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Riemann : Research of Mathematics and Mathematics Education
Published by Universitas Katolik Santo Agustinus Hippo
ISSN : 27218848     EISSN : 2721883X     DOI : https://doi.org/10.38114/pgnbcd43
Core Subject : Education,
Education Mathematics
Riemann: Research of Mathematics and Mathematics Education Journal Riemann is peer-reviewed journal that contains the work of the field of educational research or teaching mathematics, mathematics, mathematical applications, mathematical computerization, and models of mathematics education in the learning process. Journal Riemann is published Thrice a year, every April, September, and December. The focus and scope of the Journal Riemann covers the following topics: Mathematics Teaching Mathematical Applications Mathematical Computerization Model of Mathematics Education
Arjuna Subject : Ilmu Sosial - Pendidikan
Articles 120 Documents
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Pareto-TSP Decision Support Framework for Cafe Location Selection in Tuban Regency Andy Haryoko; Gusti Uripno; Suprapto; Mario Fahmi Syahrial
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.210

Abstract

The cafe industry in Indonesia faces a business failure rate of 60-70% within the first three years, primarily caused by poor location selection, lacking systematic, data-driven methods (Lahindah et al., 2020; Nugraheni & Suparna, 2024). Existing studies tend to address location selection and route optimization independently. This separation leaves a gap in integrated multi-objective frameworks applicable to the Indonesian small-to-medium enterprise (SME) context. Unlike prior single-domain approaches, this study contributes a unified, replicable Decision Support System (DSS) that simultaneously integrates the Analytic Hierarchy Process (AHP), Pareto Multi-Objective Optimization, and the Traveling Salesman Problem (TSP) heuristic for optimal cafe location selection and logistics route efficiency. A sequential explanatory mixed-method design was applied, combining quantitative computational modeling with qualitative expert validation, across eight candidate locations in Tuban Regency, East Java, using spatial data from the Central Bureau of Statistics, OpenStreetMap, and Google Places API. Seven weighted criteria were evaluated via AHP (consistency ratio < 0.1), Pareto frontier analysis was conducted to identify non-dominated solutions, and three TSP algorithms (Nearest Neighbor, 2-Opt, Simulated Annealing) were implemented and compared. Results indicate that location L01 (Jl. Basuki Rahmat) achieved the highest DSS score of 0.797, a ranking that remained stable across the full sensitivity range of DSS weightings scenarios tested. The Simulated Annealing algorithm produced the most efficient distribution route of 4.22 km, reducing travel distance by 5.2% compared to the Nearest Neighbor baseline. Empirical validation against real-world Tuban data, measured as the proportion of parameters matching field observations within a 10% deviation threshold, demonstrated an 87.5% agreementrate. The proposed framework provides a replicable, transparent, and data-driven decision tool for SME cafe investors and municipal spatial planners.
Mathematical Communication Skills Analysis through the Discovery Learning Approach with the Help of the Quizizz Application Misrawati; Yus Mochamad Cholily; Alfiani Athma Putri Rosyadi
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.214

Abstract

Mathematical communication skills are crucial in the digital era, but students often experience cognitive barriers in abstract composition and inverse function materials. Evaluation of the impact of innovative digital learning is generally still dominated by a macro quantitative approach, thus ignoring specific cognitive dynamics based on students' initial abilities. This descriptive qualitative study aims to describe the profile of mathematical communication skills (drawing, math expression, written text) of students in the Quizizz-assisted Discovery Learning model in terms of their Prior Mathematical Ability (PMA). Through a purposive sampling technique, 6 subjects were selected from a total of 27 students in the experimental class to represent the high, medium, and low PMA clusters. Data were collected through triangulation of test achievement graphs, analysis of student worksheet results, and in-depth clinical interviews. The results of the study revealed three main findings: (1) The high groups showed established metacognition and fluency of layered representations across all indicators. (2) The medium groups manifested a cognitive bypass anomaly, where students tactically sacrificed the drawing aspect for the sake of efficient algebraic-verbal calculation time (cognitive trade-off). (3) The low groups experienced the paradox of digital gamification; The Quizizz feature helps with short-term memory retention in written text, but the pressure of the fast-paced game rhythm triggers impulsive cognitive styles and time-constrained anxiety, which leads to careless errors in algebraic expressions during manual written tests. In conclusion, the integration of gamification technology does not have a linear impact on all levels of student ability, requiring intervention in the form of time regulation, differentiation, and scaffolding to minimize cognitive barriers in lower groups.
Profiling Prospective Mathematics Teachers’ 4C Skills through Case-Based Assessment in a Statistics Methods Course Israil Sitepu; Sinta Dameria Simanjuntak; Ribka Kariani Sembiring
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.216

Abstract

The integration of 21st-century competencies, particularly critical thinking, communication, creativity, and collaborative awareness, has become an important focus in higher education, including statistics education for prospective mathematics teachers. However, assessment practices in statistics courses continue to emphasize procedural calculations rather than evaluating students’ reasoning, interpretation, and communication of statistical findings in authentic contexts. Furthermore, few studies have explored students’ competency profiles through case-based assessment in statistics education using an analytic rubric. This study aimed to explore students’ competency profiles across the four 4C dimensions through a case-based assessment in the Statistics Methods course. A descriptive exploratory approach was employed involving 24 third-semester undergraduate students enrolled in the Mathematics Education Program at Universitas Katolik Santo Thomas. The assessment consisted of four contextual case-based questions, each designed to represent one of the four dimensions: critical thinking, communication, creativity, and collaborative awareness. Students’ written responses were analyzed using a four-level analytic rubric developed as a preliminary assessment instrument. The findings indicate that communication (M = 3.63) and critical thinking (M = 3.45) demonstrated the highest performance, whereas creativity (M = 2.95) and collaborative awareness (M = 2.95) showed comparatively lower performance. Overall, the assessment provided diagnostic information for identifying students’ strengths and areas requiring further instructional support across the four competency dimensions. These findings highlight the value of case-based assessment as an approach for mapping students’ competency profiles and informing the development of more balanced assessment practices in statistics education for prospective mathematics teachers.
High School Students’ Mathematical Literacy Profiles Based on Quitter Type of Adversity Quotient Petrus Fendiyanto; Nella Mauletania; Yan Ayu Lintang Sagita; Arinda Cyntiani
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.218

Abstract

Mathematical literacy is a crucial competence for addressing the challenges of the 21st century, as it enables individuals to formulate, employ, and interpret mathematics in various real-life contexts. However, results from the Program for International Student Assessment (PISA) indicate that Indonesian students’ mathematical literacy remains relatively low. In addition to cognitive factors, non-cognitive factors, such as Adversity Quotient, are considered to influence students’ ability to solve mathematical problems. This study aimed to describe the mathematical literacy profile of high school students with the quitter type of Adversity Quotient. This research employed a qualitative descriptive approach involving two eleventh-grade students with the quitter type who were selected through purposive sampling based on the results of the Adversity Quotient questionnaire. Data were collected using an Adversity Quotient questionnaire, a PISA-based mathematical literacy test covering the processes of formulate, employ, and interpret, and semi-structured interviews. The data were analyzed through data reduction, data display, and conclusion drawing. The results indicate that students with the quitter type demonstrate low mathematical literacy. The greatest weakness was observed in the interpret process, followed by the formulate process, whereas the employ process was relatively better, although still limited. The students experienced difficulties in identifying relevant information, applying appropriate mathematical concepts to develop problem-solving strategies, and interpreting and evaluating solutions within the problem context. The findings indicate that students with the quitter type exhibit weaknesses across all mathematical literacy processes, with the most prominent difficulty occurring in interpreting solutions to contextual mathematical problems.
Cognitive Load and Learned Helplessness in Mathematics Learning: Examining Intrinsic, Extraneous, and Germane Effects Ahmad Hartanto; Muhamad Gilar Jatisunda; Azin Taufik; Dexter C. Aligaya
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.219

Abstract

Difficulties in mathematics learning are often attributed to students' limited ability, while the role of cognitive demands imposed by instructional conditions remains insufficiently understood. In particular, the relationships between intrinsic, extraneous, and germane cognitive load and learned helplessness in mathematics learning have received limited empirical attention. This study examined these relationships using a quantitative correlational design involving 149 Grade 10 students from a public secondary school. Data were collected using an adapted questionnaire based on the Cognitive Load Theory framework and a learned helplessness scale. Multiple linear regression analysis was performed after confirming instrument validity, reliability, and the classical assumptions of regression. The results revealed that intrinsic cognitive load (β = 0.181, p = 0.013) and extraneous cognitive load (β = 0.478, p < 0.001) positively predicted learned helplessness, whereas germane cognitive load (β = −0.238, p = 0.001) showed a significant negative relationship. The regression model explained 35.9% of the variance in learned helplessness (R² = 0.359), with extraneous cognitive load emerging as the strongest predictor. These findings provide additional empirical evidence that students' psychological responses to mathematical difficulties are associated with the cognitive demands created by instructional design. The study highlights the importance of minimizing unnecessary cognitive load while promoting meaningful cognitive engagement to support students' persistence and confidence in mathematics learning.
Integrating Zep Quiz in Phenomenon-Based Learning via Design Thinking to Enhance Student’s Numeracy Habsanul Aisyah; Ida Dwijayanti; Achmad Buchori
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.234

Abstract

Low numeracy skills and students' motivation in understanding data phenomena remain major challenges in secondary school mathematics. This study aims to develop and validate a learning design prototype utilizing Phenomenon-Based Learning (PhBL) integrated Zep Quiz to address 10th-grade students’ numeracy obstacles. Employing a mixed-methods exploratory sequential design within a Design Thinking framework, the research involved 117 students across three secondary schools. Data were collected through a validated 10-item contextual essay test (CVI=0.87, Cronbach’s =0.82), a 20-item digital questionnaire, and a 5 criterion observation rubric. The initial Empathy Map phase revealed that students’ primary obstacles lie in interpreting contextual data. Consequently, the ideation process produced a PhBL-Zep Quiz prototype focused on investigating real-world phenomena through gamification. Quantitative analysis using a Paired Samples t-test demonstrated a significant improvement in students’ mean numeracy scores, rising from 57.53 to 63.33 (t = 13.356, p < 0.001), with a large intervention effect size (Cohen’s d = 1.24). Concurrently, a positive shift occurred students’ numeracy profiles, moving predominantly from the “Needs Intervention” category to “Proficient” and “Advanced”, achieving an 82% classical completion rate. The findings indicate that the synergy of PhBL and Zep Quiz effectively enhances students’ numeracy literacy. This study implies that such integration provides a novel gamified scaffolding strategy, specifically bridging the gap between abstract concepts and students’ contextual data interpretation skills.
Prospective Mathematics Teachers' Readiness for Integrating Artificial Intelligence into Mathematics Learning Kuswari Hernawati; Muhammad Irfan; Rofi Amiyani
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.235

Abstract

Artificial Intelligence (AI) has emerged as a transformative technology in education, making teacher readiness a critical factor for its successful integration into mathematics learning. This study aimed to examine the readiness of prospective mathematics teachers to integrate AI-based learning media. A quantitative descriptive survey was conducted involving 83 pre-service mathematics teachers who had completed or were enrolled in a microteaching course. Data were collected using a validated questionnaire covering four dimensions of readiness: knowledge, skills, ethics, and collaboration. Descriptive statistical analysis revealed an overall readiness score of 3.8, indicating that participants were generally ready to integrate AI into mathematics instruction. The ethics dimension achieved the highest mean score (4.2, very ready), reflecting strong awareness of responsible AI use. Knowledge (3.8) and skills (3.6) were categorized as ready, while collaboration (3.4) was rated as fairly ready, suggesting the need to strengthen teamwork and communication through AI-supported learning environments. These findings indicate that prospective mathematics teachers possess a solid foundation for AI integration but require further support in pedagogical application and collaborative competence. The study recommends embedding AI literacy, ethical AI practices, and project-based learning experiences into teacher education programs to enhance future teachers' readiness for AI-supported mathematics education.
Developing of Flipbook-Assisted Experiential Learning Media to Enhance Vocational Students’ Mathematical Critical Thinking Anik Yuliani; Aflich Yusnita Fitrianna; Norma Alias
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.237

Abstract

Mathematical critical thinking skills are essential for vocational students, yet traditional instruction often struggles to teach abstract deductive proofs within rigid school schedules. While digital media is widely used, there remains a pedagogical gap in integrating structured experiential cycles into interactive platforms to foster higher-order reasoning. This study aims to develop and evaluate an interactive flipbook integrated with Kolb’s experiential learning model to address this limitation. Utilizing the 4D development method (Define, Design, Develop, Disseminate), the platform's operational practicality was evaluated by teaching practitioners and a small group of 20 students, followed by a field implementation phase with a cohort of 30 vocational students (N = 30) facing mathematical induction topics. Data were gathered through expert validation sheets, teacher practicality questionnaires, and critical thinking pre-/post-tests. The results demonstrate that the developed media achieved excellent expert validity across content, media, and language parameters. Furthermore, it attained a high operational practicality rate of 84.00% from teaching practitioners, acting as an autonomous scaffolding tool. Importantly, the media proved highly effective, yielding an overall student critical thinking score of 79.00%, with peak performance in variable identification (90.00%) and argument validation (88.00%). These findings indicate that anchoring experiential loops within a scannable digital format systematically drives uniform cognitive gains, offering a robust pedagogical vehicle for vocational mathematics education.
Interplay Between SOLO Taxonomy and Analytical Thinking in Mathematical Literacy Problem Solving Agung Putra Wijaya; Caswita; Nurain Suryadinata
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.238

Abstract

Previous studies indicate that the SOLO taxonomy is an effective framework for assessing the depth of students’ understanding. However, few studies have explicitly examined the interplay between the structural complexity of student responses and the underlying analytical thinking processes in mathematical literacy problem-solving. Operationally, this interplay refers to how a student’s structural response complexity (SOLO levels) is governed and facilitated by their procedural analytical dimensions (differentiating, organizing, attributing). This study aims to explore this relationship by describing junior high school students’ analytical thinking within the SOLO framework. Employing a qualitative descriptive-exploratory design, five eighth-grade students from a junior high school in Bandar Lampung were purposively selected to represent each SOLO level. Data were gathered through a mathematical literacy test consisting of three non-routine open-ended tasks focusing on space, shape, and change contexts, combined with task-based interviews. Results revealed a significant mechanism: pre-structural students failed to differentiate relevant information, while uni-structural students exhibited partial differentiation but lacked organization. Multi-structural students began organizing information, though it remained fragmented, causing cognitive stagnation. In contrast, relational students effectively organized and initiated attributing, whereas extended abstract students demonstrated full mastery of all analytical aspects. These findings indicate that higher SOLO levels are a direct manifestation of enhanced analytical thinking abilities in connecting and evaluating complex mathematical information. The study highlights that fostering this operational engine is crucial in designing instruction that moves beyond procedural drills toward robust mathematical literacy.
Refining Proof Construction through SOLO+ Taxonomy and APOS Theory in Real Analysis Wahyu Widada; Badeni; Sulaiman; Khathibul Umam Zaid Nugroho; Dewi Herawaty
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 2 (2026): EDISI AGUSTUS
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i2.239

Abstract

The transition from differential calculus to real analysis represents a significant ontological shift for undergraduate mathematics students, often accompanied by difficulties in constructing formal proofs. While existing frameworks broadly categorize imperfect proofs as procedural failures, they lack the diagnostic resolution to capture transitional cognitive states. To address this gap, this study integrates the SOLO taxonomy with APOS theory to analyze the cognitive mechanisms of students' proof construction. Employing a qualitative instrumental case study, data from written tests and task-based interviews were collected from 35 undergraduate students. These participants were purposefully selected because they had completed foundational calculus and logic courses, placing them squarely in the crucial transition stage from computational calculus to axiomatic analysis. The data were analyzed using the Constant Comparative Method. Moving beyond purely narrative descriptions, the empirical findings reveal that a majority of students (63%) operate within transition zones. Specifically, the study introduces two refined transitional states: 34% of the students were identified at the Semi-Relational level, characterized by logical gaps stemming from unstable process internalization, and 29% at the Semi-Extended Abstract level, where students display strong intuition but lack formal rigor due to rigid concept encapsulation. Ultimately, identifying these specific cognitive barriers provides a practical roadmap for educators to design targeted instructional interventions, actively helping students overcome their logical or intuitive hurdles to master formal mathematical proving successfully.

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