Architecture and evolution of semantic networks in mathematics texts

Abstract

Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the topological structure of semantic networks reflecting mathematical concepts and their relations in college-level linear algebra texts. We hypothesize that these networks will exhibit structural order, reflecting the logical sequence of topics that ensures accessibility. We find that the networks exhibit strong core-periphery architecture, where a dense core of concepts presented early is complemented with a sparse periphery presented evenly throughout the exposition; the latter is composed of many small modules each reflecting more narrow domains. Using tools from applied topology, we find that the expositional evolution of the semantic networks produces and subsequently fills knowledge gaps, and that the density of these gaps tracks negatively with community ratings of each textbook. Broadly, our study lays the groundwork for future efforts developing optimal design principles for textbook exposition and teaching in a classroom setting.

arXiv comment22 pages, 5 figures

References in corpus (15)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Fast unfolding of communities in large networks
• Modularity and community structure in networks
• A Review of Relational Machine Learning for Knowledge Graphs
• A roadmap for the computation of persistent homology
• Robust Detection of Dynamic Community Structure in Networks
• Structure and dynamics of core-periphery networks
• Persistent Homology of Complex Networks
• Topological strata of weighted complex networks
• Persistent homology of time-dependent functional networks constructed from coupled time series
• Emergence of core-peripheries in networks
• Learning about knowledge: A complex network approach
• The emergent integrated network structure of scientific research
• On the reorderability of node-filtered order complexes
• The landscape of NeuroImage-ing research

Cited by in corpus (3)

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