A mathematical analysis of semantic maps, with theoretical and applied implications for blended learning software

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Tang, M., David, H., Byrne, R. & Tran, J. (2012). A mathematical analysis of semantic maps, with theoretical and applied implications for blended learning software. International Journal on E-Learning, 11(1), 95-104. Chesapeake, VA: AACE.
Retrieved from http://www.editlib.org/p/33280.

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Journal Information

International Journal on E-Learning
ISSN 1537-2456
Volume 11, Issue 1, January 2012
Association for the Advancement of Computing in Education (AACE)  Chesapeake, VA

More Information on IJEL

Authors

Michael Tang, University of Colorado Denver, USA; Hyerle David, Thinking Maps, USA; Roxanne Byrne, University of Colorado Denver, USA; John Tran, Ratheon Corporation, Boston MA, USA

Abstract

This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps ®, based on Albert Upton’s semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of learning in education on all levels. From one point of view he was behind his times because in the 1960’s semantic analysis was passé in academic circles having been replaced by modern linguistics (Smith, 2004, Chomsky, 1968). On the other hand, Upton could be considered ahead of his time because of the emergence of the importance of semantics and formal logic in computer science and other disciplines (Auwera, 2008; Hoenig; 2008; Yamashiro, 2006, Ma, 2004; Ploux, 2003, Lakoff, 1978). The purpose of this analysis is to determine if the reduction of Thinking Maps (TMs), based on Upton’s semantic theory to mathematical expressions can give insight into why they have been so successful for learning. In this paper, the question is not if these maps work, but why and how they work. It is suggested that a formal analysis of a set of maps proven to work, David Hyerle’s semantic maps ( 1996, 2004, 2006, 2009), will clarify and determine reasons behind their effectiveness. This analysis will help in the better understanding of the use of visual diagrams in teaching and other areas. It is also suggested that this understanding of the why and how of semantic maps will help in the design interactive eLearning software.

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