A number of models are considered that specify how children and adults solve single-digit addition problems. It is shown that the most adequate of these in accounting for children's response latencies is a model that assumes the existence of a counter with two operations: setting and incrementing. The child adds two digits, m and n, by setting this counter to max (m,n) and then incrementing it min(in,n) times. This model also accounts for adults' latencies, though with a drastically reduced incrementing time. Some theoretical issues raised by this reduced time are considered, and an alternative model is suggested which assumes that adults usually use a memory look-up process with homogeneous retrieval times, but occasionally revert back to the counting process used by children.

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This research is concerned with patterns of reaction times that emerge when a child is taught a specific problem-solving procedure and then given extensive practice over many weeks. Preschool children who knew how to count but were unacquainted with arithmetic were taught a simple algorithm for solving single-digit addition problems and were then given extended practice. A subject performing this algorithm would generate reaction times proportional to the sum of the addends. The main finding was that, at the end of the extended practice phase, data of many subjects were best fitted by a different model predicting reaction times proportional to the minimum addend. This implies that these children are no longer using the algorithm they were originally taught. It is also interpreted as suggesting that they have invented a more efficient procedure.We are concerned in this article with the relationship of relatively skilled performance on tasks to the processes used during early phases of acquisition. In the typical information-processing experiments, performance is highly skilled and overlearned. The processes postulated are sufficient to account for skilled performance, but little is said regarding how such processes are acquired or how performance changes over time. There is no a priori reason, however, to assume that the processes used in skilled performance are identical to the processes used to solve the same problems in a relatively unpracticed state. Here we address the question of cognitive skill acquisition directly, by modeling the performance of individuals at different times in the course of their acquiring skill in procedures for solving simple addition problems. We consider in particular the relationship between the specific procedures taught to beginners

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This paper is concerned with factors that disrupt the pattern of forward reasoning characteristic of experts with accurate performance. Two experiments are described. In the first, the performances of cardiologists, psychiatrists, and surgeons in diagnostic explanation of a clinical problem in cardiology were examined. In the second, the performances of cardiologists and endocrinologists in diagnostic explanation of clinical problems within and outside their domains of expertise were examined. The performances of researchers and practicing physicians are also compared. The results of Experiment 1 replicated earlier results regarding the relationship between forward reasoning and accurate diagnosis. There were no differences in recall as a function of expertise. Experts did not show any bias toward using specific knowledge from their own areas of expertise. The results of Experiment 2 showed that the breakdown of forward reasoning was related to the structure of the task. In particular, nonsalient cues induced some backward reasoning even in subjects with accurate diagnoses. Some differences were also found between the types of explanation used by researchers and practitioners. The practitioners referred more to clinical components in their explanations, whereas the researchers focused more on the biomedical components.An important distinction made in rule-based models of problem solving involves the directionality of inferences.Forward reasoning (or forward chaining) involves the generation of a hypothesis on the basis of data given in the problem. Backward reasoning involves the generation of data on the basis of a hypothesis. The distinction between forward and backward reasoning originated not in psychology but in artificial intelligence, where early expert systems tended to use one of these two kinds of inference mechanisms exclusively. However, this distinction motivated two empirical studies (Larkin, McDermott, Simon, & Simon, 1980;Simon & Simon, 1978) that were interpreted as showing that directionality is directly related to expertise. At least on routine problems, experts used forward reasoning, whereas novices used backward reasoning.It is important to note that this interpretation was based more on theory than on data. The data, which were based on only 3 subjects, simply demonstrated the existence of the two methods of reasoning and suggested a correlation with level of expertise. The interpretation of this correlation was derived from the well-established finding in artificial intelligence that forward reasoning is an optimal inference mechanism for solving well-structured problems in the presence of a large base of relevant knowledge, whereas backward reasoning is effective when a problem is ill-structured or relevant knowledge is absent. The obvious question of the generalizability of the results exists, and the experimenters made no attempt to manipulate the conditions under which the directionality of reasoning might change. There was also a confounding between accuracy and expertise, since no a...