Abstract
A comprehensive model of instruction should include as one component a representation of the instructional subject matter. In order to represent subject matter a theory for structuring subject matter is required. A general theory for structuring and describing such structures is provided herein. Subject matter structure is composed of two components: content and tasks. The theory presented to structure content is based on the paradigm of axiomatics. Content elements consist of Primary Notions, Secondary Notions, Basic Principles and Established Principles. Two relationships, “used in the formulation of” and “used to establish,” provided the basic structure relating these Constituents. Coordinating relations associate task subsets with content constituents. Task subsets provide the theoretical analog to criterion tests. The notion of dependency is introduced and investigated briefly. Also, a method is provided for developing the complete set of dependency relationships for content constituents. Three examples are provided to further clarify the theoretical model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ashby, W. R. (1958). An Introduction to Cybernetics. New York: John Wiley and Sons, Inc.
Gagné, R. M. and Paradise, N. E. (1961). “Abilities and Learning Sets in Knowledge Acquisition.” Psychological Monographs, 518.
Gagné, R. M. (1962a). “The Acquisition of Knowledge,” Psychological Review, 69: 355–365.
Gagné, R. M., Mayor, J. R., Garstens, H. L., and Paradise, N. W. (1962b). “Factors in Acquiring Knowledge of a Mathematical Task.” Psychological Monographs, 526.
Gagné, R. M. and Bassler, O. C. (1963). “Study of Retention of Some Topics of Elementary Nonmetric Geometry.” Educational Psychology. 54: 123–131.
Hohn, F. E. (1966). Applied Boolean Algebra. New York: The Macmilan Company.
Hohn, F. E., Seshn, S., and Aufenkamp, D.D. (1957). “The theory of nets” IRE Transactions on Electronic Computers, September, 154–161.
Mendelson, E. (1970). Theory and Problems of Boolean Algebra and Switching Circuits. New York: McGraw-Hill Book Company, Inc.
Pask, G. (1969, in press). “Computer-Assisted Learning and Teaching.” Paper presented at the University of Leeds, England.
Pask, G. (1971). “Structuring Subject Matter with Multiple Relations.” Paper presented at HumRRO.
Rosenbloom, Paul C. (1950). The Elements of Mathematical Logic. Dover Publications, 1st Edition.
Suppes, P. (1957). Introduction to Logic. Princeton: Van Nostrand Reinhold Company.
Tennyson, R. D. and Boutwell, R. C. (1971). “A Quality Control Design for Validating Hierarchical Sequencing of Programmed Instruction.” NSPI Journal, May, 10: 5–10.
Tuckman, B. W. and Edwards, K. J. (1971). “A Systems Model for Instructional Design and Management.” Educational Technology. September.
Additional information
Dr. Stelzer is an independent research scientist affiliated with HumRRO in Alexandria, Va, as well as being an Instructor of Philosophy at Prince Georges Community College in Maryland.
Mr. Kingsley is an independent consultant formerly affiliated with HumRRO in Alexandria, Va.
Rights and permissions
About this article
Cite this article
Stelzer, J., Kingsley, E. Axiomatics as a paradigm for structuring subject matter. Instr Sci 3, 383–450 (1975). https://doi.org/10.1007/BF00051903
Issue Date:
DOI: https://doi.org/10.1007/BF00051903