This experiment contrasts learning by solving problems with learning by studying examples, while attempting to control for the elaborations that accompany each solution step. Subjects were given different instructional materials for a set of probability problems. They were either provided with or asked to generate solutions, and they were either provided with or asked to create their o w n explanations for the solutions. Subjects were then tested on a set of related problems. Subjects in all four conditions exhibited good performance on the near transfer test problems. On the far transfer problems, however, subjects in two cells exhibited stronger performance: those solving and elaborating on their own and those receiving both solutions and elaborations from the experimenter. There also was an indication of a generation effect in the far transfo* case, benefiting subjects w h o generated their own solutions. In addition, subjects' self-explanations on a particular concept were predictive of good performance on the corresponding subtask of the test problems.

In a previous study (Hickman & Laikin, 1990), we introduced a within-trial analogy mechanism called internal analogy that transfers both success and failure experiences between corresponding parts of the search tree for a single problem. In this paper, we describe powerful extensions to the learning procedure and their consequences on problem solving behavior First, we explain how our similarity metric can be naturally augmented to provide a more flexible partial match. To overcome the need for a static measure, however, we propose a mechanism that learns the appropriate level of partial match through feedback from previous analogical reasoning. Second, we show how this partial match mechanism controls the problem solver's search. Protocol dau from a subject working in a geometry theorem-proving domain provide support for the psychological fidelity of the extended internal analogy model.

Prior knowledge has long been recognized as an important predictor of learning, yet the term prior knowledge is often applied to related but distinct constructs. We define a specific form of prior knowledge, ancillary knowledge, as knowledge of concepts and skills that enable learners to gain the most from a target lesson. Ancillary knowledge is not prior knowledge of the lesson’s target concepts and skills, and may even fall outside the domain of the lesson. Nevertheless, ancillary knowledge affects learning of the lesson, e.g., lower ancillary knowledge can hinder performance on lesson-related tasks. We measured ancillary knowledge, prior knowledge of the domain, and controlled for general ability, and found that (a) stronger ancillary knowledge and general ability predicted better performance on transfer tasks, but (b) prior knowledge of the domain did not. This research suggests that enhancing instruction by remediating gaps in ancillary knowledge may improve learning in introductory-level courses.

When solvers have more than one strategy available for a given problem, they must make a selection. As they select and use different strategies, solvers can learn the strengths and weaknesses of each. W e study how solvers learn about the relative success rates of two strategies in the Building Sticks Task and what influence this learning has on later strategy selections. A theory of how people learn from and make such selections in an adaptive way is part of the ACT-R architecture (Anderson, 1993). W e develop a computational model within ACT- R that predicts individual subjects' selections based on their histories of success and failure. The model fits the selection behavior of two subgroups of subjects: those who select each strategy according to its probability of success and those who select the more successful strategy exclusively. W e relate these results to probability matching, a robust finding in the probability?learning literature that occurs when people select a response (e.g., guess heads vs. tails) a proportion of the time equal to the probability that the corresponding event occurs (e.g., the coin comes up heads vs. tails).