TITLE:
Applying Kolmogorov’s Proofs to the Evaluation of Instruction: Generalized and Particular (PART TWO)
AUTHORS:
John W. Oller
KEYWORDS:
Evaluation of Instruction, Kolmogorov Probability Theory, Peircean Logic of Relations, Polya’s Central Limit Theorem, Pragmatic Information, Successful Communication, TNR-Theory
JOURNAL NAME:
Open Access Library Journal,
Vol.8 No.7,
July
28,
2021
ABSTRACT: PART ONE incorporated probability theory into the theory of true narrative representations (TNR-theory). The proofs show that interactional successes in a course of study must trend toward 100% shared information. Failures converge on zero. PART TWO compares robotic responses to forced-choice test items (an independent series of events) against university students whose responses are dependent on what they learned. The proofs are also applied to experimental measures of what Haertel in 2013 referred to as “value-added” by instruction. When all factors except the course presentation can be held constant, gains in test scores can be taken as measures of value-added by instruction. Such gains as predicted by the proofs are confirmed (1) for radically diverse methods of testing the same subject-matter across time, and (2) for seven iterations of a course, tested by nearly identical test items aimed at the same subject-matter, but with improved alignment/agreement across the critical components of subject-matter, methods of presentation, and procedures of assessment.