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This chapter examines methodological and epistemological issues concerning research in science education problem solving. It presents some constructive annotations through a short review focusing on specific features of collective research that appeared in the last decades, which are characterized by certain theoretical and methodological traits. The definition of problem and problem solving within the science-learning context is extended to any cognitive challenge. In the quest for a theory, psychological neo-Piagetian constructs provided effective explanatory frameworks for students’ performance in chemistry and physics education. Epistemological problematization brought into discussion the limitation of linear approaches. The paradigm shift, initiated in the behavioral and social sciences, has affected science education research, and a series of applications based on complexity theory and nonlinear dynamics was realized and reported. The catastrophe theory model provided empirical evidence for nonlinear phenomena, modeling and explaining overload effects and students’ failures. The chapter includes a persuasive discussion on the relationship between problem solving and conceptual understanding and the nature of the corresponding latent variables is examined based on empirical evidence provided by contemporary state-of-the-art methodologies. The later endeavors on problem solving in chemistry and physics education founded a new area of investigation promising to provide new answers to old everlasting questions.

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