Equals in the wild: How mathematical equality is talked about in lessons

Equality is a nuanced concept in mathematics, and the equals sign is used and interpreted in different ways. During professional development in language-responsive teaching, a group of teachers discussed the use of ‘equals’ in algebra lessons. This article considers how three of these teachers went on to invoke equality in their classroom interactions when teaching other topics. The cases observed suggest constructive resonances between conceptions of ‘equals’ and geometric relationships, and include examples of teachers balancing precision with fluency. We argue that attention to language in one mathematical topic may extend helpfully to other topics, but this is not automatic

Mathematics in Maltese: The compilation of a bilingual English-Maltese glossary to support mathematics teaching and learning in Malta

In Malta, mathematics education is accessed bilingually through Maltese and English. While Maltese is often used for verbal interaction, English is the language of written texts, including assessments. Consequently, switches between the languages is a common feature of Maltese mathematics classrooms. Anecdotal and research evidence indicate that Maltese students benefit from the use of their home language. However, to date, there is no recognised and standardised Maltese bank of mathematics Our project aims to address this lacuna. In this article, we outline the process of compiling a bilingual glossary of mathematics terms intended for kindergarten and elementary school levels in Malta (ages 3–11 years). The purpose of the glossary is to support teachers and students in their use of the two languages for the teaching/learning process. This novel resource can serve to validate the Maltese language for mathematics and to encourage consistency of terminology across school and classroom contexts. The glossary can also be helpful in the future should we choose to introduce written Maltese for mathematics. In this article, we explain how the project was developed and how word choices were made with respect to the Maltese terms

The role of the context for pupils’ choice of solution strategies and representations when working with combinatorial problems

This paper reports on a study based on two classroom sessions in a Norwegian school where pupils in Grade 4 (age 9) worked on two combinatorial problems. Data were collected by video-recording two pairs of pupils collaborating in each session, as well as a whole-class session at the end of the second session. The pupils’ written work during the sessions was also collected as data. The classroom sessions were designed based on principles from the Theory of Didactical Situations. Data were analysed using a dialogical approach and based on theory for multiplicative structures and semiotic representations. The study shows that the pupils’ solution strategies and choice of representations in the two problems differed considerably, despite the mathematical similarity of the problems. The aim of the paper is to inquire into how the context in which the problems were set could influence the pupils’ strategies and choice of representations in the solution process, and to what extent the context also could influence whether the pupils recognised the situations as multiplicative

The Legal Philosophy Behind Zoos Confinement of Animals

In my essay, I will be diving into the controversial issue of Animal containment, focusing on zoos in the United States. I will be taking this opportunity to establish a new way of thinking about the argument which states the pros of zoos outweigh the negative effects they have on the animals who live there. Neither side of the argument has a malicious intention towards harming animals. Instead, each side shows a different approach of what it is to properly care, and respect for animal rights. Those arguing in support of zoos commonly reference arguments dating back to Aristotle. However, in my argument against zoos, I will reference instances such as Happy the Elephant who was noted as an autonomous being yet kept in confinement, and visiting the case of Cecilia the Chimpanzee who was awarded person hood in Argentina. I will also be referencing notable philosophers such as Peter Singer and Martha Nussbaum. I will point out that zoos are detrimental to animals’ psychological health, which transfers into their physical health, while simultaneously diving into animal ethics in an attempt to clarify and connect the literature referenced in my essay

Teaching talk moves to support the discussion of divisibility content in a trilingual classroom

In this article, we present our study of teaching talk moves and translanguaging practices used to support the discussion of divisibility in a Catalan–Spanish–English trilingual classroom of a secondary school. We examined a sequence of eleven lessons with a focus on seven talk moves – Switching languages, Revoicing, Recapping, Adding on, Focusing, Funneling and Eliciting. Through this we were able to identify some teaching episodes in which the attention was given to discussing specific mathematical–linguistic challenges involved in the learning and understanding of divisibility content. We illustrate this finding using an episode around the least common multiple and how interconnected moves of Switching languages, Recapping, Eliciting, Funneling and Revoicing functioned to distinguish the mathematical meaning embedded in the lcm labelling, alongside the mathematical meaning intended for the individual word names, least, common and multiple, for the noun phrase and for the concept. We comment on more briefly a second episode around the parity concept for elaborating on the same finding. Our contribution adds to recent work on mathematical–linguistic challenges in the literature and does so with unique data from the under-researched context of the trilingual mathematics classroom

Genre-based socialization practices in teaching and learning of geometric proof in language diverse classrooms

The present study reports on analysis of how two teachers in Lebanon, and their students navigated the learning and teaching of geometric proof in English, in a context in which Lebanese Arabic is the language of home and wider society. One of the teachers taught in a public school, the other in a private school. The study focuses on language socialization practices in the two grade-seven classrooms, in relation to the specific genre of geometric proof. The focus is not directly on proving as a cognitive process; rather, the study explores the interactional process of interpreting and constructing geometric proofs as a form of textual organization. This focus is consistent with the theoretical framing in which learning mathematics is understood as a process of socialization into mathematical discourses, of which the proof genre is a part. The findings reveal four main sets of socialization practices in relation to the genre of geometric proof. These sets of practices were guiding, obtaining information, deducing and attending to accuracy and precision

Trialoguing about engaging with communication and language in relation to mathematics and its education

This is our introduction to the series of eight articles in the first part of the double special issue on the challenges of ‘Engaging with communication and language in relation to mathematics and its education’. In the current article, we think together about ‘communication’ and ‘language’ in relation to mathematics and its education, by turning to reflections and examples from our decades of work as researchers and teacher educators, and in response to the articles in this first part. Following the preamble, most reflections are presented in the form of a fresh trialogue, through which we share some perspectives and anticipate several distinct approaches to communication and to language in contexts of mathematics teaching, learning and teacher education. In the epilogue, we concentrate on some of the reasons for reading the papers in this first part and the coming papers in the second part of the special issue

A prospective mathematics teacher’s shifts in tone of language from ineffective to effective written feedback on a pupil’s project

In the present study, I analyze data from a prospective mathematics teacher, Oya, and her shift in the tone of language used in self-perceived ineffective and effective written feedback on a real pupil’s mathematics project. The results indicate that, in her ineffective feedback, Oya primarily provides neutral and negative responses, often highlighting the pupil’s mistakes in a harsh and judgmental manner. In contrast, her effective feedback demonstrates a wider range of tones, including a substantial amount of neutral feedback as well as solution-oriented comments. The study underscores the importance of tone in feedback, emphasizing how different language use and word choices can support or hinder a pupil’s development. Implications for future research are provided

An operational framework for integrating content, cognition and language into planning for AEN mathematics learners within a CLIL context

The growing diversity in Content and Language Integrated Learning (CLIL) classrooms, particularly the inclusion of Additional Educational Needs (AEN) learners, highlights an urgent need for research addressing their unique challenges. These students often face compounded difficulties, navigating the dual demands of mastering subject content and developing proficiency in the instructional language, with limited frameworks to support their needs. This article presents an operational framework for integrating content, cognition, and language into planning mathematics education for AEN learners. Grounded in theoretical approaches such as communicative competence, CAPA, and pluriliteracies, the framework addresses key challenges in developing mathematical literacy. The framework provides a structured approach for planning in multilingual classrooms, offering a foundation for educators and policymakers to create equitable and effective learning environments that support mathematics learners