One of the goals of computerized tutoring systems is to optimize the learning of facts. Over a hundred years of declarative memory research have identified two robust effects that can improve such systems: the spacing and the testing effect. By making optimal use of both and adjusting the system to the individual learner using cognitive models based on declarative memory theories, such systems consistently outperform traditional methods. This adjustment process is driven by a continuously updated estimate of the rate of (...) forgetting for each item and learner on the basis of the learner's accuracy and response time. In this study, we investigated to what extent these estimates of individual rates of forgetting are stable over time and across different materials. We demonstrate that they are stable over time but not across materials. Even though most theories of human declarative memory assume a single underlying rate of forgetting, we show that, in practice, it makes sense to assume different materials are forgotten at different rates. If a computerized, adaptive fact-learning system allowed different rates of forgetting for different materials, it could adapt to individual learners more readily. (shrink)

Much of cognitive psychology focuses on effects measured in tens of milliseconds while significant educational outcomes take tens of hours to achieve. The task of bridging this gap is analyzed in terms of Newell's (1990) bands of cognition—the Biological, Cognitive, Rational, and Social Bands. The 10 millisecond effects reside in his Biological Band while the significant learning outcomes reside in his Social Band. The paper assesses three theses: The Decomposition Thesis claims that learning occurring at the Social Band can be (...) reduced to learning occurring at lower bands. The Relevance Thesis claims that instructional outcomes at the Social Band can be improved by paying attention to cognition at the lower bands. The Modeling Thesis claims that cognitive modeling provides a basis for bridging between events on the small scale and desired outcomes on the large scale. The unit-task level, at the boundary of the Cognitive and Rational Bands, is useful for assessing these theses. There is good evidence for all three theses in efforts that bridge from the unit-task level to educational applications. While there is evidence for the Decomposition Thesis all the way down to the 10 millisecond level, more work needs to be done to establish the Relevance Thesis and particularly the Modeling Thesis at the lower levels. (shrink)

The notion of optimality is often invoked informally in the literature on metacognitive control. We provide a precise formulation of the optimization problem and show that optimal time allocation strategies depend critically on certain characteristics of the learning environment, such as the extent of time pressure, and the nature of the uptake function. When the learning curve is concave, optimality requires that items at lower levels of initial competence be allocated greater time. On the other hand, with logistic learning curves, (...) optimal allocations vary with time availability in complex and surprising ways. Hence there are conditions under which optimal strategies will be relatively easy to uncover, and others in which suboptimal time allocation might be expected. The model can therefore be used to address the question of whether and when learners should be able to exercise good metacognitive control in practice. (shrink)

An analysis of student learning with the LISP tutor indicates that while LISP is complex, learning it is simple. The key to factoring out the complexity of LISP is to monitor the learning of the 500 productions in the LISP tutor which describe the programming skill. The learning of these productions follows the power‐law learning curve typical of skill acquisition. There is transfer from other programming experience to the extent that this programming experience involves the same productions. Subjects appear to (...) differ only on the general dimensions of how well they acquire the productions and how well they retain the productions. Instructional manipulations such as remediation, content of feedback, and timing of feedback are effective to the extent they give students more practice programming, and explain to students why correct solutions work. (shrink)