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…

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…

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…

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…

Limiting case analysis (LCA) is important to practicing physicists. Yet, there is little concrete guidance for physics educators, and a lack of consensus in the research community about how to help students learn, and learn from, limiting case analysis. In this study, we first review existing literature to find commonalities and variations in how…

This qualitative study aimed to examine: (1) the manner in which kindergarten children and first graders make sense of the term "area" regarding optimization problems; (2) how this manner is manifested in their decision-making and "STEAM" (science, technology, engineering, art and math) skills; and (3) how kindergarten children…

In Sri Lankan advanced level mathematics curriculum, teachers are required only to provide the intuitive idea of the concept of limit. The purpose of this study is to explore the strategies used by mathematics teachers to achieve this. Twelve in-service secondary mathematics teachers working in government and private schools participated in the…

Researchers have identified patterns of intuitive thinking that are commonly used to understand and reason about the biological world. These "cognitive construals" (anthropic, teleological, and essentialist thinking), while useful in everyday life, have also been associated with misconceptions about biological science. Although…

This paper investigated the intuitive development of the concept of integers among primary school students. In order to reveal if primary school students had an intuitive sense of integers, an assessment consisting of five questions was prepared and applied to a total 100 4th grade students. A variety of integer concepts were utilized in the…