Using social network analysis to investigate mathematical connections in U.S. and Chinese textbook problems

Textbooks, as potentially implemented curricula, play an important role in supporting classroom teaching and learning. Mathematical connections, one of the essential and hot topics advocated in mathematics education, have been emphasized in national curriculum reforms in various countries. However, little is known about the connection networks represented in school textbooks; even less has been done to compare textbooks from different countries. In this study, we propose an innovative method for examining how connections are represented in two popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school textbook problems involving quadratic relations. By using social network analysis, we identified 1129 connections, characterized connection networks into dense, moderate, and sparse digraphs, identified influential, prominent, and dual concepts and representations, and evaluated the strength between typical and reverse connections. The results revealed that the Chinese series presented a denser network of balanced between-concept connections but limited within-concept connections. The U.S. series exhibited more within-concept connections but emphasized typical connections, thus validating the potential of this innovative method. From this study, we suggest that our novel method provides a theoretical contribution to textbook analysis and connection analysis, which has rich implications for practice, for example, examining the network of connections students construct as a way to assess and to promote their conceptual understanding, and our approach opens the possibility of adopting new and efficient analytical tools from social network analysis in mathematics education research.