## 1 Introduction
The results showed that using a pre-trained language model in SBERT outperformed the other models, while max paragraph pooling outperformed mean pooling and adjusted mean pooling. The latter result can be viewed as indicating--at least for the purpose of identifying textbook sections that are relevant for a given quiz--that high semantic similarity with a single paragraph in a section is more important than high average semantic similarity across all paragraphs in a section. In this study, we carry out a thorough investigation and evaluation of text representations in the form of embeddings from pre-trained language models to be leveraged in an STS-based educational content recommendation system. In particular, we include in our evaluation the use of higher-dimensional embeddings derived from an LLM and continue to explore the potential of incorporating knowledge graphs. With respect to the latter, we do so in one of two ways: (i) by representing texts--both exercises and textbook content--based solely on pre-identified concepts, and (ii) by combining knowledge graph embeddings with contextual embeddings in various ensembles in an attempt to exploit their respective advantages. The STS-based educational content recommendation system is designed to automatically link relevant textbook content to exercises, here, extended to encompass both quizzes and study questions across three subjects. In summary, the main contributions and findings of this study are described below:* We evaluate the use of static and contextual embeddings derived from different types of pre-trained language models and a concept-based knowledge graph for STS-based educational content recommendation. The results show that higher-dimension contextual embeddings from LLM outperform both lower-dimension contextual embeddings and static embeddings trained using a knowledge graph, even when resorting to domain-specific concept filtering. * We explore the possibilities of combining the respective advantages of contextual embeddings and knowledge graph embeddings using three different ensemble methods based on both early and late fusion approaches. The results show that when using contextual embeddings from a relatively smaller language model and lower dimension (SBERT), performance improves when combined with knowledge graph embeddings in a late fusion fashion. However, when using higher-dimension embeddings from LLM (text-embedding-ada-002), there is no significant gain from any of the ensembles. * We show that by leveraging powerful embeddings from a pre-trained language model, an STS-based educational recommendation system can be developed in a wholly unsupervised manner, i.e., without relying on labeled training data. The system can accurately link exercises to relevant textbook sections: the best-performing model obtains a Recall@3 of 0.96 and an MRR of 0.87 for quizzes and a Recall@3 of 0.95 and an MRR of 0.86 for study questions across three subjects. The paper is structured as follows. In Section 2, we review existing literature and describe previous work relevant to our study, providing a comprehensive overview of the current state of educational content recommendation systems, knowledge graph embeddings, as well as methods for incorporating knowledge graphs with pre-trained language models. In Section 3, we first outline the datasets utilized in our research, which contain textbook instructive content and two types of exercises: quizzes and study questions. After that, we present the study design, models, evaluation metrics, and significant testing. Section 4 presents the results of our experiments and analyses. Subsequently, in Section 5, we delve into the implications of the results, contextualizing our findings within the broader research landscape. Finally, Section 6 provides a succinct summary of the study and its contributions.