Contribution: This article identifies possible ruptures between the ways fundamental notions of exact differential and exact differential equations (EDEs) are employed in mathematics courses and professional engineering disciplines. Background: Engineering students often experience difficulties with mathematics courses which may even lead to…

This study aimed at investigating how preservice teachers' understandings of division and reasoning about ratios support and constrain their formation of proportional relationships in terms of quantities. Six preservice teachers from a middle-grade preparation program in the USA were selected purposefully based on their mathematics performance in…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

This study investigates the challenges faced by second-year undergraduate engineering students in understanding Stokes' theorem in vector calculus, focusing on the misconceptions found in interconnected concepts that form its foundation. Stokes' theorem involves the application of line integrals, surface integrals, the curl of a vector field, and…

Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

Digital game-based learning (DGBL) has emerged as an effective strategy to enhance students' learning effectiveness. Concept mapping, recognized as a valuable tool for knowledge construction, has been widely implemented in educational settings. However, research indicates challenges when integrating concept maps into games, particularly when the…

The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

This article draws from Hiroko Kawaguchi Warshauer's conceptualisation of productive struggle, which capitalises on experiences that elicit struggle, that is, those that require students to 'expend intellectual effort' and that are productive, in the sense that they seek to 'advance thinking and deepen' understanding of mathematical concepts and…

This 5-year longitudinal study examined whether high mathematics achievers in primary school had cognitive advantages before entering formal education. High mathematics achievement was defined as performing above Pc 90 in Grades 1 and 3. The predominantly White sample (M[subscript age] in preschool: 64 months) included 31 high achievers (12 girls)…

This case study investigated the relationship between five undergraduate interior design students' reasoning with numerical units and reasoning about length and area. The multiplicative concepts frame participants' coordination of numerical units. Differences were found between participants' reasoning about length and area, based on their…

In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…

In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the…

Processing rational numbers is difficult for many children. The natural number bias is one possible explanation for why children struggle with rational numbers. It refers to the tendency to overgeneralize the properties of natural numbers. In this study, it is argued that in order to be successful in rational number tasks, individuals need to…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Entrepreneurship education is critical in encouraging students' innovation, creativity, and entrepreneurial spirit. It provides essential skills and knowledge, enabling them to open their creative potential and apply innovative thinking across diverse professional fields. With the widespread application of large language models in education,…