Worked examples are instructional devices that provide an expert's problem solution for a learner to study. Worked-examples research is a cognitive-experimental program that has relevance to classroom in-struction and the broader educational research community. A frame-work for organizing the findings of this research is proposed, leading to instructional design principles. For instance, one instructional de-sign principle suggests that effective examples have highly integrated components. They employ multiple modalities in presentation and em-phasize conceptual structure by labeling or segmenting. At the lesson level, effective instruction employs multiple examples for each concep-tual problem type, varies example formats within problem type, and employs surface features to signal deep structure. Also, examples should be presented in close proximity to matched practice problems. More-over, learners can be encouraged through direct training or by the structure of the worked example to actively self:explain examples. Worked examples are associated with early stages of skill develop-ment, but the design principles are relevant to constructivist research and teaching. The Historical Context In recent years, learning from "worked examples " has received a consider-able amount of attention from researchers (e.g., Chi, Bassok, Lewis, Reimann, & Glaser, 1989; Ward & Sweller, 1990), particularly in such fields as mathematics, physics, and computer programming. Although there is no precise definition, worked examples share certain family resemblance (Wittgenstein, 1953). As instructional devices, they typically include a problem statement and a proce-dure for solving the problem; together, these are meant to show how other similar problems might be solved. In a sense, they provide an expert's problem-

... importance for initial skill acquisition in well-structured domains. In addition, research has provided knowledge in regards to structuring worked-out examples and how to effectively combine self-explanation activity and instructional explanations. The goal of the present project was to develop a computer-based learning environment in which teachers can learn how to use worked-out examples. Examples of favorably and unfavorably designed worked-out examples were the primary source of information for the teachers. The examples (of worked-out examples) were not in themselves worked-out examples if one views them from a design perspective as the (design) solution steps were not given. We have labeled this type of examples "solved example problems." We investigated to what extent learning from such solved example problems could be fostered by self-explanation prompts and by providing instructional explanations. The results of our 2x2 design (80 student teachers) showed that prompting selfexplanations in particular had favorable effects. Hence, self-explanations fostered learning not only from worked-out examples but also from solved example problems. Supplementary instructional explanations only partially enhanced learning and at times they were even detrimental.

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Abstract. The feedback given by e-learning tools that support incrementally solving problems in mathematics, logic, physics, etc. is limited, or laborious to specify. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically calculate feedback when users make erroneous steps in a calculation. Although we need the power of a full programming language to specify strategies, we carefully distinguish between context-free and non-contextfree sublanguages of our strategy language. This separation is the key to automatically calculating all kinds of desirable feedback. 1

Although problem solving supported by Cognitive Tutors has been shown to be successful in fostering initial acquisition of cognitive skills, this approach does not seem to be optimal with respect to focusing the learner on the domain principles to be learned. In order to foster a deep understanding of domain principles, we developed a Cognitive Tutor that contained, on the basis of the theoretical rational of examplebased learning, faded worked-out examples. We conducted two experiments in which we compared the example-enriched Cognitive Tutor with a standard Cognitive Tutor. In Experiment 1, we found no significant differences in the effectiveness of the two tutor versions. However, the example-enriched Cogntive Tutor was more efficient (i.e., students needed less learning time). A problem that was observed is that students had great problems in appropriately using the example-enriched tutor. In Experiment 2, we, therefore, provided students with additional instructions on how to use the tutor. Results showed that students in fact acquired a deeper conceptual understanding when they worked with the example-enriched tutor and they needed less learning time than in the standard Tutor. The results are suggestive of ways in which instructional models of problemsolving and example-based learning can be fruitfully combined.

This article provides an overview description of the four-component instructional design system (4C/ID-model) developed originally by van Merriënboer and others in the early 1990s (van Merriënboer, Jelsma, & Paas, 1992) for the design of training programs for complex skills. It discusses the structure of training blueprints for complex learning and associated instructional methods. The basic claim is that four interrelated components are essential in blueprints for complex learning: (a) learning tasks, (b) supportive information, (c) just-in-time (JIT) information, and (d) part-task practice. Instructional methods for each component are coupled to the basic learning processes involved in complex learning and a fully worked-out example of a training blueprint for “searching for literature ” is provided. Readers who benefit from a structured advance organizer should consider reading the appendix at the end of this article before reading the entire article. The instructional design enterprise is a bit like an ocean liner—huge, slow, ponderous, and requiring large amounts of energy and a great deal of time to move it even one degree off its current path. Recent discussions and developments in the field concern rapid technological and societal changes and the resulting need for very complex knowledge at work (Berryman, 1993; Cascio, 1995); new constructivist design theories for problem solving (Jonassen, 1994;

Research has shown that it is effective to combine example study and problem solving in the initial acquisition of cognitive skills. Present methods for combining these learning modes are, however, static and do not support a transition from example study in early stages of skill acquisition to later problem solving. Against this background, we propose a successive integration of problemsolving elements into example study until the learners solve problems on their own (i.e., complete example increasingly more incomplete examples problem to-besolved) . We tested the effectiveness of such a fading procedure against the traditional method of employing exampleproblem pairs. In a field experiment and in a more controlled lab experiment, we found that the fading procedure fosters learning, at least when near transfer performance is considered. Moreover, this effect is mediated by a lower number of errors under the fading condition as compared to the example-problem condition.

The current research investigates a combination of two instructional approaches, tutored problem solving and worked-examples. Tutored problem solving with automated tutors has proven to be an effective instructional method. Worked-out examples have been shown to be an effective complement to untutored problem solving, but it is largely unknown whether they are an effective complement to tutored problem solving. Further, while computer-based learning environments offer the possibility of adaptively transitioning from examples to problems while tailoring to an individual learner, the effectiveness of such machine-adapted example fading is largely unstudied. To address these research questions, one lab and one classroom experiment were conducted. Both studies compared a standard Cognitive Tutor with two example-enhanced Cognitive Tutors, in which the fading of worked-out examples occurred either fixed or adaptively. Results indicate that the adaptive fading of worked-out examples leads to higher transfer performance on delayed post-tests than the other two methods.

Abstract. Strategies specify how a wide range of exercises can be solved incrementally, such as bringing a logic proposition to disjunctive normal form, reducing a matrix, or calculating with fractions. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically calculate feedback, for example when a user makes an erroneous step in a calculation. We can automatically generate worked-out examples, track the progress of a student by inspecting submitted intermediate answers, and report back suggestions in case the student deviates from the strategy. Thus it becomes less labor-intensive and less ad-hoc to specify new exercise domains and exercises within that domain. A strategy describes valid sequences of rewrite rules, which turns tracking intermediate steps into a parsing problem. This is a promising view at interactive exercises because it allows us to take advantage of many years of experience in parsing sentences of context-free languages, and transfer this knowledge and technology to the domain of stepwise solving exercises. In this paper we work out the similarities between parsing and solving exercises incrementally, we discuss generating feedback on strategies, and the implementation of a strategy recognizer.

1 This document is a work product developed by Dr. Richard Clark of the University of Southern California and submitted to satisfy contract DAAD 19-99-D-0046-0004 from TRADOC to the Institute for Creative Technology and the Rossier School of Education to provide “Workshops-TDAD ” under account number 53-4400-8040. The opinions expressed in this document are those of the Principle Investigator and not those of TRADOC or the University of Southern California. 1