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Educational technology research and development - Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often,...  相似文献   
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Instructional Science - Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior...  相似文献   
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Multiple studies have shown benefits of problem-solving prior to instruction (cf. Productive Failure, Invention) in comparison to direct instruction. However, students’ solutions prior to instruction are usually erroneous or incomplete. In analogy to guided discovery learning, it might therefore be fruitful to lead students towards the discovery of the canonical solution. In two quasi-experimental studies with 104 students and 175 students, respectively, we compared three conditions: problem-solving prior to instruction, guided problem-solving prior to instruction in which students were led towards the discovery of relevant solution components, and direct instruction. We replicated the beneficial effects of problem-solving prior to instruction in comparison to direct instruction on posttest items testing for conceptual knowledge. Our process analysis further revealed that guidance helped students to invent better solutions. However, the solution quality did not correlate with the posttest results in the guided condition, indicating that leading students towards the solution does not additionally promote learning. This interpretation is supported by the finding that the two conditions with problem-solving prior to instruction did not differ significantly at posttest. The second study replicated these findings with a greater sample size. The results indicate that different mechanisms underlie guided discovery learning and problem-solving prior to instruction: In guided discovery learning, the discovery of an underlying model is inherent to the method. In contrast, the effectiveness of problem-solving prior to instruction does not depend on students’ discovery of the canonical solution, but on the cognitive processes related to problem-solving, which prepare students for a deeper understanding during subsequent instruction.  相似文献   
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Recently, there has been a growing interest in learning approaches that combine two phases: an initial problem-solving phase followed by an instruction phase (PS-I). Two often cited examples of instructional approaches following the PS-I scheme include Productive Failure and Invention. Despite the growing interest in PS-I approaches, to the best of our knowledge, there has not yet been a comprehensive attempt to summarize the features that define PS-I and to explain the patterns of results. Therefore, the first goal of this paper is to map the landscape of different PS-I implementations, to identify commonalities and differences in designs, and to associate the identified design features with patterns in the learning outcomes. The review shows that PS-I fosters learning only if specific design features (namely contrasting cases or building instruction on student solutions) are implemented. The second goal is to identify a set of interconnected cognitive mechanisms that may account for these outcomes. Empirical evidence from PS-I literature is associated with these mechanisms and supports an initial theory of PS-I. Finally, positive and negative effects of PS-I are explained using the suggested mechanisms.  相似文献   
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