The problem and the aim of the study. Critical thinking is a skill that students must master to keep up with 21st-century learning developments. Critical thinking skills encourage students to develop the ability to make decisions. In higher education, critical thinking skills are crucial in various majors, one of which is the mathematics education major, especially in learning integral calculus. Integrals are one of the important topics because they are widely applied in the real world and subsequent lectures. However, in fact, students’ critical thinking skills on the topic of integral mathematics are relatively low. Students’ abilities are limited to procedural knowledge, while their conceptual understanding is weak. Therefore, learning is needed that can connect concepts to the real world, which supports students’ conceptual understanding, as well as learning innovations that can improve students’ critical thinking skills. In line with technological developments, it is necessary to update mathematics learning through the use of ICT-based learning media in the form of e-modules. The purpose of this study is to describe the results of the innovation in the development of an e-module for integral calculus based on Augmented Reality (AR) with a Culturally Responsive STEM (CRS) approach to support students’ critical thinking skills.
Research methods. This research is a design research development study. This development research went through an iterative cycle by implementing formative evaluation, consisting of the preliminary design and formative evaluation stages. This study involved 37 mathematics education students in the field test. Data collection techniques used were walkthroughs, observations, interviews, questionnaires, documentation, and tests. Data were analyzed based on the research stages. The indicator of success of this research is the resulting product in the form of an AR-based integral calculus e-module with a valid, practical, and effective CRS approach to improve students’ critical thinking skills.
Results. The results showed that the MathARNa e-module met the criteria of being very valid (material = 94.8%; media = 97.6%), very practical (91%), and effective in improving students’ critical thinking skills (p < 0.05). The average critical thinking score increased from 42.32 to 58.59, categorized as high. The integration of AR technology allows students to dynamically visualize integral concepts, while the CRS approach presents a local cultural context that increases learning relevance and engagement. These findings support constructivist and culturally responsive teaching theories that contextual and culturally experience-based learning can improve students’ conceptual understanding and higher-order thinking skills.
Conclusion. AR-based integral calculus e-module with a CRS approach can be an effective learning resource for improving students’ critical thinking skills. The e-module’s context relates to the real world, allowing students to learn integral concepts effectively.
Keywords: e-modules, calculus integral, culturally responsive STEM, augmented reality, critical thinking skills
For Citation: Saraswati, S., Nugroho, M. W., & Hartiningrum, E. S. N. (2026). MathARNa: Integrating Augmented Reality and Culturally Responsive STEM in Calculus E-modules to Enhance Students’ Critical Thinking Skills. Perspektivy nauki i obrazovania = Perspectives of Science and Education, (2), 633–649. https://doi.org/10.32744/pse.2026.2.39
Authors:
Sari Saraswati (Indonesia, East Java, Jombang) — Lecturer in Mathematics Education Study Program. Faculty of Education. Hasyim Asy’ari University
Meriana Wahyu Nugroho (Indonesia, East Java, Jombang) — Lecturer in Civil Engineering Study Program. Faculty of Engineering. Hasyim Asy’ari University
Esty Saraswati Nur Hartiningrum (Indonesia, East Java, Jombang) — Lecturer in Mathematics Education Study Program. Faculty of Teacher Training and Education. PGRI Jombang University
© S. Saraswati, M. W. Nugroho, E. S. N. Hartiningrum, 2026
The author’s declared no conflicts of interest
Received: 11 July 2025 | Approved: 12 September 2025 | Published: 30 April 2026
This is an open access article distributed under a Creative Commons Attribution-ShareAlike International License (CC-BY-SA 4.0)
that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal
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