This paper presents a novel methodological framework for analyzing and optimizing educational curricula through the lens of complex network theory. Its significance lies in providing a quantitative, data-driven approach to curriculum design, moving beyond traditional qualitative assessments, particularly in the context of interdisciplinary integration.
The key innovations of this work include:
- Quantitative Curriculum Mapping: The paper systematically constructs concept networks where curriculum contents are represented as nodes and their epistemological relationships (dependencies, relatedness) as edges. By applying various complex network metrics—such as degree, closeness, and betweenness centrality, along with properties like density, diameter, and clustering coefficient—it quantifies the structural characteristics of curricula. This allows for a precise identification of the most central or influential concepts and how content naturally clusters.
- Dynamic Analysis of Subject Integration: A crucial innovation is demonstrating how the network properties and the importance of individual concepts change when two distinct subjects (Physics and Mathematics, in this case) are integrated into a single, combined network. This analysis reveals emergent interdisciplinary connections that are not apparent when subjects are considered in isolation, and identifies concepts that act as vital bridges between disciplines, highlighting opportunities for integrated learning.
- Identification of Pedagogically Significant Content: The framework offers a systematic means to distinguish between “transversal” concepts (foundational skills broadly applicable across the curriculum) and “conceptually rich” concepts (those that serve as hubs connecting diverse topics). This distinction provides actionable insights for curriculum designers to prioritize content that is critical for overall understanding and interdisciplinary coherence.
- Systematic Relationship Assessment: The development of an automated, rigorous method for manually reviewing and recording all N(N-1)/2 potential relationships between concepts ensures consistency and reduces bias in the construction of the network, thereby enhancing the objectivity of the analysis.
The main prior ingredients upon which this research builds are:
- Complex Network Theory: This serves as the foundational mathematical and computational toolkit. Concepts like nodes, edges, various centrality measures (degree, closeness, betweenness), and community detection algorithms (e.g., Infomap, used here) are directly adopted from this field to model and analyze the curriculum structure. The paper leverages the established power of network science to uncover hidden relationships and organizational principles within complex systems.
- Educational Concept Mapping: The idea of representing knowledge domains and their interconnections graphically through concept maps has a long history in education. This paper advances this tradition by adopting the rigorous quantitative methods of complex network theory, moving beyond qualitative visual representations to provide measurable insights into curricular coherence and concept importance.
- Contemporary Pedagogical Principles: The motivation for the study is deeply rooted in modern educational thought, particularly the emphasis on interdisciplinary learning, competency-based education, and the need to move beyond rigid subject silos. The network analysis framework provides a practical, evidence-based tool to support these pedagogical goals by identifying natural connections and optimal content organization for integrated approaches.
- Specific Curricular Content Analysis: The practical application of the methodology requires a detailed, expert-led analysis of actual curriculum documents. In this study, the specific contents and their expert-defined relationships within the Spanish high school Physics and Mathematics curricula form the empirical data upon which the networks are built and analyzed.