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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 95 Documents
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Exploring the Growth of a Junior High School Student’s Mathematical Understanding and Higher-Order Thinking Efuansyah; Syamsulrizal
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.164

Abstract

Mathematical understanding develops dynamically and plays an important role in fostering higher-order thinking skills (HOTS). However, studies using the Pirie–Kieren framework have not consistently examined the relationship between the growth of mathematical understanding and higher-order thinking. This study aims to explore the growth of a junior high school student’s mathematical understanding at Junior High School Number 8 Lubuklinggau, and higher-order thinking within the framework of Pirie-Kieren. This study employed a descriptive exploratory approach involving one eighth-grade student with high mathematical ability, selected purposively. The student completed a System of Linear Equations in Two Variables (SPLDV) task designed based on the Pirie–Kieren layers of understanding. Data were collected through observations, interviews, and documentation, and were analyzed thematically. The results show that the student’s mathematical understanding exhibited growth in a dynamic and nonlinear manner, progressing from primitive knowing to structuring, with recurring folding-back. Along this progression, the student demonstrated higher-order thinking, including recognizing concepts, applying prior knowledge in new contexts, constructing mathematical models, identifying properties, abstracting ideas, reflecting on processes, and connecting concepts. These findings indicate that the growth of mathematical understanding is closely associated with the development of higher-order thinking, suggesting that both evolve simultaneously during the learning process.
Didactic Obstacles in Trigonometric Ratios: Insights into Students’ Mathematical Understanding Hayuningrat, Silfia; Suryadi, Didi; Rofiki, Imam
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.166

Abstract

This study examines the relationship between the knowledge prescribed in the school curriculum, the knowledge enacted by mathematics teachers, and the knowledge constructed by students in learning trigonometric ratios through the perspective of Didactic Transposition Theory. A qualitative intrinsic case study was conducted with one mathematics teacher and 22 tenth-grade students in an Indonesian senior high school. Data were collected from curriculum documents, teaching notes, classroom observations, interviews, and two tests designed to capture students’ conceptual understanding. The data were analyzed using document analysis, content analysis, and descriptive analysis. The findings show that although students’ understanding of trigonometric ratios improved during instruction, the enacted classroom practices mainly emphasized trigonometric ratios as fixed relationships among the sides of right triangles. Consequently, students tended to interpret sine, cosine, and tangent primarily as geometric ratios rather than as functions of angles. This emphasis limited students’ ability to connect geometric reasoning with functional interpretations of trigonometric relationships. These results highlight the importance of strengthening instructional coherence in curriculum implementation so that classroom teaching better supports the development of both geometric and functional understanding of trigonometry.
Improving Creative Thinking Skill with Linear Equation Worksheet Based on Tri-N Activity Sulistyowati, Fitria; Widodo, Sri Adi; Tapo, Maria Marfiani; Utami, Wikan budi; Vaz, Benjamin Laurentino
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.167

Abstract

Tri-N or Niteni, Nirokake, Nambahi (observing, imitating, adding) is a learning approach initiated by the Father of Indonesian Education, Ki Hadjar Dewantara. Tri-N is an adaptable approach that is easy to apply in every learning material, including mathematics. This research and development aims to develop an e-worksheet based on Tri-N for system of linear equations in two variables to improve junior high school students' creative thinking skills using the Liveworksheet Platform. The study employed the ADDIE development model, with stages: analysis, design, development, implementation, and evaluation although it was limited to the development stage to focus on validity and practicality. The results of this research include: (1) an e-worksheet based on Tri-N in a two-variable linear equation system has been produced to improve the creative thinking skills of junior high school students, (2) the validity test of the e-worksheet developed shows that 98.60% is categorized as very valid, and (3) the practicality test of the e-worksheet shows that 67.14% of students strongly agree and 31.90% of students agree on each aspect of the assessment. So, it can be concluded that e-worksheet based on Tri-N in a two-variable linear equation system is valid and practical for improving junior high school students' creative thinking skills. It is hoped that the research can become a reference in further research to test the effectiveness of the e-worksheet.
Implementing STEM-Based Mathematics Learning in Indonesian High Schools: Teachers’ Understanding, Challenges, and Supporting Factors Kurniawan, Indra; Sugiman; Syukrul Hamdi
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.176

Abstract

STEM is a learning approach that can enhance students' mathematical skills by linking mathematics with science, technology, and engineering, thereby increasing students’ motivation. This study analyzed teachers' understanding and the challenges they face in implementing STEM-based mathematics instruction. A phenomenology-informed qualitative study explored the experiences of 12 mathematics teachers across six provinces in Indonesia: West Java, Central Java, East Java, Yogyakarta, West Sumatra, and West Nusa Tenggara. Data were collected through online interviews and analyzed using the Bogdan & Biklen technique, including data reduction, axial coding, theme determination, and conclusion and interpretation. The results indicate that teachers view STEM-based mathematics as a means to connect subjects, develop critical 21st-century skills, and apply knowledge in real-life contexts. They implement STEM through project-based, interdisciplinary lessons that increase student engagement, despite challenges such as time constraints, curriculum demands, and differences in student readiness. Effective STEM instruction relies on professional development, school support, and sufficient resources to enable teachers to integrate STEM concepts confidently into mathematics teaching. These findings highlight the importance of providing structured guidance, adequate teaching materials, and policy support to enhance teachers’ capacity to deliver STEM-based mathematics effectively, bridging theory and practice for meaningful student learning.
Does Project-Based Learning Equally Foster Critical and Creative Thinking? Arfin Arfin; Melania Eva Wulanningtyas; Andy Leonardo Louismono; Oriza Stepanus
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.180

Abstract

This research explored the effectiveness of the Project-Based Learning (PjBL) instructional model in improving critical and creative thinking skills among students at SMAK 1 Bina Bakti Bandung, Indonesia. Employing a one-group pretest-posttest quasi-experimental design, the research examined how students’ critical and creative thinking skills developed after participating in a series of PjBL learning activities in polynomial topic. The findings revealed significant improvements in both critical and creative thinking skills. Critical thinking showed notably increases in all indicators (analysis, synthesis, problem solving, inference, evaluation) with the most substantial changes in synthesis and problem solving. Likewise, creative thinking also showed a remarkable improvement in all indicators (flexibility, originality, elaboration, reflection, and fluency) particularly in elaboration and fluency. The effect sizes of critical and creative thinking were measured at 0.804 and 0.949 respectively, indicating the strong impact of PjBL in improving both domains. While critical thinking exhibited comparatively elevated scores both prior to and following the intervention, the extent of enhancement was more pronounced in creative thinking. It was suggested by these results that while a relatively strong foundation in critical thinking had already been demonstrated by the students, their creative thinking skills were particularly effectively enhanced by the implementation of PjBL.
Exploration of Jejamok Games as Local Wisdom: Basis for Developing E-Comics for Integer Learning Handayani, Ratih; Putri, Ratu Ilma Indra; Zulkardi; Darmawijoyo
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.181

Abstract

The persistent challenges students face in understanding integers indicate the need for learning approaches that connect abstract mathematical concepts with meaningful real-life experiences. Although culturally grounded contexts have been widely recommended in mathematics education, there remains a limited understanding of how specific traditional games can be systematically interpreted to reveal their embedded mathematical structures and support conceptual learning. This study seeks to investigate the Jejamok traditional game from North Lampung through an ethnomathematics perspective to identify its potential as a context for learning integer concepts and as a basis for developing instructional media. A qualitative exploratory approach was employed, involving literature review, field observations, and interviews with local community members and teachers. The findings reveal that Jejamok embodies several key mathematical ideas related to integers, including (1) positive and negative values represented through capture and release actions, (2) addition and subtraction of integers through score changes, and (3) comparison of quantities and strategic decision-making based on game situations. These concepts emerge naturally from the game’s scoring system and player interactions, providing a meaningful bridge between informal experiences and formal mathematical understanding. Furthermore, the game structure reflects a form of situated mathematical representation that supports progressive mathematization within the PMRI framework. In addition, Jejamok reflects important cultural values such as cooperation, sportsmanship, and nengah nyappur, which contribute to social learning. These findings suggest that Jejamok can serve not only as a contextual learning resource but also as a conceptual foundation for developing culturally responsive instructional media, such as e-comics. This study contributes to the development of culturally grounded mathematics instruction by offering an empirically supported and theoretically informed model for connecting local cultural practices with formal mathematical learning.
Enhancing Students' Problem-Solving Skills through Ethnomathematics-Based Geometry Learning with an Android Mobile Application Hodiyanto; Setyaningsih, Erna; Hasan, Buaddin; Palobo, Markus; Bidya Nath Koirala
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.182

Abstract

Despite the growing integration of technology in mathematics education, research on mobile learning platforms embedding local cultural contexts—particularly ethnomathematics—remains limited at the junior secondary level in Indonesia. Mathematical problem-solving ability remains a persistent challenge among students, necessitating Android-based learning media as a more engaging instructional solution. This investigation examined the extent to which an Android-based interactive mobile learning (m-learning) platform, integrated with ethnomathematics derived from Pontianak's local culture. A quasi-experimental posttest-only control-group design was adopted for this purpose. From nine classes at SMP Negeri 2 Pontianak, 60 participants were selected via cluster random sampling—30 in the experimental group receiving m-learning instruction and 30 in the comparison group receiving instruction without m-learning. Assessment of mathematical problem-solving capacity was conducted through a descriptive test comprising three items structured around Polya's four-stage indicators, with empirically established validity coefficients ranging from 0.94 to 0.96 and a reliability coefficient of 0.78. Statistical examination involved a one-tailed independent samples t-test for group comparison, supplemented by Cohen's d for effect size quantification. Findings revealed that learners exposed to m-learning instruction demonstrated substantially superior mathematical problem-solving performance compared to their counterparts in the conventional group (mean = 84.67 vs 72.63; p < 0.05), with a large effect magnitude (Cohen's d = 1.3). These outcomes affirm that the ethnomathematics-embedded Android-based m-learning platform constitutes an efficacious and educationally meaningful intervention for cultivating students' mathematical problem-solving proficiency. Nevertheless, further research on a broader scale is warranted to enhance the generalizability of these findings, along with the incorporation of a pretest to more rigorously assess gains and establish stronger causal evidence of the intervention's effectiveness.
Analysis of Junior High School Students' Multiple Mathematical Representation (MMR) Ability in Solving Fraction Problems Luluk Faridah; Mustofa; Emmy Hamidah; Heny Ekawati Haryono
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.187

Abstract

This study aims to analyze the multiple representations of mathematics (MMR) of junior high school students with high, medium, and low abilities in solving fraction problems. This study uses a descriptive qualitative method. The subjects of this study were 6 students taken from 32 seventh-grade students of SMP Negeri 2 Sukodadi. The research instrument consisted of a problem-solving test and a semi-structured interview guide (task-based) that refers to the aspects of multiple representations, namely (1) symbolizing; (2) describing (visually, verbally, and symbolically); and (3) referring to the answer. Data were analyzed through data condensation, data presentation, and drawing conclusions, with time triangulation to ensure the validity of the findings. The results of the study show that, based on student scores and data obtained, students are in the high category; there are 11 students (34.375%), with an average score of 100. There are 10 students in the medium category (31.25%), with an average score of 62.5. And 11 students in the low category (34.375%), with an average score below 50. Based on the multiple representations used, 12.5% of students in the high category meet all indicators of multiple representations. 12.5% of students in the medium category meet 3 indicators, with 2 representations. 75% of students in the low category only meet 1 indicator (describing visually/verbally). These findings indicate the need for us to achieve success in solving mathematical problems.
How Cognitive Styles Shape Creative Mathematical Thinking Afifah, Dian Septi Nur; Saraswati, Grafika; Hayuningrat, Silfia
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.192

Abstract

Creative thinking is widely recognized as a core component of higher-order thinking in mathematics education; however, its development among Indonesian students remains a persistent challenge, as reflected in large-scale international assessments such as PISA 2018. Differences in students’ cognitive styles particularly reflective, impulsive, and slow-inaccurate styles are assumed to shape cognitive processing and mathematical problem-solving performance, yet empirical evidence remains limited. This study aims to examine students’ creative thinking ability in mathematical problem solving from the perspective of these cognitive styles. Employing a qualitative descriptive approach, the participants were eighth-grade students from SMP Negeri 2 Sumbergempol Tulungagung, classified using the Matching Familiar Figure Test (MFFT). Data were obtained through problem-solving tests and semi-structured interviews and analyzed through methodological triangulation. The findings indicate that students with reflective cognitive styles exhibit a high level of creative thinking, characterized by fluency, flexibility, and originality. In contrast, students with impulsive and slow-inaccurate cognitive styles demonstrate moderate creative performance, predominantly reflected in elaborative responses. These results highlight the need for differentiated instructional strategies that align with students’ cognitive characteristics. The study contributes to the growing body of literature on cognitive style-based instruction and offers pedagogical insights for fostering creative thinking in mathematics classrooms.
The Impact of TPACK and Self-Efficacy on Motivation to Use Technology for Prospective Mathematics Teachers Aqib, Mohammad Auzai; Badrus
Riemann: Research of Mathematics and Mathematics Education Vol. 8 No. 1 (2026): EDISI APRIL
Publisher : Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38114/riemann.v8i1.194

Abstract

In the 21st-century education era, technology integration has become an essential need in mathematics learning. Although the Technological Pedagogical and Content Knowledge (TPACK) framework has become a popular conceptual standard, there remains a research gap regarding how the interaction between technical knowledge (TPACK) and Self-Efficacy simultaneously influences student teachers' motivation to adopt technology. The phenomenon in the field shows that mastery of technology is often not directly proportional to teachers' willingness to implement it in the classroom. This study aims to analyse the impact of TPACK and Self-Efficacy on the motivation of student mathematics teachers in integrating technology into their learning practices. This study uses a quantitative approach with a multivariable regression design. The research subjects consisted of 58 students in mathematics education programs from three universities in Indonesia who were selected through simple random sampling. Data were collected using a Likert-scale questionnaire and analysed using Partial Least Squares Structural Equation Modelling (PLS-SEM) in SmartPLS 4.0. The main findings indicate that Self-Efficacy has a positive and statistically significant influence on prospective teachers' motivation in using technology (t = 6.27; P < 0.05). In contrast, TPACK did not show a significant direct influence on motivation (P = 0.827). Simultaneously, both variables influenced motivation, with an R2 value of 0.422, indicating that this model explained 42.2% of the variance in motivation to use technology in the moderate category. The results of this study confirm that technical-pedagogical knowledge (TPACK) alone is insufficient to encourage technology adoption without being grounded in an individual's belief in their own abilities. Therefore, teacher education programs should prioritise strengthening Self-Efficacy through structured practice, technology-based teaching simulations, and providing constructive feedback to ensure prospective teachers are not only theoretically competent but also practically motivated.

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