## 2 Materials and Methods
### Adaptive System Description  
Education has often implemented one-size-fits-all models that prioritize fixed outcomes rather than focusing on individual learners and their needs. However, AI-adaptive learning has been developed as an alternative, offering a personalized approach to meet each student's unique needs through tailored teaching methods. AI-enabled adaptive learning systems apply AI to customize the educational journey for each student. They analyze data on students' performance and then adjust the learning path and content accordingly. HECOF integrated the Adaptemy AI-Adaptive Learning Engine to build accurate learner models and to provide recommendations. The Adaptemy AI Engine creates and updates accurate learner models and provides multi-layered adaptation and recommendations that encapsulate effective learning strategies. The engine makes use of a learner model, a curriculum model, and a content model. The Adaptemy AI-Adaptive Learning Engine makes use of content and curriculum modeling to support its applicability across different courses. Furthermore, it uses machine learning to continuously update the models. Item Response Theory (IRT), Bayesian Networks, and Knowledge Space Theory are the underlying foundations of the Adaptemy AI-Adaptive Learning Engine. A student's response to an assessment item gives probabilistic evidence related to one concept. This evidence further updates the learner model across the whole curriculum. The curriculum model defines the prerequisite relationships between the knowledge items (concepts). The content model encapsulates metadata that reflects how content objects are used and learner content metrics. Content objects may have some intended sequence and are linked to curriculum concepts. The learner model encapsulates ability estimates on skills and knowledge in an overlay to the curriculum model [56; 57; 58]. The Adaptemy AI-Adaptive Learning Engine structure aligns with the classical adaptive learning system (ALS) architecture, which typically consists of a Domain Model (DM), a learner model (LM), and an Adaptation Engine [57]. The Domain Model represents the formal structure of the knowledge domain. It contains both the content model, including content metadata, and the curriculum model, including conceptual relationships and learning objectives. The learner model stores information about the student's knowledge state, misconceptions, preferences, and learning history. The Adaptation Engine uses AI techniques to personalize content sequencing, assessments, and feedback in real time and to orchestrate the learning experiences and learning strategies. To better support complex task decomposition and micro-level diagnostics in STEM domains, this framework has been extended to include a Sub-skills Model, which captures fine-grained skill mastery using data-driven inference. As a result, HECOF maintains fidelity to a well-established adaptive learning framework while enhancing its precision and transparency, key features for domains requiring stepwise conceptual and procedural understanding. The learning experiences in the HECOF system were designed within Adaptemy's adaptive learning design framework, and the Adaptemy AI Engine was configured using the designed learning experiences to personalize the curriculum sequence and content sequencing, to provide real-time feedback, and to support individualized progression based on learner performance data. Adaptemy's adaptive learning design considers adaptive learning design a thought process, rooted in asking questions like 'what should the learning experience depend on?' and 'If you were the learner's personal tutor, how would you help them? when creating learner-centered experiences. The learning experience design is created through designing learning loops, which are then used to configure the AI-Adaptive Learning Engine to orchestrate the learning experiences for students.