Accession Number : ADA117377

Title :   Rule Space, the Product Space of Two Score Components in Signed-Number Subtraction: An Approach to Dealing with Inconsistent Use of Erroneous Rules.

Descriptive Note : Research rept.,


Personal Author(s) : Tatsuoka,Kikumi K ; Baillie,Robert

PDF Url : ADA117377

Report Date : Mar 1982

Pagination or Media Count : 45

Abstract : Students responses to a 40-item test on signed-number subtraction are viewed as consisting of two different components, the sign and absolute value parts. Each component is scored zero-one for wrong or correct of the corresponding part of the answer. The traditional scoring yields a score of one only when both components have scores of one. By taking the values of the extended caution index for the absolute value component as the x-axis and those for the sign component as the y-axis, all pairs of component patterns produced by consistent or inconsistent application of various rules or random errors are mapped into the ECI product space. A simulation study showed that the response patterns generated by changing the binary score of any one item in the response patterns of an erroneous rule cluster together in the ECI product space. Moreover, the response patterns resulting from the same kind of misconceptions fall closer together than those resulting from very different kinds. This property of the ECI product space opens up a promising way to handle large numbers of 'bugs' or rules quantitatively. But the ECIs are not defined in the cases of perfect or zero scores. Typically, there are many incomplete rules (e.g., all signs of the responses are right but absolute value parts are taken by some erroneous rule). (Author)

Descriptors :   *Students, *Scoring, *Adaptive training, Perception(Psychology), Consistency, Clustering, Valves, Students, Scoring, Response, Geometry, Computer aided instruction, Selection, Indexes, Education

Subject Categories : Humanities and History

Distribution Statement : APPROVED FOR PUBLIC RELEASE