Implementasi Konsep Analisis Real dalam Penyelesaian Masalah Matematika

Elis Setiawati; Windri Gusnita; Annisah Kurniati; Suci Yuniati; Depriwana Rahmi

doi:10.62383/bilangan.v3i5.774

Authors

Elis Setiawati Universitas Islam Negeri Sultan Syarif Kasim Riau
Windri Gusnita Universitas Islam Negeri Sultan Syarif Kasim Riau
Annisah Kurniati Universitas Islam Negeri Sultan Syarif Kasim Riau
Suci Yuniati Universitas Islam Negeri Sultan Syarif Kasim Riau
Depriwana Rahmi Universitas Islam Negeri Sultan Syarif Kasim Riau

DOI:

https://doi.org/10.62383/bilangan.v3i5.774

Keywords:

Augmented Reality (AR), Mathematics Learning, Polya’s Method, Problem Solving, Real Analysis

Abstract

Real analysis is one of the main branches of mathematics that serves as a fundamental foundation for the development of science and technology. This study emphasizes the understanding of basic concepts such as real numbers, limits, continuity, the principle of mathematical induction, as well as deductive and axiomatic approaches as a strong framework for mathematical proofs. This research employs the Systematic Literature Review (SLR) method by examining articles and journals related to both the theoretical aspects and the implementation of real analysis in solving mathematical problems. The findings indicate that the application of Polya’s method, visualization through demonstration, and the use of modern technology such as augmented reality (AR) can enhance the effectiveness of real analysis learning. These approaches help students connect abstract concepts with real applications, thereby strengthening logical, systematic, critical, and rigorous thinking skills. However, several learning difficulties are also identified, including the complexity of the material, weak learning habits, social influences, and inappropriate teaching strategies. Therefore, more applicative, interactive, and contextual learning strategies are needed to support the achievement of learning objectives. The conclusion of this review highlights that the integration of theoretical understanding, problem-solving methods, and innovative technology is a strategic step to improve students’ thinking quality in real analysis courses. Thus, real analysis is not only positioned as a theoretical subject but also as a medium for developing problem-solving abilities and higher-order thinking skills that are relevant to both academic needs and real-world applications.

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