Kant's commitment to autonomy raises difficult questions about the very possibility of Kantian moral education, since appeal to external pedagogical guidance threatens to be in contradiction with autonomous virtue. Furthermore, moral education seems to involve getting good at something through repetition; but Kant seems to eschew the notion of…

The aims of this article are to document the types of signs that young children make to represent their mathematical thinking, and to determine the extent to which features of usage-based language acquisition are evident in children's early graphical communications made in mathematical contexts. Studies of young children's symbolic principles in…

Describing the processes of metaphor comprehension has been a hot topic of discussion among researchers throughout the past four decades. One of the major challenges has been to find a mechanism that can describe the processes involved in the comprehension of various kinds of metaphors. This article suggests that different types of metaphors could…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…

Communication is best understood as occurring along three dimensions: interactional, conceptual, and linguistic. However, few studies have examined early parent-child communication along all three dimensions simultaneously. This study examines these three dimensions of communication in Norwegian parent-child interactions during play. Thirty-nine…

This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

Research in Organic Chemistry education has revealed students' challenges in mechanistic reasoning. When solving mechanistic tasks, students tend to focus on explicit surface features, apply fragmented conceptual knowledge, rely on rote-memorization and, hence, often struggle to build well-grounded causal explanations. When taking a resource…

This paper describes the design of an instrument to assess secondary school students' proficiency in structure-property reasoning (SPR). Design criteria for the instrument required that it should be based on a comprehensive model for structure-property reasoning, assess both reproductive and productive use of structure-property reasoning, be…

For several decades, there has been a push to advance students' knowledge and abilities in science, technology, engineering, and mathematics (STEM). One capacity that has been linked positively to STEM achievement is relational reasoning, which involves identifying associations between objects, ideas, and situations. Yet, few studies have examined…

The expectation for doctoral research to contribute to knowledge is closely related to examiners' attention to conceptual and theoretical components in the thesis. These components require abstract thinking and familiarity with a number of research ideas that are difficult to teach and learn. We argue that these can be made more accessible to…

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students' covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A…

Understanding ongoing chemical processes in the laboratory requires constant shifting between different representational levels--the macroscopic, submicroscopic, and symbolic levels--and analysis of the various mechanistic features of each of these levels. Thus, the ability to explain observations of chemical phenomena with regard to their…

The need for data literacy is an increasingly pressing priority in society, but most of the work in data-centred education has focused on developing skills at the middle school, secondary, and post-secondary levels, with little attention on the potential for engaging elementary-aged students in reasoning with and about data. This paper reports…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

This study investigates Contemporary Mathematical Instruction Competence (CMIC) using the PISA 2022 dataset. The research aims to identify the underlying dimensions of CMIC and assess their consistency across different cultural contexts. Variables were selected from teacher surveys in PISA 2022, focusing on mathematical reasoning, cognitive…