discuss salient features of problem solving theory

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Problem-solving concepts and theories

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• 1 Mississippi StateUniversity, College of Veterinary Medicine, USA. [email protected]
• PMID: 14648495
• DOI: 10.3138/jvme.30.3.226

Many educators, especially those involved in professional curricula, are interested in problem solving and in how to support students' development into successful problem solvers. The following article serves as an overview of educational research on problem solving. Several concepts are defined and the transition from one theory to another is discussed. Educational theories describing problem solving in the context of behavioral, cognitive, and information-processing pedagogy are discussed. The final section of the article describes prior findings regarding expert-novice differences in problem solving of various kinds.

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

• Review Article
• Published: 18 July 2016
• Volume 29 , pages 693–715, ( 2017 )

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• Katharina Loibl 1 ,
• Ido Roll 2 &
• Nikol Rummel 3  

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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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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.

*Papers included in overview (Table 1 )

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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

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Title: problem theory.

Abstract: The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here is why, Why are we Turing complete? Being Turing complete also means that somehow our brain implements the function that a universal Turing machine implements. The point is that evolution achieved Turing completeness, and then the explanation should be evolutionary, but our explanation is mathematical. The trick is to introduce a mathematical theory of problems, under the basic assumption that solving more problems provides more survival opportunities. So we build a problem theory by fusing set and computing theories. Then we construct a series of resolvers, where each resolver is defined by its computing capacity, that exhibits the following property: all problems solved by a resolver are also solved by the next resolver in the series if certain condition is satisfied. The last of the conditions is to be Turing complete. This series defines a resolvers hierarchy that could be seen as a framework for the evolution of cognition. Then the answer to our question would be: to solve most problems. By the way, the problem theory defines adaptation, perception, and learning, and it shows that there are just three ways to resolve any problem: routine, trial, and analogy. And, most importantly, this theory demonstrates how problems can be used to found mathematics and computing on biology.

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