Error detection processes in statistical problem solving

Problem solvers' error detection processes were studied by instructing 16 subjects to think aloud when solving two statistical problems. The evaluative episodes occurring in subjects' protocols were analyzed into Affirmative evaluation, Direct error-hypotheses, Error suspicion, and Standard check episodes, the last three of which are assumed to cover all main types of error detection processes. Most errors (78%) were found to have contributed to a solution part that triggered some evaluative episode. However, only one-third of the undetected errors had contributed to such a solution part. The Standard check episodes, seen as centrally-invoked, only led to the detection of few errors in proportion to the number of times they were performed. Evidence was found for two types of spontaneous error detections, one occurring abruptly and the other as a result of a more elaborated error detection process, initiated by the solver perceiving the solution as dissatisfying or strange. The perception of a symptom was a fairly reliable source of information about errors. However, subjects often did not manage to detect the error after having noticed a symptom. The closer a relevant Error suspicion episode followed an error, the greater was the probability of detecting the error. Good problem solvers detected a higher proportion of their errors compared to poor problem solvers, probably due to differences in the processes leading up to the triggering of an evaluative episode rather than to differences after the episode had been triggered.     

Sequencing in social repair: A Markov grammar of children's discourse about transgressions

A Markov grammar was developed to account for the sequence of conversational moves in discourse about transgressions. This discourse interrupts ongoing activity and functions to repair the social fabric when inappropriate or awkward behavior has attracted the attention of interactants. A corpus of 1248 such interchanges, obtained in 90 hr of observation in kindergarten through fourth grade classrooms, was the basis of the grammar. Beginning with theoretical assumptions about the canonical form of these interchanges, the process of grammar development was explicitly described and the direction given by pragmatic considerations (such as attaining a balance between parsimony and accuracy) was discussed. The resultant grammar accounted for 83% of the corpus and served as a framework within which age and context effects on the discourse were explored. Loglinear analyses of multiway contingency tables at each transition point in the grammar revealed that the presence vs absence of an adult in the interchange affected the relative preferences for different alternatives at one juncture, but that subjects' ages did not influence the sequencing of discourse as described by the model. The overall approach was considered in relation to the more traditional uses of Markov models and its strengths, weaknesses, and future promise for discourse analysis were discussed.