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…

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…

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…

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…

Deciphering teachers' paths to their disciplinary professional identities can make important elements of their tacit knowledge explicit and available to their students.

A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many "conceptual metaphors" (CMs), metaphorical mappings between abstract concepts and experiential source domains,…

Students' informal inferential reasoning (IIR) is often inconsistent with the normative logic underlying formal statistical methods such as Analysis of Variance (ANOVA), even after instruction. In two experiments reported here, student's IIR was assessed using an intuitive ANOVA task at the beginning and end of a statistics course. In both…

More than a thousand Grade 10 Physical Science learners from four South African provinces participated in a study that probed their conceptions of energy. The purpose was to determine the learners' conceptual resources, i.e. their initial conceptions, and identify the potentially productive resources from which they may construct physics concepts.…

While Shulman argues that an important component of pedagogical content knowledge (PCK) is teachers' understanding of the alternative conceptions commonly held by students, relatively little is known about what students believe about many topics in the school curriculum. This paper focuses on a content area typically featured in Geography…

This article explores 11- to 16-year-old students' explanations for phenomena commonly studied in school chemistry from an inclusive cognitive resources or knowledge-in-pieces perspective that considers that student utterances may reflect the activation of knowledge elements at a range of levels of explicitness. We report 5 themes in student…

New Zealand's early childhood curriculum, "Te Whariki", has two learning outcomes, dispositions and working theories. While a sociocultural perspective of dispositions has received significant attention in research and teaching, "working theories" as a concept has remained somewhat nebulous. This paper describes ways teachers…

I report on what teachers in an Advanced Certificate in Education (ACE) inservice programme learned about probabilistic reasoning in relation to teaching it. I worked "on the inside" using my practice as a site for studying teaching and learning. The teachers were from three different towns in the Northern Cape province and had limited…

Recent neuropsychological research suggests that intuition and emotion play a role in our reasoning when we are confronted with moral dilemmas. Incorporating intuition and emotion into moral reflection is a rather new idea in the educational world, where rational reasoning is preferred. To develop a teaching and learning strategy to address this…