The development, interview testing, and generalization of a theory based model of conceptual structurres for solving routine trigonometry problems

Richard Skemp's theory of conceptual structures (schemas) was adapted by hypothesizing two types of schemast (a) an underlying parent schema; and (b) a problem solving schema which contains paths for problem solving. Three interpretations of the definitions of the trigonometric functions were identified: (a) the right triangle interpretation; (b) the coordinate system interpretation; and (c) the unit circle interpretation. For each interpretation representative problems were chosen and methods of solution analysed. From the methods of solutions the relevant concepts and specific actions employed were identified. The parent schema was constructed by placing the concepts in a geometric configuration with two concepts joined by a line if and only if some action joined those concepts. The problem solving schema was formed by joining the concepts at the vertices by lines which were labeled to describe the actions they represent. The preliminary model thus constructed was tested and refined by interviewing four subjects of varying abilities from a trigonometry class and then analyzing those interviews according to instructions developed from the adaptation of Skemp's theory and the problem solving methods. Interview analysis included constructing representations of the parent and problem solving schemas possessed by each subject in each interpretation. The refined Model was then used to interview two additional subjects from another trigonometry class and to analyse the interviews. Interview analysis indicated strong face validity in that the Model was found to contain the problem solving paths used by the subjects. Cross validation was also found to be strong. Reliability of analysis was found to be strong in the less complex schemas and somewhat weaker when more complex schemas were involved. The Model was found to be a viable model of conceptual structures in which problem solving can be described and to have potential value for both instruction and research. Suggestions for further research on the Model and for using the Model in both instruction and research are included.

Name thesis:degree_name

Ed. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Community College Instruction

Department dc:contributor.department

Community College Instruction

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1981

Author dc:creator

• Burch, Warren J.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/74190

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/74190