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AbstraetAn all-or-none learning model is presented which makes predictions for response latencies in pairedassociate learning. The predicted latencies decrease on trials following the last error of a criterion run and accurately describe the latency data of an experiment by Peterson (1965). Problem Peterson (1965) has stated that "For an incremental view of learning, the latency of response would be expected to decrease after the S stops making errors. However, decreasing latencies after errors cease are difficult to incorporate into an all-or-none model of learning." Peterson (1965) gave 15 undergraduates 20 trials to learn 10 paired-associates. The stimuli were 10 consonant bigrams, and the responses were the digits 1 to 8. He found that the group mean latency decreased on the 10 trials following an SIS last error. He interpreted the data as indicating that "Speed of occurence (of the correct response) appears to be a measure of strength of an association which changes gradually over trials. tt The question of crucial importance to learning theory is not whether learning is strictly' 'all-or-none." Rather it is whether learning is grossly discrete or approximately continuous. A grossly discrete process may have a number of individual mechanisms, each strictly allor-none. When cast in these terms, the Peterson (1965) data are not at all at variance with a discrete, all-ornone position on learning.As a case in point, suppose that a complete stimulusresponse association is formed strictly on one triaL Behavioristically, an association is defined as the occurrence of a particular response to a presented stimulus. Assume further that the association is first stored in an imperfect, temporary memory and later transferred to a perfect, relatively permanent memory. Then response latency would be a direct function of retrieval time or memory search time, and it would not be unreasonable to expect that retrieval of the association from temporary memory would take longer than retrieval from permanent memory. These notions lead to an all-or-none learning model which may be defined by the following explicit assumptions;1. The response given on a trial to a particular stimulus item depends only on the state of conditioning of the individual stimulus-response association.
AbstraetAn all-or-none learning model is presented which makes predictions for response latencies in pairedassociate learning. The predicted latencies decrease on trials following the last error of a criterion run and accurately describe the latency data of an experiment by Peterson (1965). Problem Peterson (1965) has stated that "For an incremental view of learning, the latency of response would be expected to decrease after the S stops making errors. However, decreasing latencies after errors cease are difficult to incorporate into an all-or-none model of learning." Peterson (1965) gave 15 undergraduates 20 trials to learn 10 paired-associates. The stimuli were 10 consonant bigrams, and the responses were the digits 1 to 8. He found that the group mean latency decreased on the 10 trials following an SIS last error. He interpreted the data as indicating that "Speed of occurence (of the correct response) appears to be a measure of strength of an association which changes gradually over trials. tt The question of crucial importance to learning theory is not whether learning is strictly' 'all-or-none." Rather it is whether learning is grossly discrete or approximately continuous. A grossly discrete process may have a number of individual mechanisms, each strictly allor-none. When cast in these terms, the Peterson (1965) data are not at all at variance with a discrete, all-ornone position on learning.As a case in point, suppose that a complete stimulusresponse association is formed strictly on one triaL Behavioristically, an association is defined as the occurrence of a particular response to a presented stimulus. Assume further that the association is first stored in an imperfect, temporary memory and later transferred to a perfect, relatively permanent memory. Then response latency would be a direct function of retrieval time or memory search time, and it would not be unreasonable to expect that retrieval of the association from temporary memory would take longer than retrieval from permanent memory. These notions lead to an all-or-none learning model which may be defined by the following explicit assumptions;1. The response given on a trial to a particular stimulus item depends only on the state of conditioning of the individual stimulus-response association.
Behavioral fluency is that combination of accuracy plus speed of responding that enables competent individuals to function efficiently and effectively in their natural environments. Evolving from the methodology of free-operant conditioning, the practice of precision teaching set the stage for discoveries about relations between behavior frequency and specific outcomes, notably retention and maintenance of performance, endurance or resistance to distraction, and application or transfer of training. The use of frequency aims in instructional programming by Haughton and his associates led to formulation of empirically determined performance frequency ranges that define fluency. Use of fluency-based instructional methods has led to unprecedented gains in educational cost effectiveness, and has the potential for significantly improving education and training in general. This article traces the development of concepts, procedures, and findings associated with fluency and discusses their implications for instructional design and practice. It invites further controlled research and experimental analyses of phenomena that may be significant in the future evolution of educational technology and in the analysis of complex behavior.
Efforts to improve instructional task design often make reference to the mental structures, such as Bschemas^(e.g., Gick & Holyoak, 1983) or Bidentical elements^(Thorndike & Woodworth, 1901), that are common to both the instructional and target tasks. This component based (e.g., Singley & Anderson, 1989) approach has been employed in psychometrics (Tatsuoka, 1983), cognitive science (Koedinger & MacLaren, 2002), and most recently in educational data mining (Cen, Koedinger, & Junker, 2006). A typical assumption of these theory based models is that an itemization of Bknowledge components^shared between tasks is sufficient to predict transfer between these tasks. In this paper we step back from these more cognitive theory based models of transfer and suggest a psychometric measurement model that removes most cognitive assumptions, thus allowing us to understand the data without the bias of a theory of transfer or domain knowledge. The goal of this work is to help provide a methodology that allows researchers to analyse complex data without the theoretical assumptions clearly part of other methods. Our experimentally controlled examples illustrate the non-intuitive nature of some transfer situations which motivates the necessity of the unbiased analysis that our model provides. We explain how to use this Contextual Performance Factors Analysis (CPFA) model to measure learning progress of related skills at a fine granularity. This CPFA analysis then allows us to answer questions regarding the best order of practice for related skills and the appropriate amount of repetition depending on whether students are succeeding or failing with each individual practice problem. We conclude by describing how the model
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