An Interactive and Dynamic Algebra Learning Environment: A Six-Principle Design Framework Validated Through Design-Based Research

University-level Linear Algebra is widely recognised as the most challenging transition point in undergraduate mathematics, yet technology-enhanced learning environments for this course remain under-researched. This paper presents the Interactive and Dynamic Algebra Learning Environment (IDALE), a six-principle design framework developed and empirically validated through a full Design-Based Research (DBR) cycle at Universitas Negeri Makassar, Indonesia, during the 2023/2024 academic year. The study involved 36 students in an experimental class and 26 in an independent replication class across 14 instructional sessions. IDALE integrates six interdependent principles, each grounded in an established learning theory: Dual Representation Integration, Digital System-Based Self-Exploration, Contextual and Task-Based Collaboration, Integrated Axiomatic-Procedural Learning, Instant Feedback and Structured Validation, and Adaptive Dynamics and Learning Autonomy. These principles are enacted through a five-phase learning trajectory spanning mindful, joyful, and meaningful deep learning dimensions. Empirical results demonstrated a 97.2% pass rate against a 65% benchmark, 97.2% cumulative positive student response, and consistent active engagement of at least two-thirds of students from Session 5 through Session 14. Replication class findings corroborated cross-instructor transferability. IDALE constitutes a theoretically grounded, practically actionable, and empirically validated framework for designing interactive digital mathematics learning environments in higher education.