About this Research Topic

Background

Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry.

Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century.
Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference.

Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats.
Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem.

This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).

Ecological rationality situates rationality in the ecological environments and structures of the world, the internal structures of the human mind, as well as their reciprocal interactions. It melts the notion of rationality with an ecological dimension.
The ecological rationality perspective allows a novel way of viewing typical aspects of Mathematics Education, pointing at its fundamental links with Cognitive Psychology.

Our aim for this Research Topic is to illustrate the dialogue between these two disciplines. That is, understanding the cognitive engineering of competencies to understand numbers and number systems, for mathematical reasoning and for problem solving, that requires positioning oneself at the interface of these two realms of inquiry. The focus of this Research Topic will be on these three contexts with a particular interest for Problem Solving in general.

We will look at so called „Insight Problems“. These are problems that require a change in representation by a restructuring process. Those stemming from Mathematics can shed light on cognitive aspects, which deserve the attention of psychologists. Many different difficulties can be detected, from self-imposed solution constraints to functional fixedness, to solution mechanization and misunderstanding.

Through different approaches, the present Research topic will provide analysis of the various principles that inhibit people from finding the correct solution -or any solution-, helping to identify ways to improve the ability to solve creative problems. Themes that strongly emerge from the contributions in the present Research Topic include the relative roles of conscious and unconscious processes, the relationship between language and thought, and the roles of special processes particular to insight, as against routine processes found widely, also in procedural problem solving.

Keywords: Cognition, Reasoning, Problem solving Numerical competencies, Heuristics

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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