Optimal Sequential Rules for Computer-Based Instruction

The purpose of this article is to formulate sequential rules for adapting the appropriate amount of instruction to learning needs in the context of computer-based instruction. The framework for the approach is derived from Bayesian decision theory. Both a threshold and linear utility structure are considered. The binomial distribution as well as Kelley's regression line from classical test theory are adopted as the psychometric model involved. Optimal sequential rules will be derived both for the situation that collateral information but no prior knowledge about student's true level of functioning is available and for the situation that a beta distribution representing student's prior knowledge is assumed. An empirical example of sequential instructional decision making for concept-learning in medicine concludes the article.

[1]  Huynh Huynh,et al.  Statistical consideration of mastery scores , 1976 .

[2]  Hendrik J. Vos An intelligent tutoring system for classifying students into instructional treatments with mastery scores , 1994 .

[3]  R. Owen,et al.  A Bayesian Sequential Procedure for Quantal Response in the Context of Adaptive Mental Testing , 1975 .

[4]  A Dehaan,et al.  Speller: A reflexive ITS to support the learning of second language spelling , 1994 .

[5]  Niels H. Veldhuijzen Setting cutting scores: A minimum information approach , 1982 .

[6]  T. Govindaraj,et al.  Integration of Interactive Interfaces with Intelligent Tutoring Systems: An Implementation , 1993 .

[7]  Huynh Huynh,et al.  A nonrandomized minimax solution for passing scores in the binomial error model , 1980 .

[8]  Robert D. Tennyson,et al.  The Minnesota adaptive instructional system: An Intelligent CBI system , 1984 .

[9]  David Lindley,et al.  The Use of More Realistic Utility Functions in Educational Applications. , 1978 .

[10]  Ronald K. Hambleton,et al.  On de Encountered Using Decision Theory to Set Cutoff Scores , 1984 .

[11]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[12]  Howard Wainer,et al.  Computerized Adaptive Testing: A Primer , 2000 .

[13]  Wim J. van der Linden,et al.  Optimal Cutting Scores Using A Linear Loss Function , 1977 .

[14]  N. Raju,et al.  A Logistic Regression Model for Personnel Selection , 1991 .

[15]  H J Vos,et al.  A Simultaneous Approach to Optimizing Treatment Assignments with Mastery Scores. , 1997, Multivariate behavioral research.

[16]  Anthony R. Zara,et al.  Procedures for Selecting Items for Computerized Adaptive Tests. , 1989 .

[17]  Ronald K. Hambleton,et al.  A BAYESIAN DECISION-THEORETIC PROCEDURE FOR USE WITH CRITERION-REFERENCED TESTS1 , 1975 .

[18]  Charles E. Davis A Primer on Decision Analysis for Individually Prescribed Instruction. ACT Technical Bulletin No. 17. , 1973 .

[19]  Kathleen M. Sheehan,et al.  Using Bayesian Decision Theory to Design a Computerized Mastery Test , 1990 .

[20]  Ronald K. Hambleton,et al.  Testing and Decision-Making Procedures for Selected Individualized Instructional Programs1 , 1974 .

[21]  Gerald S. Rogers,et al.  Mathematical Statistics: A Decision Theoretic Approach , 1967 .

[22]  N. Petersen,et al.  An Expected Utility Model for “Optimal” Selection , 1976 .

[23]  Hendrik J. Vos Simultaneous optimization of quota‐restricted selection decisions with mastery scores , 1997 .

[24]  Timothy S. Gegg-Harrison Adapting instruction to the student's capabilities , 1992 .

[25]  R. A. FISHER Tables for Statisticians and Biometricians , 1933, Nature.

[26]  Hans J. Vos Applications of Bayesian Decision Theory to Intelligent Tutoring Systems. Research Report 94-16. , 1994 .

[27]  Ronald K. Hambleton,et al.  TOWARD AN INTEGRATION OF THEORY AND METHOD FOR CRITERION-REFERENCED TESTS1,2 , 1973 .

[28]  George Morgan A criterion-referenced measurement model with corrections for guessing and carelessness , 1979 .

[29]  Roger B. Dannenberg,et al.  Instructional Design and Intelligent Tutoring: Theory and the Precision of Design. , 1993 .

[30]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[31]  Rebecca Zwick,et al.  A Simulation Study of Methods for Assessing Differential Item Functioning in Computerized Adaptive Tests , 1994 .

[32]  Willem J. van der Linden,et al.  A compensatory approach to optimal selection with mastery scores , 1994 .

[33]  Hendrik J. Vos,et al.  A minimax sequential procedure in the context of computerized adaptive mastery testing , 1997 .

[34]  Willem J. van der Linden,et al.  Decision models for use with criterion-referenced tests , 1980 .