In this study, the statistical properties of extended caution indices are investigated, and their relationships to Guttman scales and to item and person response curves are discussed. Further, these indices are standardized, and an example of their potential usefulness for diagnosing students' misconceptions is shown. (Author/BW)

Errors, or "bugs", in addition and subtraction problems of signed numbers are driven by misconceptions or incomplete knowledge at various components of procedural tasks, and result in erroneous rules of operation for carrying out computational problems. These rules, including the right one, are represented by the responses to a…

A probablistic approach to classification and diagnosis of erroneous rules of operations that result from misconceptions ("bugs") in a procedural domain of arithmetic is introcuced. Variability of response errors is explicitly treated through item response theory. As a concrete example, a signed-number subtraction dataset is analyzed.…

An index measuring the degree to which a binary response pattern conforms to some baseline pattern was defined and named the Pattern Conformity Index (PCI). One way of conceptualizing what the PCI measures is the extent to which each individual's particular response pattern contributes to, or detracts from, the overall consistency found in the…

A probabilistic approach is introduced to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ("bugs") in a procedural domain of arithmetic. The model is contrasted with the deterministic approach which has commonly been used in the field of artificial intelligence, and the advantage of treating the…

A 40-item free response test on signed-number subtraction was administered to 172 eighth graders. Their responses are viewed as consisting of two different components, the sign and absolute value. Each component is scored zero for wrong or one for correct, yielding a score of one only when both components have scores of one. By taking the values…

Several extended caution indices (ECIs) have been introduced earlier as a link between two distinctly different approaches: one based on standard statistics and the other, a model-based approach, utilizing item response theory (IRT). Expected values and variance of some ECIs are derived and their statistical properties are compared and discussed.…

This study introduces the individual consistency index (ICI), which measures the extent to which patterns of responses to parallel sets of items remain consistent over time. ICI is used as an error diagnostic tool to detect aberrant response patterns resulting from the consistent application of erroneous rules of operation. (Author/PN)

The present study examined the effect of three modes of feedback on the seriousness of error types committed on a post-test. The effect of the feedback made on post-test errors was found to be differential and dependent upon the seriousness of errors committed on the pre-test. (Author/LMO)

Diagnosing cognitive errors possessed by examinees can be considered as a pattern classification problem that is designed to classify a sequential input of stimuli into one of several predetermined groups. The sequential inputs in this paper's context are item responses, and the predetermined groups are various states of knowledge resulting from…

The rule space model permits measurement of cognitive skill acquisition and error diagnosis. Further discussion introduces Bayesian hypothesis testing and bug distribution. An illustration involves an artificial intelligence approach to testing fractions and arithmetic. (Author/GDC)

This study examined whether the item response curves from a two-parameter model reflected characteristics of the mathematics items, each of which required unique cognitive tasks. A computer program performed error analysis of test performance. Cognitive subtasks appeared to influence the slopes and difficulties of item response curves. (GDC)

Forty-six junior high students were administered six tests after a variety of instructional units using PLATO and classroom instruction. Twenty-seven procedural errors in signed-number arithmetic problems were classified into two groups to facilitate investigating error changes at different times and designing remedial instruction. (BS)

Implementation of an adaptive achievement test for teaching signed-numbers operations to junior high students is described. A computer program capable of finding 240 basic errors in signed-number computations was written on the PLATO system and used for analyzing a 64-item conventional test, as well as an adaptive test of addition problems. The…

This study introduced a probabilistic model utilizing item response theory (IRT) for dealing with a variety of misconceptions. The model can be used for evaluating the transition behavior of error types, advancement of learning stages, or the stability and persistence of particular misconceptions. Moreover, it apparently can be used for relating…