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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For a discussion on the different processes triggered by contrasting cases in comparison to rich problems, see Loibl and Rummel (2014b).
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.
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). https://doi.org/10.1007/s10648-016-9379-x
- Contrasting cases
- Learning mechanisms
- Problem solving
- Productive Failure
- Student solutions
- Compare and contrast