Reconceptualizing authenticity in problem-based learning for linear algebra course: A multi-stakeholder analysis of video-based hybrid instruction
Keywords:
Hybrid online learning, Linear Algebra, Problem-based learning, Multi-stakeholder analysis, Video-based learningAbstract
This study develops an integrated video-based hybrid online learning model with problem-based learning (PBL) for Linear Algebra instruction in resource-constrained contexts. A qualitative case study with three experts and five students using thematic analysis yielded 13 codes organized into five themes: technological challenges, video characteristics, hybrid architecture, PBL implementation, and motivation strategies. Findings reveal that 100% of participants identified infrastructure constraints as primary barriers, necessitating downloadable mobile-optimized content. Optimal video specifications include 15-20 minute instructor-led explanations with embedded interactivity. The study reconceptualizes 'authentic problems' for abstract mathematics from contextual realism to conceptual genuineness, demonstrating that effective PBL engages genuine mathematical thinking—comparing representations, investigating theorems, exploring counterexamples, rather than forced real-world applications. The developed three-phase hybrid model integrates asynchronous video foundation, synchronous collaborative problem-solving, and asynchronous portfolio consolidation. Multi-stakeholder convergence on core principles provides robust design guidance, while divergences regarding scaffolding and accessibility illuminate implementation challenges. The study contributes theoretically by challenging traditional PBL frameworks for abstract domains and methodologically by demonstrating that integrating expert pedagogical knowledge with student experiential perspectives yields contextually feasible models. Practical implications address institutional digital learning policies, LMS developer feature priorities, and educator implementation guidelines adaptable across resource-constrained contexts globally.
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