Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

Preservice middle school mathematics teachers' (PMTs) beliefs about a mathematics teacher and mathematics teaching were investigated through the metaphors they generated. Third- and fourth-year PMTs (N = 249) at four universities in Türkiye participated in two anonymous metaphor tasks for a mathematics teacher and mathematics teaching. PMTs'…

This study examines the presence of three conceptual metaphors for fractions -- The measuring stick metaphor, Arithmetic is motion along a path, and Arithmetic is object construction -- in four common and popular Swedish mathematics textbook series for years 1-3. I analyse the introduction of fractions and the kinds of tasks students are given in…

What tales would students tell about their mathematical experiences? Are they stories of triumph, boredom, despair, exhilaration, or, perhaps, all of these emotions? How do teachers access these stories to understand students' experiences and build from them? In this article, the authors describe a task, The Math Metaphor, and how it was used in a…

This paper problematizes the metaphors of unpacking, deconstructing, and decompressing mathematics that are prevalent in discourses about mathematics teacher knowledge. It is argued that the logic of these metaphors is based on the reversibility of packing, constructing, and compressing mathematics and seems to suggest the view that knowledge is…

Mathematics remains a gatekeeper in schools; educators and researchers must carefully consider how diverse mathematical practices can be recognised and valued. To explore how math is recognised in the craft of weaving, which has been described as highly mathematical with roots in innovations by women, I interviewed 22 experienced weavers about…

This research aims to determine the metaphorical perceptions of gifted and normally developing students attending primary education regarding solving mathematical problems. In the research, the qualitative research method was employed. In the 2022-2023 academic year, 206 students studying at the primary school level in Turkey were determined…

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

Unpacking middle school students' mathematical relationships is important as a step towards improving mathematical relationships. In this study, 500 middle school students drew personifications of mathematics. We examined these personifications of mathematics for insight into their relationships with mathematics. Using constant comparative…

Teaching using the principles of mathematical resilience can lead to a broad range of implementations with different emphases, all intended to mitigate the development of mathematical anxiety in learners and its attendant problems. This article considers 12 primary teachers' responses to the challenge of developing mathematical resilience within…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists (N=11) to gain insight into the cognitive processes and skills that they use in…

Students' beliefs and attitudes have a direct impact on their behavior and engagement in the learning of mathematics. This study examined students' beliefs of dynamic mathematics lessons through the lens of the contemporary theory of metaphor. Participants of the study were grade 10 students in a Macao private secondary school. 51 students…

We examine the relationship between how teachers talk about teaching and their actual teaching practices. Analyses of their talk were based on extensive transcripts and writings and focused on metaphors and images invoked when discussing knowledge, learning, and teaching. Three distinct and coherent webs of association were identified, which we…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…