ArtEM: Enhancing the Understanding of Integer and Modular Arithmetic Through Interactive Learning Software

Abstract

Integer and modular arithmetic is a fundamental area of mathematics, with extensive applications in computer science, and is essential for cryptographic protocols, error correction, and algorithm efficiency. However, students often struggle to understand its abstract nature, especially when transitioning from theoretical knowledge to practical applications. To address these issues, interactive educational software can play a crucial role in supporting the learning process. In this study, we present ArtEM (Integer and Modular Arithmetic), a Java-based tool that was developed to assist both students and instructors in exploring topics related to integer and modular arithmetic. ArtEM offers an intuitive approach, allowing users to experiment and to gain a deeper understanding of the subject. A survey conducted among students at the University of Alicante (Spain) assessed their satisfaction with ArtEM, which enabled a detailed analysis of key aspects, including its usability, content quality, and didactic effectiveness. These dimensions were crucial in evaluating how well ArtEM supports learning and enhances the overall educational experience. The results indicated that students found ArtEM user-friendly, providing a seamless learning experience. Feedback on content quality emphasised its relevance and clarity, while participants noted that the tool effectively supported their learning objectives. Data analysis also demonstrated that ArtEM improved students' understanding of complex concepts, encouraged independent learning, and contributed to improved academic performance. A remarkable improvement in students' ability to apply theoretical knowledge to practical scenarios was observed, underscoring the effectiveness of ArtEM in fostering deeper learning and better educational outcomes.