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Mastering Maths�Lead teacher professional development

June 2024

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Welcome and introductions

• Quick introductions
• Aims
• Overview
• How the Mastering Maths research study works

4

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Introductions

• Name
• College
• Qualifications for this role (prior experience)
• One word to describe your feelings (about the role) right now

5

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Aims of this professional development

By the end of this professional development, lead teachers should:

• Understand the MM programme and the LT role in the programme
• Have developed a team ethos and collaborative ways of working
• Have experienced high quality lesson study and developed expertise in running lesson study
• Have a detailed understanding of the design of Lessons 6, 7 and 9

​

6

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Programme overview

Name, Department

7

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The Mastering Maths research study (nutshell)

• Funder (EEF), Delivery partner (UoN and Lead Teachers), Evaluation partner (NatCen)
• 140 teachers, single or pairs
• About 7000 students
• Control group and intervention group (randomisation)
• Comparison between survey responses and results of students in each group (about 3500)
• Conclusions drawn

​

8

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The Mastering Maths research study: �the intervention

• Lead teachers
• Trial teachers
• Two days ‘full cohort’, (regional) professional development
• Lesson study cluster groups
• Five cycles of
• Plan a lesson (understanding the design)
• Teach the lesson to all GCSE classes
• Gather for lesson study focusing on that lesson

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Based on an explicit theory of change (coming up in next session)

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Which lessons?

• Lessons A and B (Now 11 and 12)
• Lessons 1 to 5
• Lessons 6 to 10

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• Choosing lessons

In the Dropbox

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10

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For each lesson

11

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Your role and our role

YOU look after your teachers

• Provide professional development (whole cohort and lesson study)
• Decide which lessons
• Access to the lessons
• Keep records (delivery log, attendance)
• Nurture and support your teachers

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12

WE look after you

• Provide professional development
• Provide support materials
• Nurture and support you
• Quality assurance

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About learning and the five key principles

Quick starter

• Five minutes silence to think
• Two post-it notes
• What is learning? (yellow)
• What is not learning? (pink)

​

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Theory-informed design of an improvement intervention programme

Designing a programme to improve mathematics learning requires theories that provide models of

1. What it means to learn in general
2. What it means to learn mathematics in particular
3. The role of resources in teaching

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+ an understanding of design as a process

Design cycle

Design cycle

Problem situation

1. Students – failed to achieve a high grade at GCSE.
2. Students have low self-efficacy and confidence in mathematics
3. Students have little conceptual understanding – have primarily been taught rules and procedures that they forget
4. Students follow a 9-month programme and resit the examination

Aims:

1. Improved exam pass rates in mathematics
2. Improved student self-efficacy (and confidence) in mathematics

Levels of design:

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Strategic:“concerned with the overall structure of the product set and how it will relate to the user-system”.

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Tactical: is at the level of the internal structure of the product: that is, it is focused on specifying the core design principles of the product.

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Technical: focuses on the development of individual, often material resources of the product: for example, classroom.

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Burkhardt (2009)

Design cycle

Design:

Professional development

Classroom materials

Tactical design of programme

Theoretical constructs

Wenger:

communities of practice

learning

architectures of design for learning

Boundary objects

Didactical transposition

Key design aims of CfEM Teaching for Mastery programme:

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1. incorporate Teaching for Mastery key principles
2. target key topics of students’ understanding (cognitive conflict)
3. provide insight into signature pedagogies
4. build collaborative teacher communities of inquiry around change in pedagogy

Tactical design of programme

Theoretical constructs

Wenger:

communities of practice

learning

architectures of design for learning

Boundary objects

Didactical transposition

Learning

�A Social Theory of (Professional) Learning�

Wenger (1988) Communities of Practice: Learning, Meaning and Identity

design

�(Professional) Learning�

Wenger (1988) Communities of Practice: Learning, Meaning and Identity

Professional development key principles

Effective Professional Development is:

• Experiential: stimulating & drawing on teachers’ experiences.
• Sustained: cycles of planning, predicting, enactment & reflection.
• Grounded: practical, well-resourced; related to context & culture.
• Safe: teachers able to speak their minds, permission to take risks.
• Collaborative: involving networks of teachers & administrators.
• Informed: by outside expertise and research.
• Provocative: involving both pressure and support.
• Focused: attentive to the development of the mathematics itself.

​

(Guskey, 2002; Joubert and Sutherland, 2009; Villegas-Reimers, 2003; �and many others…)

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What does dialogic learning look like?

Teacher communities key principles:

• Collaborative, in and across schools/colleges
• Teachers engage in collaborative lesson research

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Teacher communities:

School C

Programme

Tactical design of programme

Theoretical constructs

Wenger:

communities of practice

learning

architectures of design for learning

Boundary objects

Didactical transposition

Design cycle

Design:

Professional development

Classroom materials

​

Develop fluency and conceptual understanding

• “become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.”

Reason mathematically

• “by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language”

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Solve problems

• “by applying their mathematics to a variety of routine and non- routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.”

Three Strands of the NC for England

Five key principles

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Instruments

Object

Subject

Instrument mediated

goal-directed actions

an artefact has the potential to support actions, whereas it becomes instrumental in its use when the user has a mental scheme that supports both technical and conceptual abilities to realise this potential in a specific situation.

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Theoretical perspective of design for (professional) learning

Boundary objects supporting teacher learning leading to student learning

Boundary objects supporting teacher learning leading to student learning

Design for cognitive conflict as a boundary object

Boundary objects supporting teacher learning leading to student learning

Discussion

In what ways does the double number line serve as a boundary object for teachers in developing their learning of Teaching for Mastery?

Tactical design of programme

Theoretical constructs

Wenger:

communities of practice

learning

architectures of design for learning

Boundary objects

Didactical transposition

Theory of Change

Researching teaching for mastery

EDUCATION & TRAINING FOUNDATION

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Theory of Change

Researching teaching for mastery

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Theory of Change

Researching teaching for mastery

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Theory of Change

Researching teaching for mastery

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Theory of Change

Researching teaching for mastery

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Theory of Change

Five key principles

• Developed for the sector by the sector
• Reflected throughout our work with teachers and students
• Handbook

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49

Teaching for Mastery: �Five Key Principles

Handbook

• https://www.et-foundation.co.uk/wp-content/uploads/2023/06/CfE_Mastery_handbook_final.pdf

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And the NCETM 5 big ideas?

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Results of the CfEM RCT

• Geoff talk 10-15 minutes
• Discussion and sharing 10 – 15 minutes

52

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Teaching for Mastery in FE: �efficacy trial

Researching mastery teaching in FE

Aimed to �understand how improved teaching can lead to increased student understanding of mathematics which results in improved attainment.

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The question more specifically asked: �Can adopting a teaching for mastery approach lead to improved student attainment in GCSE resits?

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55

2019 – 20

2020 – 21

2021 – 22

2022 – 23

Researching mastery teaching in FE

Efficacy RCT

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Three-armed Randomised Controlled Trial

Researching teaching for mastery

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Two intervention models:

ALL Group 1(full intervention) and Group 2 (partial intervention) teachers:

• provided with lessons A&B + 1 – 5 (lesson plans, presentation, worksheets etc);
• asked to teach the lessons at the appropriate times (Windows 1 to 5) to ALL their GCSE resit classes;
• asked to adopt the approaches modelled by the lessons in other lessons.

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Two intervention models:

Group 1(full intervention) teachers:

• additionally took part in a modified lesson study process focused on each of the five lessons 1 – 5 in turn. Three planned to be face-to-face and two (lessons 3 & 4) online.

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60

2019 – 20

2020 – 21

2021 – 22

2022 – 23

Impact evaluation

Implementation and process evaluation

Researching mastery teaching in FE

Evaluation of the trial

Impact evaluation

GCSE scores of students in all groups (quantitative).

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Implementation and process evaluation (IPE)

Data about how the intervention was implemented (mostly qualitative).

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Outcomes (impact evaluation)

Impact

Our impact analysis detects a small positive effect for each intervention model. �

There is most impact on students from the most deprived backgrounds (as measured by free school meals) who were taught by teachers in the full-intervention. 

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The full intervention has greater impact against the business-as-usual control than the partial intervention model leading to the tentative conclusion that the lesson study practices of the full intervention add value to the Teaching for Mastery programme in terms of impact on outcomes.

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Impact

The positive effect sizes (above business-as-usual practice) are 0.06 for the full intervention and 0.04 for the partial intervention.

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The effect size for the most deprived students taught by full-intervention group teachers is 0.1 (we have 85% confidence in this result).

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A similar differential impact for the most deprived students taught by partial-intervention group teachers is not detected

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Impact

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What does that mean for students and colleges?

Impact

In line with Education Endowment Foundation reporting, �these effect sizes suggest

Business as usual

Months of teaching

8

Outcomes (implementation and process evaluation)

Discussion

• Three groups

​

• Juliane, Dave, Sarah R, Luan, Valeria
• Lewis, Steve, Oxana, Aga
• Sarah G, Zohra, Natacha, Elaine, Alastair

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• What would you want to tell your colleagues about? Or tweet about? Or put on Linked In?
• Why?

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Lesson study

Lesson Study and research questions

Geoff Wake

Lesson study

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Lesson study

Effective Professional Development is

Experiential: stimulating & drawing on teachers’ experiences.

Sustained: cycles of planning, predicting, enactment & reflection.

Grounded: practical, well-resourced; related to context & culture.

Safe: teachers able to speak their minds, permission to take risks.

Collaborative: involving networks of teachers & administrators.

Informed: by outside expertise and research.

Provocative: involving both pressure and support.

Focused: attentive to the development of the mathematics itself.

(Guskey, 2002; Joubert and Sutherland, 2009; Villegas-Reimers, 2003; �and many others…)

​

​

73

Effective Professional Development is

CfEM lesson study lessons are �research lessons

Lessons where as teachers we inquire/research into what effective teaching for mastery is.

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This is a collective and collaborative endeavour

​

They are experiential, sustained, grounded, safe, collaborative, informed, provocative and focused.

​

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CfEM lesson study lessons are �research lessons

Lessons where as teachers we inquire/research into what effective teaching for mastery is.

​

This is a collective and collaborative endeavour

​

Lessons are experiential, sustained, grounded, safe, collaborative, informed, provocative and focused.

​

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Lesson study cycle

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Lesson study cycle

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Lesson study cycle

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Phases of the lesson

1. Presentation
• Teacher presents the problem
• Students discuss the problem
2. Developing a solution
• Students develop ideas individually
• Students share ideas
• Teacher observes students, makes notes for later
3. Progress through discussion
• Students share their solution ideas with whole class
• Students critique solutions, identifying strong and weak points.
4. Summarizing and reflecting
• Teacher summarizes group findings, identifies important ideas, generalizes
• Students summarize what they have learned themselves

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Pedagogical moves

Hatsumon

• the teacher’s questions or actions designed to provoke students’ deep thinking.

Kikanjunshi

• the teacher monitoring and analyzing student work, making notes, selecting students to present and in what order.

Neriage

• collaborative whole class discussion; refining students’ ideas and integrating and synthesising ideas.

Matome

• the teacher or students summarizing what has been learned.

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Lesson study cycle

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Lesson study cycle

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Lesson study cycle

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Lesson A research questions

Pedagogic focus

How does the teacher use the student tasks to help develop understanding of mathematical structure?

​

Maths focus

In what ways do students use representations to consider mathematical structure to develop their mathematical understanding of highest common factor and lowest common multiple?

​

84

Lesson B research questions

Pedagogic focus

How is the lesson developed and brought to a close in ways that values and builds upon what students already know?

​

Maths focus

What evidence do you observe of students’ prior learning about area and volume and how do they work with or modify this?

​

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Designing for lesson study within the constraints of a randomised control trial

Marie Joubert

Geoff Wake

Presentation given at the World Alliance of Lesson Study annual conference

What this talk is and isn’t

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It is: about designing research within given constraints

​

It isn’t: about the outcomes of the research

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Context

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At 16, large numbers of students do not achieve a ‘pass’ in national GCSE examinations

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Funding to continue studying (usually at Further Education college) requires them to re-take mathematics

​

One year course – effectively 8 months

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National focus on Mastery in mathematics

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Our research : �Mastering Mathematics �– a randomised controlled trial

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TfM RCT: three-armed Randomised Controlled Trial

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CLR (lesson study process)

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Question: in the context of a randomised control trial …

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• Students: the same experience of mastery

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• Teachers: the same understanding of mastery (both groups)
• The same lesson study experience (full intervention)

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• Lead teachers: running cluster meetings in the same way

How do you provide a uniform experience?

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What we did

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CLR (lesson study) process

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Lessons

Research theme

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Teaching for Mastery: �Five Key Principles

Mastering Maths – about the lessons

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• Define and inform an approach to Mastering Mathematics

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• Designed in alignment with, and exemplify, the Key Principles

An example

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CLR process

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Research questions

Pedagogic focus: In what ways does the teacher develop and bring the lesson to a close to support a culture where everyone believes everyone can succeed?

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Maths focus: In what ways do students use representations to access the structure of mathematical problems?

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Lead teachers

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Lead teachers

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Cluster meetings

100

Observing the lesson

100

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Cluster meetings

101

Introduction to the next lesson

101

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Lessons for Lesson Study

• For lesson design:
• Clear, shared design principles
• Change mechanisms such as agreed lesson structures that embody and support key principles
• For Lesson study
• Support for Lead Teachers essential
• A version of Lesson Study can work within a randomised control trial

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Discussion

Your experiences of Lesson Study: as a participant or LT… and questions

• Juliane
• Sarah R
• Alastair
• Lewis
• Aga
• Elaine
• Zohra

Group 1

Group 2

• Steve
• Dave
• Sarah G
• Natacha
• Oxana
• Valeria
• Luan

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Lesson study: practical guidance

And how we are going to do LS in the next 2½ days

Practical guidance

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LS in the next 2½ days

• 3 lessons, 3 lesson study groups, 3 lead teachers, 3 teachers … students and observers
• Today
• Introduction to the lesson by lead teacher
• Others take the role of trial teacher
• Prepare for the lesson (practice for the teachers)
• Tomorrow and Wednesday
• Lesson takes place
• Post-lesson discussion
• Post-post-lesson discussion

​

​

107

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Timings

• 2:15 – 4:45 Work in Lesson study groups (take a 15 break when it works for your group)
• 4:45 Reconvene

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Review: walking and talking

• In pairs (someone you don’t know well and with different experiences)
• Walk and talk: review the day, your thoughts and questions
• What have you learned? (About the trials, lesson study, people you’ll be working with, yourself …)
• What do you want to share about what you’ve learned?
• What questions do you have?

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• Reconvene at 5:15

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Close

• Tonight: dinner at 7:30
• Tomorrow: start at 9
• Charlotte from NatCen will be with us

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Mastering Maths �Lead teacher professional development

25^th June 2024

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Plan for this morning

• Oxana teaches lesson 6
• Everyone else in Juliane’s group observes – as lesson study researchers
• Every else is a ‘student’
• Some quick input on post-lesson discussions
• Post lesson discussion
• Student experience of the lesson

​

• (More of the same this afternoon)

112

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How should you behave as a student?

• Discussion

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How should you behave as an observer?

• You are a RESEARCHER
• Don’t be tempted to help the students
• Remember the research questions:
• In which ways does the lesson develop the students’ understanding and fluency related to averages?
• How do students use different representations of data to develop their understanding?

​

​

114

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Post-lesson discussions and research questions

• Led by the lead teacher (Juliane)
• The teacher (Oxana) shares her experience
• The observers describe and analyse what they observed (focus on research questions, student responses)
• In which ways does the lesson develop the students’ understanding and fluency related to averages?
• How do students use different representations of data to develop their understanding?

​

115

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Aims of this professional development

By the end of this professional development, lead teachers should:

• Understand the MM programme and the LT role in the programme
• Have developed a team ethos and collaborative ways of working
• Have experienced high quality lesson study and developed expertise in running lesson study
• Have a detailed understanding of the design of Lessons 6, 7 and 9

​

116

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Practical stuff (Corrine)

• Claiming expenses
• Setting up as suppliers
• Taxis

​

117

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Lead teachers

118

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119

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Your role as a Lead Teacher

• Relationships
• Preparation
• Organisation and logistics
• Which lessons and when to choose?
• Teaching the first lesson
• Clusters
• Your own teaching
• Cluster meeting support materials (guidance)
• Padlet shared space

120

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Cluster meetings

• Research lesson in the morning –advantages and disadvantages
• Using RQs to think about the next lesson
• Re-showing the video

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121

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Challenges for teachers

• Class discussion
• Prior knowledge
• Allowing time for productive struggle
• Standing back (not interfering/helping)
• Time (take two lessons)

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September professional development

Familiarise with lessons

Prepare for TT professional development

​

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September/October professional development for trial teachers

• Our role and your role
• Dates
• Locations
• Teams of LTs
• What’s an RCT?
• Efficacy trial
• Mastery (Lesson A and Lesson B)
• Cluster meeting 0

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Elements

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Name, Department

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31 July 2024

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Elements

Name, Department

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31 July 2024

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Elements

Graph Example

Graph Example

Name, Department

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All items on these slides are editable. You can change the colour, outline and size easily as you do with other PowerPoint shapes.

Please see slides at the end of this template for chart and table style guides. Copy and paste these items onto this page for ease.

Elements

Table Example

Name, Department

130

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All items on these slides are editable. You can change the colour, outline and size easily as you do with other PowerPoint shapes.

Elements

Editable Map

Name, Department

131

31 July 2024

All items on these slides are editable. You can change the colour, outline and size easily as you do with other PowerPoint shapes.

Elements

Editable Icons

Name, Department

132

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Top Presentation Tips

• Keep it simple
• Always think about your audience
• Limit transitions and animations
• Respect the University of Nottingham brand and identity
• Use visuals and high-quality images
• Use video or audio
• Use colour
• Think about
• Prepare and practice