Figure - available from: Educational Studies in Mathematics
This content is subject to copyright. Terms and conditions apply.
Source publication
(Accepted for Publication in Educational Studies in Mathematics. Published version may contain modifications.) In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways...
Similar publications
Middle markers are characterized by a distribution halfway between grammar and the lexicon: with some verbs, middle marking encodes valency change, while with others it obligatorily occurs with no obvious synchronic motivation. Despite the existing cross-linguistic work on middle markers, their history is still largely unknown. In the typological l...
Citations
... Recently, Melhuish et al. (2023) characterised partial meanings for quotient groups important for students' proving activity. They highlighted two broad meanings, focused on quotient group creation (e.g. ...
... Concurrently, "structure" is lost through homomorphism. Prior references to collapsing (Melhuish & Fagan, 2018) have highlighted this conceptual aspect and our mathematicians conveyed orderly aspects to this collapse, such as quotient group construction, that may also be useful for students (Melhuish et al., 2023). Nevertheless, we observe that simultaneous structure-preservation and structure loss is linguistically confusing and may cause conceptual difficulty for students trying to distinguish which parts are preserved and which are lost. ...
Isomorphism and homomorphism are fundamental topics in abstract algebra, but how mathematicians characterise the utility of these concepts remains understudied. Based on interviews with nine research-active mathematicians, we confirmed use of previously noted conceptual metaphors and noted new metaphors and metaphor clusters. We expand on prior work by highlighting five thematic contrasts between metaphors for these concepts: context dependent sameness, classification of objects versus computing maps, indistinguishable versus distinct objects, structure-preservation versus structure loss, and information gain versus structure loss. Implications include the centrality of sameness to thinking about isomorphism and homomorphism but the need for care in how that sameness is framed; the value of being able to attend to the object and map; the importance of being able to determine which structures are preserved and which are lost in context; and the existence of a conceptual purpose for homomorphism as a tool for changing perspectives.
... /feduc. . 2019) and abstract algebra education research (Soto-Johnson et al., 2008;Melhuish et al., 2023). Regarding the field of linear algebra education research, a comprehensive overview of the years 2008 to 2017 is provided by Stewart et al. (2019a)-themes, results and perspectives from contemporary research are discussed detailing how "students reason about a variety of topic areas in linear algebra, as well as studies that provide evidence of promising directions for supporting students success through various teaching interventions and experiments in the classroom" (Stewart et al., 2019a, p. 1,017) in order to derive possible directions for future research. ...
Algebra is a crucial component of mathematics education as it introduces learners to the mathematical world of modeling relationships and handling abstract quantities. The increasing volume of scholarly work in the field has been analyzed qualitatively in numerous systematic reviews—a quantitative breakdown of the field, however, remains a desideratum to date. With this study we contribute to closing this gap by reporting on the results of a bibliometric analysis. We retrieved data from Scopus and Web of Science databases and analyzed 1,825 articles published between 2003 and 2022. On the one hand, we provide insight into the current state of algebra education from primary up to tertiary education by describing the scientific production and its bibliographic topography. On the other hand, we analyzed the data to identify trends and future directions. The results of our study indicate, among other aspects, that APOS Theory and Realistic Mathematics Education are emerging themes in the field that have great potential to shape future research.
