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AKSIOMA : Jurnal Matematika dan Pendidikan Matematika
Published by Universitas PGRI Semarang
ISSN : 20862725     EISSN : 25797646     DOI : https://doi.org/10.26877/2djdzk74
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Aksioma: Jurnal Matematika dan Pendidikan Matematika invites original research articles that have not been simultaneously submitted to another journal or conference. The whole spectrum of research in mathematics education is welcome, which includes, but is not limited to, the following topics: 1. Realistic Mathematics Education; 2. Ethnomathematics; 3. ICT in Mathematics Education; 4. Teaching and learning process of mathematics 5. Assessment and Evaluation of Mathematics Education; 6. Creativity and Innovation in Mathematics Teaching and Learning; 7. Mathematical Thinking Ability; 8. Applied Mathematics.
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Articles 50 Documents
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Improvement of students’ mathematical problem-solving ability through kuga story-based learning with wordwall Moh.Saiful Amri; Naning Kurniawati; M. Husen Al Farisy
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/1gxgct82

Abstract

Mathematics learning, particularly solving word problems, remains challenging for students due to conceptual gaps and difficulties in identifying relevant information in problem situations. This study examines students’ mathematical problem-solving outcomes after using KUGA story-based geometry quizzes integrated with Wordwall as an interactive, game-based learning medium. The study employed a quantitative approach with a one-group pretest-posttest design. The participants were 21 seventh-grade students from MTs Hidayatul Islam. Data were collected through pretests, posttests, and documentation. KUGA was used to provide story-based geometry quiz content, while Wordwall served as an interactive digital platform for presenting and delivering the quizzes in a game-based format. Data were analyzed through normality testing, followed by the Wilcoxon Signed-Rank test and N-Gain analysis to examine changes in students’ mathematical problem-solving outcomes. The results showed an increase in the mean score from 67.14 on the pretest to 82.38 on the posttest. The Wilcoxon Signed-Rank test indicated a statistically significant difference between the pretest and posttest scores (p < 0.001). The N-Gain score was 0.4536, categorized as moderate. These results indicate an improvement in students’ mathematical problem-solving outcomes following the implementation of KUGA story-based geometry quizzes integrated with Wordwall. However, because the study used a one-group pretest-posttest design without a control group, the observed improvement cannot be attributed solely to the intervention. Therefore, the findings should be interpreted as evidence of improvement following the implementation rather than definitive evidence of a causal effect.
Enhancing students' statistical conceptual understanding and learning independence through contextual worksheet-assisted discovery learning Alya Suryani Alya Suryani; Nova Nurhanifah; Tina Sri Sumartini
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/xstbpd09

Abstract

While statistical conceptual understanding and learning independence are crucial in mathematics education, traditional instruction often restricts opportunities for active exploration. Although discovery learning and contextual materials have been examined independently, their integrated impact on these dual outcomes in junior high school statistics remains underexplored. Therefore, this study aimed to investigate the enhancement of students' statistical conceptual understanding and learning independence through Contextual Worksheet-Assisted Discovery Learning. Employing a quantitative pre-experimental (one-group pretest-posttest) design, the research involved 29 ninth-grade students at an Islamic junior high school in Garut Regency, Indonesia. Data collected via conceptual tests and self-report questionnaires were analyzed using paired-sample t-tests, Wilcoxon signed-rank tests, and N-Gain analysis. The results demonstrated a significant improvement in statistical conceptual understanding, with mean scores rising from 64.97 (SD = 15.37) to 76.14 (SD = 19.20) (t(28) = −5.239, p < .001), achieving a moderate N-Gain of 0.41. Concurrently, learning independence significantly increased from 28.34 to 30.41 (Z = −3.167, p = .002). These findings suggest that integrating discovery learning with contextual worksheets provides an effective, structured environment that fosters both conceptual exploration and autonomous learning. Although the absence of a control group limits definitive causal claims, this pedagogical approach shows substantial promise for advancing statistical education in secondary schools.
Optimal control of microalgae growth using linear quadratic regulator method with particle swarm optimization suci yongki setyowati
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/yxd0eq15

Abstract

Microalgae represent a significant and promising resource for a multitude of industrial applications. The lipids extracted from microalgae are used to produce biofuels, as dietary supplements for humans and animals, and as sources of vitamins or proteins in the pharmaceutical industry. Furthermore, microalgae serve as agents for carbon dioxide capture and wastewater treatment (Kumar et al., 2010). This study examines the optimal regulation of microalgal proliferation by controlling variables such as carbon dioxide and nutrients using the Linear Quadratic Regulator (LQR) methodology. Within the framework of the LQR approach, the weight matrices Q and R are commonly established through trial and error, a time-consuming process that does not guarantee a globally optimal solution. This manuscript advocates implementing Particle Swarm Optimization (PSO) to precisely determine the matrix values Q and R, thereby supplanting traditional manual tuning. PSO is a metaheuristic algorithm predicated on the collective behaviors observed in avian flocking and piscine schooling. Compared with the Firefly Algorithm previously applied to this problem, PSO offers a simpler velocity-position update mechanism, fewer algorithmic control parameters to calibrate, and a lower computational burden per iteration, while still maintaining a strong balance between exploration and exploitation of the search space. The principal novelty of this study lies in the application of PSO rather than the Firefly Algorithm to automatically tune the LQR weight matrices for the Thornton microalgae growth model, accompanied by an explicit, iteration-by-iteration account of the convergence behavior of the swarm, an aspect that has not been reported in prior LQR-based microalgae control studies. The use of PSO is expected to enhance microalgal growth, resulting in substantially increased biomass production. Simulation findings indicate that the LQR approach in isolation yields a 21.7% increase in algal concentration from the baseline concentration, whereas the LQR method, when augmented by PSO optimization, results in an approximate 64.5% enhancement in algal concentration from the initial level, thereby underscoring the advantage of PSO-assisted weight optimization over both the unoptimized LQR controller and the previously reported LQR–Firefly Algorithm combination.
From words to matrices: uncovering students' errors in solving contextual matrix algebra problems Shafira Meiria Rahmasari; Sidik Nurrasa; Nalim; Md. Mahmudul Alam
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/wr9rnz46

Abstract

Contextual problems in matrix algebra require students not only to perform matrix operations but also to construct mathematical models and interpret results meaningfully. However, many students encounter difficulties when translating real-world situations into matrix representations. This study aims to identify the types of errors students make when solving contextual matrix algebra problems and to explore the underlying factors contributing to these errors. Employing a qualitative descriptive design, the study involved sixteen Mathematics Education students who had completed a Matrix Algebra course. Data were collected through contextual matrix algebra tests and semi-structured interviews. Data were analyzed using methodological triangulation. The results revealed four categories of errors: conceptual, mathematical modeling, procedural, and interpretation. Mathematical modeling errors emerged as the most dominant category, particularly in constructing matrix representations and determining the appropriate order of matrix operations. Conceptual errors were associated with misconceptions about matrix structures and operations, whereas procedural errors involved calculation inaccuracies. Interpretation errors occurred when students failed to connect mathematical results to the problem's context. These findings indicate that students’ difficulties extend beyond computational skills and are closely related to their ability to understand, model, and interpret contextual situations mathematically. Therefore, instructional practices should emphasize contextual problem-solving and mathematical modeling to foster deeper conceptual understanding and higher-order thinking skills in learning matrix algebra.
A Descriptive qualitative analysis of junior high school students' ability to understand mathematical concepts in fractional materials Nia Mei Astuti; Dwi Rahmawati; Ira Vahlia
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/y5j9nh60

Abstract

The focus of this research is to examine junior high school (Grade VII) students' ability to understand mathematical concepts when solving fraction problems, using a qualitative, descriptive design. The analysis focuses on three abilities: restating concepts, presenting concepts in different forms of mathematical representation, and applying concepts or algorithms to obtain solutions. The novelty of this study lies in combining tiered categorization (high, medium, low) with an in-depth qualitative description of each ability group, enabling identification of students' achievement characteristics on each indicator in greater detail than in previous similar studies. The research was conducted at a public junior high school in Metro City, based on pre-survey results showing a low completion rate among students in solving fraction problems. Six of the 26 students in Class VII A were selected through purposive sampling, taking into account variation in pre-survey scores to ensure proportional representation of the high-, medium-, and low-ability groups. Data were obtained through a written test on fraction material that mathematics teachers and lecturers had validated, then analyzed through the stages of data reduction, data presentation, and conclusion drawing. The results place students' concept understanding in the medium category, with an average score of 52 and an average ability percentage of 61.1%. Students in the high group were able to meet all three indicators; the medium group was able to use mathematical representations and problem-solving algorithms, but was not yet consistent in restating concepts; while the low group had not shown achievement on any of the three indicators. These findings are specific to the research subjects and are not intended to be generalized broadly. This study provides a diagnostic picture of students' patterns of understanding of fraction concepts that can inform teachers in designing instruction that places greater emphasis on the meaning of concepts before students move on to related material, such as ratio and proportion, with the limitation that the subjects were drawn from a single school.
Development of macromedia flash-based mathematics media integrated with discovery learning to improve students' problem-solving ability Jessica Debora Simbolon; Githa Stien Tuntunan
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/y4wbmy60

Abstract

This study aimed to develop Macromedia Flash-based learning media integrated with a discovery learning approach and to evaluate its validity, practicality, and effectiveness in enhancing students' mathematical problem-solving skills. The research employed a research and development (R&D) design using the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). The participants were 60 Grade X students from SMA Negeri 5 Medan, comprising 30 students in Trial I (Class X MIPA 4) and 30 students in Trial II (Class X MIPA 9). Data were collected through expert validation sheets, classroom observations, mathematical problem-solving tests, and student response questionnaires. The results showed that the developed learning media achieved a high level of validity, indicated by an overall expert evaluation score of 3.71. The media also demonstrated strong practicality, supported by positive classroom implementation and student responses, with the average response score increasing from 3.54 in Trial I to 3.64 in Trial II. Regarding effectiveness, students' mathematical problem-solving abilities improved, as evidenced by an N-gain of 0.21 (low) in Trial I and 0.34 (medium) in Trial II. Furthermore, classical mastery increased from 54% in Trial I to 90% in Trial II, and learning objective achievement across three indicators improved from 67.1%, 69.8%, and 65% in Trial I to 79%, 79.8%, and 75.5% in Trial II, respectively. Overall, the findings indicate that Macromedia Flash-based learning media integrated with discovery learning is a valid, practical, and effective instructional tool for improving students' mathematical problem-solving abilities.
Development and validity of the local wisdom-based moduloka e-module to support elementary school students' problem-solving skills Ainur Rohmah; Fitriyah Amaliyah; Lovika Ardana Riswari
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/cgtsp750

Abstract

Developing contextual digital teaching materials that integrate local wisdom is essential to support mathematics learning in primary schools. This study aimed to develop and validate MODULOKA, an e-module based on Jepara's local wisdom, focusing on fractions for fourth-grade students. The study employed a Research and Development (R&D) method using the ADDIE model, limited to the analysis, design, and development stages. Participants in the needs analysis stage included one teacher and ten fourth-grade students, while product validation involved two media experts and three subject matter experts. Data were collected through observations, needs-analysis questionnaires, and validation sheets, all using a 5-point Likert scale. The validation results indicated that MODULOKA achieved a media validity score of 91.2% ("Very Valid") and a content validity score of 88% ("Very Valid"). Product revisions were made based on the validators' feedback, including adding a glossary, improving material presentation, and refining local wisdom visualizations. Consequently, MODULOKA was deemed highly valid and suitable as digital teaching material for fraction lessons that incorporate Jepara's local wisdom. Future research is required to assess the practicality and effectiveness of MODULOKA, including its potential to support mathematical problem-solving skills through classroom implementation.
The effect of problem based learning model with scientific approach on the mathematical communication skills Budi Santoso Budi; Christina Eva Nuryani Eva; Siska Candra Ningsih Siska
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/rj0nsr58

Abstract

Mathematical communication is a crucial competency for students in mathematics education; nevertheless, learners frequently struggle to articulate and convey mathematical concepts. This research examined the impact of integrating the Problem-Based Learning (PBL) model with a scientific approach on the mathematical communication abilities of secondary school students. Utilizing a quantitative design with a quasi-experimental approach, specifically a posttest-only control group design, the study selected participants via cluster random sampling, involving 56 students from two classes at SMA Negeri 1 Purwonegoro during the 2025/2026 academic year. Class X-8, consisting of 30 students, was assigned as the experimental class and received the PBL model integrated with a scientific approach, while Class X-6, consisting of 26 students, served as the control class and received conventional learning. Data collection relied on mathematical communication assessments and instructional observations. Subsequent analysis using normality, homogeneity, and independent samples t-tests in SPSS yielded a significance score of 0.017 (p < 0.05), thereby rejecting the null hypothesis (H₀) and accepting the alternative hypothesis (H₁). The results confirm that incorporating a scientific approach into PBL substantially enhances students' mathematical communication skills. Furthermore, the instructional implementation attained an average score of 88%, placing it in the "very good" category.
Designing translation learning trajectory using tayub dance context through RME assisted by GeoGebra Zahra Fadila; Farida Nursyahidah; Noviana Dini Rahmawati; Margaretha Madha Melissa
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/0g20hz36

Abstract

The concept of translation plays a crucial role in geometry education, fostering students' spatial understanding, visual thinking, and transformational reasoning. Despite its importance, many students still struggle to abstract the concept of translation, demonstrating a low level of conceptual understanding and a limited ability to apply it in a coordinate context. To address this gap, this study introduces a culturally grounded, context-based learning design that integrates Tayub dancers' movement into translation learning. This study aims to develop a learning trajectory that supports students’ conceptual understanding of translation through meaningful and realistic mathematical experiences. This study involved 32 ninth-grade students from a public junior high school in Semarang. It employed a validation study design research methodology that included three phases: preliminary design, teaching experiment, and retrospective analysis. The learning activities were implemented using the Realistic Mathematics Education (RME) approach assisted by GeoGebra. The resulting Learning Trajectory (LT) consisted of three interrelated activities: analyzing a video of Tayub dance movements to identify translation features; deriving formal rules for translation vectors through the “box arc” strategy and GeoGebra exploration; and solving a contextual problem involving the design of dancer formations. The findings indicate that integrating culturally relevant contexts and visual media into RME effectively enhances students' understanding of translation. This research contributes to the field by offering a novel approach that bridges ethnomathematics and the teaching of formal geometric transformations, and by serving as a reference for future studies seeking to incorporate local wisdom and technology into mathematics education.
The effect of the game-based learning model based on bar diagram board medium on students' mathematical representation ability Yovita Puspasari; Wahyu Nurmalasari; Hidayatus Samawiya
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 2 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/70dtxv70

Abstract

Students' ability to represent mathematical concepts verbally, visually, and symbolically is a crucial skill in learning mathematics, as it supports understanding and the meaningful expression of mathematical ideas. Observations and interviews at SDN 2 Ngantru showed that, out of 38 students, only 6 (15.79%) met the minimum competency achievement criteria (KKTP), indicating the need for a learning model capable of fostering student engagement, one of which is Game-Based Learning supported by a bar-diagram board medium. This study aims to determine the effect of the Game-Based Learning model, using a bar-diagram board medium, on the mathematical representation ability of fourth-grade elementary school students. Using a quantitative approach with a quasi-experimental Non-Equivalent Control Group Design, the study involved 50 fourth-grade students at SDN 2 Ngantru, selected through saturated sampling, comprising 25 students from class IV-A (control group) and 25 from class IV-B (experimental group). Data were collected through tests, observation, and questionnaires. The data analysis technique used prerequisite tests (normality and homogeneity), an Analysis of Covariance (ANCOVA) with the pretest score as a covariate to control for initial ability differences between groups, an Independent Samples t-test as a complementary analysis, and an N-Gain effectiveness test. The ANCOVA results showed a statistically significant difference in posttest scores between groups after controlling for the pretest score (F = 48.156; p < 0.001; partial eta squared = 0.506), consistent with the hypothesis test results (significance value of 0.001 < 0.05) indicating that the null hypothesis was rejected. The experimental class's average posttest score of 83.36 was higher than the control class's 76.48, with an N-Gain of 60.18% (fairly effective) for the experimental class and 41.83% (less effective) for the control class.

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