**Reviewed by Lisa McGrath and Richard Miles**

8 January 2019

**Katsampoxaki-Hodgetts, K. & Hatzitheodoridou, E. (2019). Academic English for Mathematics. Disigma Publications.**

As EAP practitioners, mathematics is perhaps one of the more daunting discourses we encounter. The publication of Academic English for Mathematics is therefore a welcome resource.

The book is divided into 12 chapters, each covering relevant topics for a university mathematics curriculum, as well as areas that students have most likely encountered at upper secondary school. These topics are well chosen and include cornerstones of mathematical development, such as Euclid’s parallel postulate. It was difficult to discern a sense of progression in the chapters in terms of the level of complexity of the mathematics covered. For example, Chapter 5 deals with an axiomatic approach to probability, whereas Chapter 8 deals with elementary properties of triangles. Nonetheless, students are likely to find these topics both relevant and engaging.

At the start of each chapter, the authors usefully list the mathematical theme in the spotlight, and the vocabulary and EAP skills to be developed. This is followed by a wealth of vocabulary learning exercises and tasks targeting the acquisition of key mathematical concepts together with tasks raising awareness of mathematical procedures. We particularly liked the “how to speak maths” tasks (which draw attention to the integration of running text and symbolic mathematics), the inclusion of audio-visual material as task stimuli, and discussion tasks. We felt that the wording of some of the tasks and explanations could be revisited for clarity, so as to make the book more user-friendly in a self-study context.

While much of the book is geared specifically towards English for Mathematics, some generic EAP skills are also addressed such as paragraph structure, the language of seminar discussions, paraphrasing and tentative language. These sections are perhaps a little less developed than the language tasks built around mathematical discourse. For example, on paraphrasing the advice is to change word form and information structure, and we do not quite agree that all the examples of tentative language given are in fact performing a hedging function in the extracts provided.

The book is very clearly presented. Key terms are bolded and the multimodal nature of mathematical discourse is clearly accounted for in the many diagrams and figures included. Other nice touches include references to the American Mathematical Society to support claims regarding mathematical writing conventions, the use of “remarks”, set out as they would be in a mathematics research paper, and a section on writing for different mathematical audiences.

On the whole, this is an ambitious and impressive book that largely succeeds in its aims. While some elements of the material are challenging (for teachers and students alike), the examples and tasks develop aspects of language that students will undoubtedly need to study mathematics through the medium of English. This is a valuable resource for EAP lecturers, and may well provide insights for mathematics lecturers seeking to scaffold their students into the language of the discipline.

Reviewed by:

Lisa McGrath, Senior Lecturer in Educational Linguistics, Sheffield Institute of Education, Sheffield Hallam University, Charles Street, Sheffield, S1 2LX, 0114 2255503 l.mcgrath@shu.ac.uk

Richard Miles, Senior Lecturer in Mathematics and Secondary Education, Sheffield Institute of Education, Charles Street, Sheffield, S1 2LX, 0114 225 5555 r.miles@shu.ac.uk