Book Title: The Academic Language of Mathematics

Book Description

The Academic Language of Mathematics is an openly licensed, web‑based textbook designed to bridge the gap between mathematical content knowledge and the academic English needed to study and communicate mathematics effectively in higher education. Aimed at any student encountering mathematics as part of their degree, it is especially relevant for STEM learners working in English‑medium instruction (EMI) contexts and for students with English as an additional language.

The book consists of eight chapters which systematically guide students through the lexical, structural and textual features of mathematical academic language, drawing on fundamental topics that all STEM students meet in their first years (such as differentiation, integration, sequences and series, vectors, matrices and mathematical writing). Each chapter is organised into seven sections that move from working with key terms in isolation to using them in sentences, paragraphs and longer texts, and then analysing how mathematical ideas are presented and argued for in different genres.

Pedagogically, the book is grounded in content‑based instruction and the lexical approach, prioritising lexis and phraseology over decontextualised grammar drills, while still making relevant structures explicit. It treats “mathematical vocabulary” broadly, including technical terms (for example, calculate the differential) and more general academic phraseology (for example, conceptualised as, rooted in), and presents these within collocations, near synonyms and word families to build deep, transferable knowledge. Later sections draw on genre theory to help students analyse and produce texts such as explanations, application paragraphs and reflective commentary, with attention to information structure (given/new), linking devices, and the rhetorical functions of common patterns in mathematical discourse.

The textbook offers interactive exercises, dialogues, matching tasks, grammar‑aware analysis tables and guided activities that explicitly connect mathematical concepts with the language used to talk and write about them. Materials are multi‑modal: students engage with written texts, audio‑visual resources and dialogue scripts that model realistic peer and lecturer interaction around mathematical topics. An English–Chinese glossary,  supports bilingual and transnational cohorts such as those in the SWJTU–Leeds Joint School, and the resource is designed to be dynamic, adaptable and extendable by other teachers and institutions.

Funded by the Libraries Open Textbook Project at the University of Leeds, the book is published on the Pressbooks platform as an open textbook, benefiting from library support on accessibility, copyright, and open licensing, and from open peer review of both content and learning design. By combining specialist expertise in mathematics and English for Academic Purposes, and by involving students in the development process, The Academic Language of Mathematics offers a unique, practical resource for helping diverse learners gain confidence with both mathematical ideas and the language they need to communicate them.