Empower
Educators

10·Mathematics · KS3 to A Level

Fluent Mathematicians,
Confident Schools

One book for the whole department — the head of maths who has to build the curriculum and the teacher who has to teach the bottom set on Friday afternoon. Built on what the specifications actually say, read from the current documents.

  1. 1Curriculum
  2. 2Fluency
  3. 3Reasoning
  4. 4Evidence
  5. 5Standard
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70 pages · 67 sections · 3.5 MB

Cover of Fluent Mathematicians, Confident Schools

Mathematics is the subject everyone has an opinion about, and the one where a scheme of work is most often mistaken for a curriculum. A list of topics in an order is not a sequence — a sequence records what has to be secure before the next thing can be taught.

This booklet is written for the whole department at once. A head of maths can read it as a curriculum and quality-assurance document; a teacher can open it at the page they need on a Friday afternoon. The specifications were read from the current documents rather than from summaries, and where the boards differ the difference is stated rather than blended.

Written to
The current GCSE and A Level mathematics specifications, read in full
Intended for
For department CPD, planning and curriculum review
Extent
70 pages · 67 sections

·Look inside

Real pages, straight from the PDF

Click any page to see it full size.

·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