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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2020
- Source ID
- 10.1098/rspa.2019.0741
Entities
People
- Ann Sizemore Blevins
- Danielle Bassett
- Nicolas H Christianson
Organizations
- Alfred P. Sloan Foundation
- Army Research Office
- Eunice Kennedy Shriver National Institute of Child Health and Human Development
- Harvard University
- Institute for Scientific Interchange
- John D. and Catherine T. MacArthur Foundation
- National Institute of Mental Health
- National Institute of Neurological Disorders and Stroke
- National Science Foundation
- Office of Naval Research
- United States Army Research Laboratory
- University of Pennsylvania