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Program Studi Pendidikan Matematika Universitas Katolik Santo Agustinus Hippo Jl. Ilong, Dusun Gasing Pal 4, Amboyo Utara, Ngabang, Landak - Kalimantan Barat Email: riemann@sanagustin.ac.id Website: https://www.sanagustin.ac.id
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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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From Recognition to Logical Deduction: Assessing the van Hiele Levels of Geometric Thinking Among Students of Diverse Disciplines Palobo, Markus; Nasruddin; Yonarlianto Tembang; Oswaldus Dadi
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.v8i1.145

Abstract

This study investigates the geometric thinking levels of university students using the van Hiele model as an analytical framework. A total of 85 students from four academic programs—Mathematics Education, Primary School Teacher Education, Agricultural Science, and Informatics Engineering—at Universitas Musamus participated in the study. The Van Hiele Geometry Test (VHGT), consisting of 25 multiple-choice items across five cognitive levels, was administered. Data were analyzed using descriptive statistical methods, including percentage distribution and level classification based on students’ mastery of at least three out of five items at each van Hiele level. In addition, an item-based diagnostic analysis was conducted to identify patterns of misconceptions in students’ responses. Comparative analysis across academic programs and gender was also performed to examine subgroup differences. The results revealed that most students were operating at the lower levels of geometric thinking: Level 0 (Pre-recognition), Level 1 (Visualization), and Level 2 (Analysis). Only two students reached Level 3 (Informal Deduction), and none achieved higher levels. Diagnostic findings indicated persistent misconceptions, particularly reliance on visual prototypes and difficulties in property-based reasoning. These findings highlight the need for instructional strategies aligned with students’ cognitive levels to promote higher-order geometric reasoning. This study contributes to the literature by providing insights into cross-disciplinary differences in geometric thinking at the tertiary level.
Embodied Cognition in  an OSNK Mathematics Olympiad Winner: Geometry vs. Algebra Problem Solving Hamdan Yuafie Ni’am; Suwarno
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.v8i1.146

Abstract

This study aims to describe the characteristics of embodied cognition that emerge when a student who won the National Science Olympiad (OSN) in Mathematics solves OSN-level geometry and algebra problems for the first time. This study uses a qualitative descriptive approach with one subject, namely an 11th-grade student who won the 2025 District OSN. Data were collected through video and audio recordings using two mobile phones, multimodal observation sheets, and reflective interviews. Two types of problems were used as instruments: geometry and algebra. The data were analyzed using the interactive model of Miles, Huberman, and Saldaña. The results showed that the subject's embodied cognition in solving OSN-level mathematics problems was manifested through the integration of gestures and utterances. Writing gestures appeared consistently and dominantly across all stages of problem-solving, both in geometry and algebra questions, as a means of organizing information, planning, and executing solutions. Representational and pointing gestures were limited and used contextually in both geometry and algebra questions to aid visualization and confirm solution steps. In terms of utterances, the subject showed relatively stable patterns through variations in tone of voice, facial expressions, gaze direction, and body posture that supported the thinking process. These findings confirm that mathematical problem-solving involves the simultaneous integration of verbal and nonverbal aspects, with embodied cognition playing an important role in supporting high-level mathematical thinking
From Intended to Enacted: A Situated Analysis of TPACK-in-Action Through Video-Stimulated Recall in Geometry Classrooms Hanifah, Umi; Masriyah, Masriyah; Sari, Ayu Silvi Lisvian; Saadah, Nurus; Cahyani, Jessica Dwi Nur
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.v8i1.148

Abstract

The integration of digital technology into mathematics classrooms remains inconsistent despite the development of the Technological Pedagogical Content Knowledge (TPACK) framework. This study investigates the persistent "know–do gap" by proposing a conceptual framework consisting of intended, enacted, and reflected TPACK. A qualitative multiple-case study was conducted with four secondary mathematics teachers in East Java, Indonesia. Data were triangulated from lesson plans, dual-camera classroom observations, and video-stimulated recall (VSR) interviews. Findings reveal a significant discrepancy: while teachers designed sophisticated technology-rich lessons, 65% of planned activities were shortened or abandoned during enactment. This regression to traditional instruction was primarily driven by excessive dual cognitive load and real-time classroom management pressures. VSR successfully uncovered teachers’ tacit reasoning, serving as a cognitive trigger for reflective improvement. The study concludes that TPACK is a situated and dynamic competence rather than a static body of knowledge. Implications suggest that professional development should move beyond technical training toward structured video-reflection cycles to develop teachers' adaptive orchestration and real-time decision-making skills.
Developing Digital Eco-Mathematics Teaching Materials: A Pathway to Foster Critical Thinking and Environmental Awareness Saputro, Totok Victor Didik; Silvester; Sadewo, Yosua Damas; Purnasari, Pebria Dheni; Sampouw, Falenthino; Tarigas, Laurensius Robi; Hassen, Nurselam
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.v8i1.150

Abstract

The development of digital Eco-Mathematics teaching materials presents a significant opportunity to enhance elementary education by fostering critical thinking skills and environmental awareness among students. Existing mathematics learning materials rarely integrate environmental contexts in a structured and digital format, particularly in border areas, leading to limited opportunities for students to develop both competencies simultaneously. Moreover, students in border areas often experience limited access to contextual and innovative learning resources, which contributes to low levels of critical thinking skills and environmental awareness. This research aims to develop and evaluate these materials for fifth-grade students in elementary schools located in the Indonesia–Malaysia border area. Utilizing the Tesser & Akker framework, the study employs a design research approach consisting of a Preliminary Study and a Formative Evaluation to guide the development process. The analysis focuses on the validity, practicality, and effectiveness of the teaching materials in terms of educational outcomes. The findings indicate that the developed Eco-Mathematics materials meet the criteria for validity, practicality, and effectiveness. These results highlight the contribution of this study in providing an innovative integration of environmental contexts into digital mathematics learning, which effectively supports the enhancement of students’ critical thinking skills and environmental awareness, particularly in under-resourced border areas
Students' Critical Thinking Dispositions: Truth Seeking and Systematic Syamsulrizal; Supratman; Sahidi
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.v8i1.151

Abstract

This study aims to describe students’ critical thinking dispositions in the aspects of truth-seeking and systematic thinking in mathematical problem-solving. This research employed a qualitative descriptive design involving two ninth-grade students selected through purposive sampling based on high mathematical ability. Data were collected through problem-solving tasks and semi-structured interviews and analyzed using indicators of truth-seeking (identifying relevant information, evaluating assumptions, and using accurate data) and systematic thinking (organizing solution steps logically, using appropriate mathematical notation, and verifying results). Data validity was ensured through triangulation of written responses and interview data. The findings reveal that students are generally able to organize relevant data, follow logical procedures, and obtain correct answers, indicating the presence of procedural-level critical thinking dispositions. However, students demonstrate weaknesses in verifying assumptions and evaluating final results, showing that reflective aspects of critical thinking are not yet fully developed. These findings highlight a gap between procedural competence and the depth of critical thinking dispositions, where correct answers do not necessarily reflect strong critical thinking. This study contributes theoretically by emphasizing that critical thinking involves not only cognitive skills but also reflective habits that require explicit development. Practically, the results suggest the need for instructional strategies that encourage students to recheck their work, question assumptions, and reflect on their reasoning processes.
Interpreting the ε–δ Definition: Hermeneutic Insights into Students’ Ways of Thinking Prihandhika, Aditya; Ramadani, Iqbal
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.v8i1.154

Abstract

This study aims to reveal the hermeneutic insight in the formation of students’ ways of thinking (WoT) toward the precise meaning of the limit concept in differential calculus. Formally, the concept of limit is defined through the relationship between ε (epsilon) and δ (delta), namely that for every ε > 0, there exists a δ > 0 such that if 0 < |x − a| < δ, then |f(x) − L| < ε, expressing a precise dependency between function values and domain values. However, students often interpret this definition in ways that do not fully capture its relational meaning. This qualitative case study involved 28 undergraduate students and used written tasks, interviews, and classroom observations to collect data. The analysis integrates the WoT framework, which consists of empirical, procedural, and theoretical ways of thinking, with a hermeneutic perspective to explore how students construct meaning. The findings show that most students’ reasoning is dominated by empirical and procedural ways of thinking of the ε–δ, reflected in substitution, approximation, and symbolic manipulation. From a hermeneutic perspective, these patterns indicate that students interpret limit within restricted interpretative horizons. Only a few students demonstrate theoretical reasoning, suggesting an emerging integration between prior understanding and formal structure. These findings suggest that students’ difficulties with limits are not only cognitive but also interpretative, highlighting the importance of supporting meaning-making in calculus learning.
Is mathematics still scary? Primary school pupils' perceptions of mathematics Mubarik; Ibnu Hadjar; Welli Meinarni; Annisa Dwi Kurniawati
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.v8i1.155

Abstract

For a long time, research has shown that mathematics is an unpleasant subject. This study examines whether mathematics remains scary today. Previous research has limitations, particularly in terms of why primary school students have negative perception of mathematics. This study uses a descriptive qualitative design supported by quantitative data to obtain more in-depth results. The subjects of this study were 153 fifth-grade students from nine primary schools in the city of Palu, selected at random. Data were collected via a questionnaire, and responses were categorized as positive or negative. Based on this, 109 students (71%) gave negative responses, namely "mathematics has a lot of formulas", "mathematics is difficult", "mathematics is scary", and "mathematics is boring". Meanwhile, 44 other students (29%) gave positive responses, namely "mathematics is challenging" and "mathematics is enjoyable". Subsequently, six participants were selected who were representatives of each type of response to be interviewed. Data credibility was tested using the member check technique. Then, it was analyzed using three stages, namely data condensation (summarizing and connecting meaning between data), data presentation (displaying data in tables and descriptions) and drawing conclusions (connecting data with theory, data categorization, and data interpretation). The results of this study indicate that many primary school students still find mathematics intimidating. This perception is driven by two factors: the nature of mathematics and the way it is taught. This situation necessitates the continued development of learning strategies that can shift students' perceptions from negative to positive.
Can STEM Learning Supported by Dynamic Mathematics Software (DMS) Enhance Students’ Complex Problem Solving in Climate Change? Azhar, Lillian Dhian Nafiatul; Pamungkas, Megita Dwi; Krisma, Dita Aldila
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.v8i1.156

Abstract

The development of students’ Complex Problem Solving (CPS) skills remains constrained by mathematics instruction that is primarily procedural and insufficiently connected to real-world global issues, particularly climate change. To address this limitation, the present study investigates whether STEM learning supported by Dynamic Mathematics Software (DMS) can improve senior high school students’ CPS abilities within climate change contexts. A quasi-experimental, non-equivalent pretest–posttest control group design was implemented with 69 eleventh-grade students. The experimental group participated in STEM learning integrated with DMS, while the control group received direct instruction on the same climate change context. Data were analyzed using descriptive statistics, Wilcoxon signed-rank tests, paired-sample t-tests, N-Gain, and Cohen’s D. Results showed that the experimental group achieved a high N-gain score (0.79), whereas the control group attained a low gain (0.29). The magnitude of this increase is also reflected in the effect size Cohen's d values, 5.893 in the experimental class and 2.438 in the control class. These findings suggest that STEM learning supported by Dynamic Mathematics Software constitutes an effective pedagogical strategy for advancing students’ complex problem-solving skills and strengthening mathematics education
Numeracy Literacy Worksheet: Identifying High School Students' Needs In Mathematics Learning Nugroho, Purna Bayu; Meilasari, Venty
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.v8i1.157

Abstract

This study aims to analyze the need for numeracy literacy worksheets by identifying students' needs in mathematics learning. This study uses a descriptive qualitative approach. The data in this study were obtained from the results of interviews with students and teachers. Test the validity of the data in this study using source triangulation and member checking. Data analysis techniques use interactive analysis techniques (data collection, data reduction, data presentation, and conclusions). The results of this study indicate that: 1) high and medium category high school students tend to have a need for numeracy literacy worksheets designed in the form of 3D games; 2) low category high school students tend not to want numeracy literacy worksheets but need ordinary mathematical worksheets designed in the form of 3D games. 3) High category students tend to need challenging and innovative worksheets, 4) Medium category students tend to need worksheets that emphasize the need for clear instructions, a variety of questions, and not too many numbers, while 5) Low category students tend to need worksheets with simple, clear, and easy-to-understand questions without long contexts.
Development a Local Wisdom-Based Ratio E-Worksheet Based on Critical Thinking Indicators Rahaju; Murniasih, Tatik Retno; Hariyani, Sri; Sumaji
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.v8i1.162

Abstract

Critical thinking skills are essential for dealing with various problems in life problems. However, many students still demonstrate low levels of these skills. This study aimed to develop a local wisdom-based ratio electronic student worksheet (E-Worksheet) designed based on critical thinking indicators and to examine its validity and practicality. The study adopted the Plomp development model, consisting of preliminary research, prototyping, and assessment phases. The participants were seventh-grade students in Singosari District, involving a small group of 10 students and a large group of 24 students. The developed web-based E-Worksheet integrates local wisdom contexts, such as Singhasari cultural heritage, Kirab Tirta Amarta Sari, and Petirtaan Watugede, into ratio learning. The validation results showed an average score of 94. 44%, categorized as highly valid. The practicality results indicated scores of 89. 29% from teachers and 80. 12% from students, both categorized as highly practical. These findings indicate that the developed E-Worksheet is valid and practical for use in mathematics learning and systematically designed based on critical thinking indicators. It has the potential to support meaningful and contextual learning. Further research is recommended to examine its effectiveness in improving students’ critical thinking skills.

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