of the venturimeter neck on the velocity coefficient and pressure drop using a numerical simulation method. Methodology: The method used in this study is numerical simulation using SolidWorks 2014 software. The simulated venturimeter model has a neck length variation of 20 mm and 30 mm, with a throat diameter of 10 mm. The fluid used is water with a temperature of 25°C, and the simulation is carried out in the Reynolds number (Re) range of 1000 to 5000. Main Findings: The results of the study showed that the greater the velocity of the incoming fluid, the Reynolds number, flow rate, and pressure drop also increased. In addition, the difference in the length of the venturimeter neck affects the pressure drop, where the venturimeter with a longer neck experiences a greater pressure drop due to the longer duration of the fluid flow. The resulting velocity coefficient is also influenced by the velocity of the incoming fluid, where the higher the velocity, the greater the flow rate value. Novelty/Originality of this study: The novelty in this research lies in the numerical approach in analyzing the relationship between the venturimeter neck size and the velocity coefficient and pressure drop. This approach allows faster and more efficient calculations compared to conventional experimental methods, thus contributing to the development of more accurate and applicable fluid flow measurement techniques.
Copyright (c) 2025 Zakaria Gaber Hanawy Beshay, Sokunthea Sin, Waleed A. Raja
Cultural Values and Their Role in Shaping the Adaptation of Realistic Mathematics Education (RME) in Indonesia: A Mixed-Methods Approach
Purpose of the study: The main objective of the study is to analyze how cultural factors influence the implementation of RME in the context of mathematics education in Indonesia. Methodology: The method used is a qualitative study employing content/document analysis of curriculum guidelines and instructional materials. Additionally, semi-structured interviews were conducted with six educators, and non-participant observations were carried out in three schools to examine the implementation of Realistic Mathematics Education (RME). Main Findings: The results of the study showed that the success of RME adaptation was influenced by local cultural values, such as community-based approaches and the context of students' daily lives. Novelty/Originality of this study: The novelty of this research lies in the in-depth analysis of the interaction between RME principles and Indonesian cultural characteristics, providing new insights into the development of more contextual and effective mathematics learning strategies.
Copyright (c) 2025 Sagir Adamu Abbas, Annabelle M. Quiño, Nayantara Abraham
Exploration Ethnomathematics in Traditional Games of Mancala in Africa and Congklak in Indonesia
Purpose of the study: Study this aiming for explore draft ethnomathematics in game traditional Mancala in Africa and congklak in Indonesia use understand relatedness between culture and mathematics in context game. Methodology: With use approach qualitative ethnography, research this collect data through observation participatory, interview in-depth, and documentation to Mancala players in Ghana and congklak in Sumatra, as well as educators at school basis. Research results show that second game this involving draft mathematics like pattern numbers, distribution strategy, operations count, and thinking logical and probable. Main Findings: Experienced players show natural mathematical thinking through efficient strategies. While Mancala remains popular in Ghana, congklak is declining in Indonesia. Observations indicate traditional games have strong potential in culture-based math education. Thus, preservation and innovation are needed to integrate them contextually into learning. Novelty/Originality of this study: The novelty of this research lies in the exploration of the concept of ethnomathematics in the games Mancala in Africa and congklak in Indonesia through a qualitative ethnographic approach, which has not been studied in depth.
Copyright (c) 2025 Rita Suharti, Krishna Prashad Bhatt, Owolabi Yemi Tolulope, Yahya A Sambo
Modification of the Fourth Order Runge Kutta Method Based on the Contra Harmonic Average
Purpose of the Study This study aims to modify the fourth-order Runge-Kutta method based on the contra harmonic mean. The research discusses the theoretical modification of the fourth-order Runge-Kutta method. Methodology The research was conducted using a literature study method. The study begins by introducing the general form of the Runge-Kutta method up to the nth order. This general form is then specialized to the fourth order. Additionally, the concept of the contra harmonic mean is introduced. After obtaining the general form of the fourth-order Runge-Kutta method and the contra harmonic mean, these two general forms are modified to derive a new formula. Main Findings Based on the results, the modified fourth-order Runge-Kutta method has the following equation form: yi+1 = yi + (h/4) * [(k1^2 + k2^2) / (k1 + k2) + 2 * (k2^2 + k3^2) / (k2 + k3) + (k3^2 + k4^2) / (k3 + k4)], with an error of order O(h^5). Numerical simulations demonstrate that the modified method provides better results compared to the original fourth-order Runge-Kutta method. Novelty/Originality of this Study The numerical simulations using the RKKCM method show improved accuracy compared to the unmodified fourth-order Runge-Kutta method, highlighting the innovation and contribution of this study.
Copyright (c) 2025 Peshawa Mohammed Khudhur, Jóhann Örn Sigurjónsson, Dara Maghdid