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Towards a Theory of When and How Problem Solving Followed by Instruction Supports Learning

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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.

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  1. For a discussion on the different processes triggered by contrasting cases in comparison to rich problems, see Loibl and Rummel (2014b).

  2. Naturally, some wording is expected to differ by condition (e.g., “invent a formula/strategy for the following problem” vs. “solve the problem using this formula/strategy”), which is not counted as confound.

  3. In the studies in no. 19, the instruction and the worksheets with contrasting cases were held constant across conditions. However, students in the I-PS condition received an additional reminder of the formula and a worked example prior to solving each worksheet, whereas students in the PS-I condition were told what invention means and what they need to invent prior to their first problem-solving attempt.


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Loibl, K., Roll, I. & Rummel, N. Towards a Theory of When and How Problem Solving Followed by Instruction Supports Learning. Educ Psychol Rev 29, 693–715 (2017).

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