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…

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…

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…

Background/purpose: Understanding gifted students' perceptions by means of metaphors, carefully examining and interpreting them may help to guide the organization of training programs and the differentiation of educational content for gifted students. This study aims to reveal the perceptions of gifted students regarding science and mathematics…

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

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…

The goal of this research is to make a theoretical reflection about connections that contributes to the development of the model for mathematical connections originally proposed by Businskas, and extended with the contributions of other researchers. This model is used in the most relevant investigations in this field. As a consequence of the…

Metaphors are recognized as bridging scientists' challenges in communication with the public. In mathematics, however, which often involves abstract concepts and relations, less attention has been paid to the role of metaphors in public communication. In this article we examine the metaphors appearing in the discourse of 10 mathematicians in five…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

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…

This article presents a case study on a secondary mathematics teacher, Mary (pseudonym), and her design of a set of instructional tasks in the context of proportional reasoning. In keeping with the way Singapore teachers generally conceive of instructional planning, we investigated the connections between four comparison tasks she designed through…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

In this study, it was aimed both to examine middle school students' perceptions of the concept of pattern and to reveal if the metaphoric perceptions which the students created in relation to the concept of pattern changed according to the variable of grade level. The metaphors in relation to the concept were carried out via the…

The aim of this study is to evaluate the classroom teacher candidates' metaphorical perceptions about the mathematics course through the visuals they create. The sample of the study consists of 36 classroom teacher candidates studying at a state university in Istanbul. The case study, which is one of the qualitative research methods, was used as…

Adopting Schiralli and Sinclair's notions of conceptual mathematics (CM) and ideational mathematics (IM), we investigated mathematicians' reasoning about continuity of complex-valued functions. While CM centers on formal mathematics as a discipline, IM focuses on how an individual perceives formal mathematics. There were four IM notions that the…