Rosa Archer is the Programme Director for the PGCE Secondary at the University of Manchester, UK. Rosa taught mathematics for many years in schools, sixth-form colleges and universities. Her research interests include lesson study and critical pedagogies on mathematics. Rosa has a passion for teaching and learning mathematics as well as inclusion and sustainability within the curriculum. Recent publications include Understanding lesson study for mathematics: A Practical Guide for Improving Teaching and Learning, Myths and Legends of Mastery in the Mathematics Curriculum: Enhancing the Breadth and Depth of Mathematics Learning in Primary Schools and The Mathematics Practitioner’s Guidebook for Collaborative Lesson Research: Authentic Lesson Study for Teaching and Learning.Siân Morgan has had a 30-year career in education. She is a Senior Lecturer at the University of Manchester, UK, working for over 10 years in initial teacher education. In 2020, she co-authored a book Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning. Her current research interests continue to focus on lesson study, professional development and mathematical pedagogy, alongside a particular passion to develop equality, diversity and inclusion and sustainability within the curriculum (social and environmental justice).David Swanson taught mathematics for many years and now teaches the PGCE Secondary Mathematics course at the University of Manchester, UK. He also researches at the university, particularly on mathematical and pedagogical concept development and critical social perspectives on education. Recent co-authored books and articles include Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning and Photojournalism and the Moss Side Riots of 1981. His latest project investigates school-student strikes against racism in the 1980s.Claire Clemmet is an experienced maths teacher and mentor who has been working as a teacher educator at the University of Nottingham, UK, since 2010. During this time she has worked on a range of ITE courses and is now the subject lead for the PGCE Secondary Mathematics course. Claire is currently completing her educational doctorate, which focuses on the role mentors play in the subject knowledge development of student teachers.Stefanie Sullivan is Deputy Head of the School of Education at the University of Nottingham, UK. Stef joined Nottingham as an experienced mathematics teacher and professional development consultant and now has over 20 years of experience of Initial Teacher Education. Stef is particularly interested in how Initial Teacher Education programmes, and the mentors who work with beginning teachers, develop confident professionals who can be successful teachers in a range of different contexts.

• Chapter 1 Models of MentoringChapter 2 The role of mentoring when learning through experienceChapter 3 Why MentoringChapter 4 Developing Reflective PracticeChapter 5 Understanding yourself as a mathematics mentorChapter 6 Exploring the knowledge a mathematics mentor needsChapter 7 Navigating the roles and responsibilities of a maths mentor Chapter 8 Supporting your beginning teacher Chapter 9 Observing a lessonChapter 10 Effective professional dialogueChapter 11 Developing a Mentoring Mathematics Department Chapter 12 The Building BlocksChapter 13 Mathematical MisconceptionsChapter 14 Developing Lesson PlanningChapter 15 Teaching the Lesson Chapter 16 Developing understanding of assessment, marking and the use of dataChapter 17 Handing the baton on

Rosa Archer is the Programme Director for the PGCE Secondary at the University of Manchester, UK. Rosa taught mathematics for many years in schools, sixth-form colleges and universities. Her research interests include lesson study and critical pedagogies on mathematics. Rosa has a passion for teaching and learning mathematics as well as inclusion and sustainability within the curriculum. Recent publications include Understanding lesson study for mathematics: A Practical Guide for Improving Teaching and Learning, Myths and Legends of Mastery in the Mathematics Curriculum: Enhancing the Breadth and Depth of Mathematics Learning in Primary Schools and The Mathematics Practitioner’s Guidebook for Collaborative Lesson Research: Authentic Lesson Study for Teaching and Learning.Siân Morgan has had a 30-year career in education. She is a Senior Lecturer at the University of Manchester, UK, working for over 10 years in initial teacher education. In 2020, she co-authored a book Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning. Her current research interests continue to focus on lesson study, professional development and mathematical pedagogy, alongside a particular passion to develop equality, diversity and inclusion and sustainability within the curriculum (social and environmental justice).David Swanson taught mathematics for many years and now teaches the PGCE Secondary Mathematics course at the University of Manchester, UK. He also researches at the university, particularly on mathematical and pedagogical concept development and critical social perspectives on education. Recent co-authored books and articles include Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning and Photojournalism and the Moss Side Riots of 1981. His latest project investigates school-student strikes against racism in the 1980s.Claire Clemmet is an experienced maths teacher and mentor who has been working as a teacher educator at the University of Nottingham, UK, since 2010. During this time she has worked on a range of ITE courses and is now the subject lead for the PGCE Secondary Mathematics course. Claire is currently completing her educational doctorate, which focuses on the role mentors play in the subject knowledge development of student teachers.Stefanie Sullivan is Deputy Head of the School of Education at the University of Nottingham, UK. Stef joined Nottingham as an experienced mathematics teacher and professional development consultant and now has over 20 years of experience of Initial Teacher Education. Stef is particularly interested in how Initial Teacher Education programmes, and the mentors who work with beginning teachers, develop confident professionals who can be successful teachers in a range of different contexts.

• Chapter 1 Models of MentoringChapter 2 The role of mentoring when learning through experienceChapter 3 Why MentoringChapter 4 Developing Reflective PracticeChapter 5 Understanding yourself as a mathematics mentorChapter 6 Exploring the knowledge a mathematics mentor needsChapter 7 Navigating the roles and responsibilities of a maths mentor Chapter 8 Supporting your beginning teacher Chapter 9 Observing a lessonChapter 10 Effective professional dialogueChapter 11 Developing a Mentoring Mathematics Department Chapter 12 The Building BlocksChapter 13 Mathematical MisconceptionsChapter 14 Developing Lesson PlanningChapter 15 Teaching the Lesson Chapter 16 Developing understanding of assessment, marking and the use of dataChapter 17 Handing the baton on

Rosa Archer is the Programme Director for the PGCE Secondary at the University of Manchester, UK. Rosa taught mathematics for many years in schools, sixth-form colleges and universities. Her research interests include lesson study and critical pedagogies on mathematics. Rosa has a passion for teaching and learning mathematics as well as inclusion and sustainability within the curriculum. Recent publications include Understanding lesson study for mathematics: A Practical Guide for Improving Teaching and Learning, Myths and Legends of Mastery in the Mathematics Curriculum: Enhancing the Breadth and Depth of Mathematics Learning in Primary Schools and The Mathematics Practitioner’s Guidebook for Collaborative Lesson Research: Authentic Lesson Study for Teaching and Learning.Siân Morgan has had a 30-year career in education. She is a Senior Lecturer at the University of Manchester, UK, working for over 10 years in initial teacher education. In 2020, she co-authored a book Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning. Her current research interests continue to focus on lesson study, professional development and mathematical pedagogy, alongside a particular passion to develop equality, diversity and inclusion and sustainability within the curriculum (social and environmental justice).David Swanson taught mathematics for many years and now teaches the PGCE Secondary Mathematics course at the University of Manchester, UK. He also researches at the university, particularly on mathematical and pedagogical concept development and critical social perspectives on education. Recent co-authored books and articles include Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning and Photojournalism and the Moss Side Riots of 1981. His latest project investigates school-student strikes against racism in the 1980s.Claire Clemmet is an experienced maths teacher and mentor who has been working as a teacher educator at the University of Nottingham, UK, since 2010. During this time she has worked on a range of ITE courses and is now the subject lead for the PGCE Secondary Mathematics course. Claire is currently completing her educational doctorate, which focuses on the role mentors play in the subject knowledge development of student teachers.Stefanie Sullivan is Deputy Head of the School of Education at the University of Nottingham, UK. Stef joined Nottingham as an experienced mathematics teacher and professional development consultant and now has over 20 years of experience of Initial Teacher Education. Stef is particularly interested in how Initial Teacher Education programmes, and the mentors who work with beginning teachers, develop confident professionals who can be successful teachers in a range of different contexts.

• Chapter 1 Models of MentoringChapter 2 The role of mentoring when learning through experienceChapter 3 Why MentoringChapter 4 Developing Reflective PracticeChapter 5 Understanding yourself as a mathematics mentorChapter 6 Exploring the knowledge a mathematics mentor needsChapter 7 Navigating the roles and responsibilities of a maths mentor Chapter 8 Supporting your beginning teacher Chapter 9 Observing a lessonChapter 10 Effective professional dialogueChapter 11 Developing a Mentoring Mathematics Department Chapter 12 The Building BlocksChapter 13 Mathematical MisconceptionsChapter 14 Developing Lesson PlanningChapter 15 Teaching the Lesson Chapter 16 Developing understanding of assessment, marking and the use of dataChapter 17 Handing the baton on