Colin Foster, University of Nottingham

There is certainly a pressing need for something that would assist school teachers in presenting mathematics in more discursive and mathematically rigorous ways, and that seems to be very much the focus of this proposal. However, none of these is similar in style to the proposed book. The conversation format is a unique feature, and the focus on mathematics and quality of explanation, depth of thinking is particularly pronounced. I could imagine the book appealing to teachers who use the materials (and books) provided by the UK Mathematics Trust, but they don't have anything like this. Many teachers would benefit considerably from the advice given (implicitly) here about how to introduce and build ideas and tackle misconceptions.

John Woolmer, Winchester College, UK

I like the proposed material which judging by the sample chapters will be well presented, at times unusual, and always stimulating and clear.

Juan Perez, Former Teacher, UK

This proposal aims to cover a genuine gap in the market of books for (primarily) Maths teachers offering a rationale and an explanation for many of the facts given to students. The proposed book brings together some beautiful mathematics, making strong connections between the foundations of the subject and the facts that are distilled and eventually presented to students. Maths teachers will find many of the ideas developed in this book of great value as "connectors" between topics, laying the foundations and the rationale of much of what they present to pupils. In summary, I am very happy to recommend the publication of this book.