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…

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…

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…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

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…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

Students in a course on the psychology of language and thought first wrote flash fiction stories and analyzed them using course concepts. As an experiential learning exercise, they subsequently analyzed those stories for a number of psycholinguistic variables using the discourse technology Coh-Metrix. Their assignment was to change a number of…

Structural concepts are fundamentals of civil engineering for students to learn, for lecturers to teach and for engineers to use. Many students however find it difficult to understand structural concepts due to their abstract nature. "Seeing and Touching Structural Concepts" has been developed as an approach to help civil engineering…

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…

The idea that characteristics acquired by an organism during its lifetime can be inherited by offspring and result in evolution is a substantial impediment to student understanding of evolution. In the current study, we performed a preliminary examination of how acquiring physical changes in a question prompt may differentially cue intuitive and…

We highlight some important conceptual issues that biologists should take into account when teaching evolutionary biology or communicating it to the public. We first present conclusions from conceptual development research on how particular human intuitions, namely design teleology and psychological essentialism, influence the understanding of…

Research in genetics and genomics is advancing at a fast pace, and thus keeping up with the most recent findings and conclusions can be very challenging. At the same time these recent findings and conclusions have made necessary a reconceptualization of genes and heredity, both in science and in science education, beyond the mostly gene-centred…

This article presents a theoretical model of the process by which students construct and elaborate explanations of scientific phenomena using visual representations. The model describes progress in the underlying conceptual processes in students' explanations as a reorganization of fine-grained knowledge elements based on the Knowledge in Pieces…