This paper describes a generative theory of bugs. It claims that all bugs of a procedural skill can be derived by a highly constrained form of problem solving acting on incomplete procedures. These procedures are characterized by formal deletion operations that model incomplete learning and forgetting. The problem solver and the deletion operator have been constrained to make it impossible to derive “star‐bugs”—algorithms that are so absurd that expert diagnosticians agree that the alogorithm will never be observed as a bug. (...) Hence, the theory not only generates the observed bugs, it fails to generate star‐bugs.The theory has been tested on an extensive data base of bugs for multidigit subtraction that was collected with the aid of the diagnostic systems buggy and debuggy. In addition to predicting bug occurrence, by adoption of additional hypotheses, the theory also makes predictions about the frequency and stability of bugs, as well as the occurrence of certain latencies in processing time during testing. Arguments are given that the theory can be applied to domains other than subtraction and that it can be extended to provide a theory of procedural learning that accounts for bug acquisition. Lastly, particular care has been taken to make the theory principled so that it can not be tailored to fit any possible data. (shrink)

In attempting to fit a model of analogical problem solving to protocol data of students solving physics problems, several unexpected observations were made. Analogies between examples and exercises (a form of case‐based reasoning) consisted of two distinct types of events. During an initialization event, the solver retrieved an example, set up a mapping between it and the problem, and decided whether the example was useful. During a transfer event, the solver inferred something about the problem's solution. Many different types of (...) initialization and transfer events were observed. Poor solvers tended to follow the example verbatim, copying each solution line over to the problem. Good solvers tried to solve the problem themselves, but referred to the example when they got stuck, or wanted to check a step, or wanted to avoid a detailed calculation. Rather than learn from analogies, both Good and Poor solvers tended to repeat analogies at subsequent similar situations. A revised version of the model is proposed (but not yet implemented) that appears to be consistent with all the findings observed in this and other studies of the same subjects. (shrink)

It is often assumed that engaging in a one‐on‐one dialogue with a tutor is more effective than listening to a lecture or reading a text. Although earlier experiments have not always supported this hypothesis, this may be due in part to allowing the tutors to cover different content than the noninteractive instruction. In 7 experiments, we tested the interaction hypothesis under the constraint that (a) all students covered the same content during instruction, (b) the task domain was qualitative physics, (c) (...) the instruction was in natural language as opposed to mathematical or other formal languages, and (d) the instruction conformed with a widely observed pattern in human tutoring: Graesser, Person, and Magliano's 5‐step frame. In the experiments, we compared 2 kinds of human tutoring (spoken and computer mediated) with 2 kinds of natural‐language‐based computer tutoring (Why2‐Atlas and Why2‐AutoTutor) and 3 control conditions that involved studying texts. The results depended on whether the students' preparation matched the content of the instruction. When novices (students who had not taken college physics) studied content that was written for intermediates (students who had taken college physics), then tutorial dialogue was reliably more beneficial than less interactive instruction, with large effect sizes. When novices studied material written for novices or intermediates studied material written for intermediates, then tutorial dialogue was not reliably more effective than the text‐based control conditions. (shrink)

It is often assumed that engaging in a one‐on‐one dialogue with a tutor is more effective than listening to a lecture or reading a text. Although earlier experiments have not always supported this hypothesis, this may be due in part to allowing the tutors to cover different content than the noninteractive instruction. In 7 experiments, we tested the interaction hypothesis under the constraint that (a) all students covered the same content during instruction, (b) the task domain was qualitative physics, (c) (...) the instruction was in natural language as opposed to mathematical or other formal languages, and (d) the instruction conformed with a widely observed pattern in human tutoring: Graesser, Person, and Magliano's 5‐step frame. In the experiments, we compared 2 kinds of human tutoring (spoken and computer mediated) with 2 kinds of natural‐language‐based computer tutoring (Why2‐Atlas and Why2‐AutoTutor) and 3 control conditions that involved studying texts. The results depended on whether the students' preparation matched the content of the instruction. When novices (students who had not taken college physics) studied content that was written for intermediates (students who had taken college physics), then tutorial dialogue was reliably more beneficial than less interactive instruction, with large effect sizes. When novices studied material written for novices or intermediates studied material written for intermediates, then tutorial dialogue was not reliably more effective than the text‐based control conditions. (shrink)