Why do creative ideas and solutions to unresolved problems benefit from taking a break? The idea of unconscious work as an explanation is so appealing that even after reading this paper, which states clearly that unconscious work is a fantasy based on no clear theory and no clear empirical evidence, some readers will claim that we are saying the…

Genetic variation is historically challenging for undergraduate students to master, potentially due to its grounding in both evolution and genetics. Traditionally, student expertise in genetic variation has been evaluated using Key Concepts. However, Cognitive Construals may add to a more nuanced picture of students' developing expertise. Here, we…

The purpose of this case study, informed by a Lakatosian perspective, is to identify how an alternative conception that originates in present learning but is related directly to subsequent learning contexts can be constructed. Before the study, one of the authors found by accident that a student who had learned about Avogadro's principle and…

Although complex analysis is part of the study programs of many mathematics undergraduates, little research has been done on how individuals interpret basic concepts from complex analysis. To address this gap, this paper investigates how experts individually think about complex path integrals. For this purpose, the commognitive framework is used…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

This study examines the behavior of individuals when two intuitive rules in their minds lead to two different outcomes concerning a problem. In the absence of the formal knowledge, intuitive rules can affect the mathematical thinking. Hence, studies have usually compared the correct answer of the related formal knowledge with the incorrect one…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

Chance favors the prepared mind, said Louis Pasteur. Sometimes, significant breakthroughs occur when we creatively integrate new information, leading to a creative insight or an Aha! moment, while at other times when we fail to use a clue, we remain stuck in our habitual thinking patterns. In this study, we hypothesized that the brain's transient…

Metaphor generation is both a creative act and a means of learning. When learning a new concept, people often create a metaphor to connect the new concept to existing knowledge. Does the manner in which people generate a metaphor, via sudden insight (Aha! moment) or deliberate analysis, influence the quality of generation and subsequent learning…

Psychologists have studied the question of what happens to naïve or intuitive concepts about science that form before accepted scientific ideas have been taught. Studies find that both the accuracy and time required to decide about the accuracy of carefully crafted statements reveal remnants of intuitive models of science. This is true even after…

This article closely examines (a) the "representational" connotation which is often implicit in many analyses of the scientific knowledge which children have (or have not) acquired when they are asked to say or show what they know and (b) the still common-place presumption that recollections are akin to the extraction of ideas from a…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

Cosmology presents students with ideas that stimulate their curiosity and brings together various concepts from STEM that call on a variety of reasoning types across multiple representational modes, involving subtleties of spacetime relations, a variety of models and evidence requiring multiple lines of high precision observations. This study…

Intuitive conceptions based on cognitive biases (teleology, anthropomorphism, and essentialism) often prove helpful in everyday life while simultaneously being problematic in scientific contexts. Nonetheless, students often have intuitive conceptions of scientific topics such as evolution. As potential approaches to enable students to…