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Tuesday, November 08, 2005




Outline of Work to be done on

Learning Theory and the Core Liberal Arts Curriculum




Overview, the use of an ontological model




A Core Liberal Arts Curriculum is introduced with the help of a theory of learning.


This curriculum supports the extension of contemporary mathematics [*].


The basic formalism is the graph, represented as a set of triples


{ < a , r , b > }


where the referent a and b are topics of discourse and r is a relational category.


In the Lifting Strategy we assist the individual student in developing a model of the curriculum in the form of a set of topics:

C  = { topics in the standard curriculum in Chapter  }

(next bead [1] )



[*] The ontological sciences are based on set theory and category theory. Some scholars suggest that ontological sciences allow a useful representation of human knowledge. The issues are subtle and interesting. For example, foundational elements to the philosophy of mathematics can be exposed and discussed. The way that the exposure occurs can be “from a member of the class” rather than from the textbook. These elements expose to the student issues related to human cognition and reasoning behavior. Ontological modeling is now used in business and government. Over the past decade, ontological modeling has become more important in social, biological and other soft sciences.