Effects of operand order and problem repetition on error priming in cognitive arithmetic.

Abstract

Abstract Error priming is an inter - trial priming effect observed in arithmetic production tasks. In general, answers retrieved earlier in a trial sequence are promoted as errors on later trials (positive error priming). This interference from previous retrievals, however, is not observed for consecutive trials. Error - answer matches at trial lags of 1 (perseveration errors) are observed to be significantly below chance (negative error priming). This investigation tested the predictions of the network interference model (Campbell & Oliphant, 1992) that error priming effects would be sensitive to operand - relatedness and operand - position between the error problem and the matched problem. For positive error priming, the predictions of the model were partially supported: Positive error priming was strongest for problems sharing a common operand in the same problem position. Negative error priming was sensitive to operand - relatedness as predicted. The study also investigated the role of intention in negative error priming by manipulating the probability of immediate problem repetition. Negative error priming was not eliminated by repetition, suggesting that intention to prevent consecutive answer repetition is not a necessary condition of negative error priming. Perseveration errors were, however, increased for trials most similar to repetition trials suggesting that repetition elicited a repetition - detection process that had some cost to general performance. Two fundamental issues motivate most research in cognitive arithmetic: the organization of numerical knowledge in memory, and the processes by which this knowledge is accessed for mathematical calculation (Ashcraft, 1992; Boysen & Capaldi, 1993; Dehaene, 1992). As in most investigations of cognitive skill, these questions are addressed primarily through the study of performance patterns (i.e., speed and accuracy) in various contexts. The study of errors can contribute in unique ways to understanding the processes underlying skilled cognition (Baars, 1992; Crowder, 1976), as both error identity and error frequency can reflect various influences on processing. For example, one phenomenon that has been informative about both the associative structure of arithmetic facts in memory and the retrieval processes by which these facts are accessed is error priming. Error priming is an inter - trial priming effect observed in simple arithmetic production tasks. When subjects answer arithmetic problems presented sequentially, the specific errors they produce are influenced by the previous problems they have recently encountered (Campbell, 1987; Campbell & Clark, 1989). The influence of previous problems on error answers is inhibitory for consecutive trials (i.e., the incidence of perseverative errors is below chance levels), but excitatory at longer trial lags (i.e., the probability of an error matching a previous correct answer is above chance). The only model of number - fact retrieval that incorporates an explicit mechanism for error priming effects is the network interference model (Campbell, 1995; Campbell & Oliphant, 1992). The purposes of the present investigation were to test the error priming predictions of the network interference model and to explore the role of intention in the inhibitory component of the error priming effect. Before outlining the experiment in detail, the error priming effect will be briefly reviewed and the network interference model and its predictions will be described. A Dual - process Model of Error Priming Error priming is observed when subjects answer long sequences of single - digit multiplication or addition problems. Campbell and Clark (1989) examined the inter - trial influence of previous retrievals on errors made under such circumstances, and observed a curvilinear function for matches between error answers and answers to previous trials. On consecutive trials, error - matching rates were below the frequency expected by chance. …