—·Contents
All 67 sections
Taken from the booklet's own contents page, so the page numbers are the real
ones.
THE CASE
01The Subject Everyone Has an Opinion Aboutp3
02Where Mathematics Departments Driftp4
THE THEORY
03How Mathematical Understanding Actually Buildsp5
04Fluency, Reasoning and the Space Betweenp6
THE PRACTICE
05Pillar 1 — Curriculum: Sequence Before Coveragep7
06Pillar 2 — Fluency: Automatic, Not Merely Correctp8
07Pillar 3 — Reasoning: The Part That Is Not Optionalp9
08Pillar 4 — Evidence: Knowing What They Cannot Dop10
09Pillar 5 — Standard: One Department, One Expectationp11
10What Should a Year 7 Actually Arrive Knowing?p12
11Three Years, Not a Run-Up to GCSEp13
TEACHING MATHEMATICS
12Modelling: The Part Students Cannot Seep14
13Questioning That Reveals Thinkingp15
14Practice That Is Worth the Timep16
46Lesson Structures That Are Not Formulasp48
47Mathematical Language and Vocabularyp49
60Six Topics, Three Waysp62
MISCONCEPTIONS
15Number and Place Valuep17
16Algebra, Ratio and Proportionp18
17Geometry, Statistics and Probabilityp19
61The Bank — Number, Indices and Surdsp63
62The Bank — Algebra, Geometry and Datap64
REPRESENTATIONS
18Models That Do Mathematical Workp20
REASONING
19Problem Solving Without the Mystiquep21
20Proof, Generalisation and Mathematical Argumentp22
58The Problem-Solving Workflowp60
ASSESSMENT
21Assessment That Changes Teachingp23
22Feedback That Students Can Act Onp24
THE FOUR BOARDS
23GCSE Mathematics, Comparedp25
24The Tier Decisionp26
63Using Board Knowledge Strategicallyp65
EXAM PREPARATION
25Using Past Papers Intelligentlyp27
A LEVEL
26The GCSE to A Level Handoverp28
27Teaching the Three Strandsp29
EVERY STUDENT
28SEND, Dyscalculia and Working Memoryp30
29High Attainers: Depth, Not Accelerationp31
59Tiering, Grouping and Genuine Challengep61
CULTURE
30A Classroom Where Being Stuck Is Normalp32
31Routines, Equipment and the Calm Maths Roomp33
32Homework and Technology, Used Deliberatelyp34
33AI in a Mathematics Departmentp35
49Talking to Parents About Mathematicsp51
FOR LEADERS
34The Head of Mathematicsp36
35Data That Leads to a Decisionp37
36Quality Assurance Without Fearp38
37Developing Mathematics Teachersp39
38The First 90 Daysp40
48Department Meetings and CPDp50
64Recommended Reading and Where It Helpsp66
65Ofsted and the Mathematics Departmentp67
SCENARIOS
39Six Situations, and Where to Look Firstp41
40Three More, and the Leadership Question Underneathp42
THE TOOLKIT
41Templates 1–3 — Curriculum and Sequencep43
42Templates 4–7 — Assessment and Misconceptionsp44
43Templates 7–10 — Monitoring and Meetingsp45
44Templates 10–12 — Self-Evaluation and Improvementp46
45Templates 12–14 — For Teachers and New Staffp47
OUTSTANDING LESSONS
50What an Outstanding Lesson Actually Looks Likep52
51Lesson 1 — Ratio, Year 8p53
52Lesson 2 — Solving Equations, Year 7p54
53Lesson 3 — Trigonometry, Year 10p55
54Lesson 4 — Problem Solving, Year 9p56
CURRICULUM
55A Scheme of Work That Records Dependenciesp57
56Years 8 to 11, in Outlinep58
57A Five-Lesson Sequence: Algebraic Manipulationp59
CLOSING
66One Department, One Standardp68
67References and Evidence Basep69