Copy - Teaching Mastery Module 5

Principle Development LeadSecondary Maths

Clare Hill

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School Development LeadSecondary Maths

Carys Hopkin

Supporting all students to succeed

Teaching MasteryModule 5

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Planning Lessons for Success for All

Quiz & Evaluation

Use the arrows in the top, right-hand corner to navigate through the trainingOr go straight to each of the chapters using the buttons below

Understanding the LO's

Understanding Students with Lower Prior Attainment

Dimensions of Depth

LPA & SEND

Click here to understand how to work through this training.

Index

Hover over each Dimension of Depth to remind yourself of their key principles.

MathematicalProblemSolving

Language & Communication

Mathematical Thinking

Conceptual Understanding

Dimensions of Depth

*Some slides require answers to be submitted before moving onto the next task

Look at this Develop Learning task. (Click to enlarge)Where can you see the Dimensions of Depth within it?

Conceptual understanding: How will this task deepen understanding of perimeter?Mathematical Thinking: What 'bigger picture' thinking skills might the students use? For example, pattern spotting, testing, comparing, conjecturing. Language & Communication: What terms might students need to use? Write an example sentence.

MathematicalProblemSolving

Language & Communication

Mathematical Thinking

Conceptual Understanding

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Dimensions of Depth

MathematicalProblemSolving

Language & Communication

Mathematical Thinking

Conceptual Understanding

Click on each Dimension of Depth to see what we picked out from this task

Dimensions of Depth

Next

This section focuses on the language of ability and attainment and what we mean when we describe students as low prior ability or attaining. The purpose of this is to establish a shared language as a team to ensure high expectations for all students.

Chapter 1

Understanding Students with Lower Prior Attainment

Mastery is built with the success of all students in mind...

Click on the image to find out more.

Lower Prior Attainment

Why is it important that we differentiate between attainment and ability?

Low Prior Attainment

The Mathematics Pipeline in England: Patterns, Interventions and Excellence. Noyes et al. University of Nottingham 2023

Think about your own experiences. Discuss or reflect upon a child that has come into year 7 well below expectation but then went on to succeed at GCSE.

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Attainment is not fixed

The Mathematics Pipline in England: Patterns, Interventions and Excellence Noyes et al. University of Nottingham 2023

Attainment is not fixed

Explicit & Direct Instruction

Student- Centred Approach

Least Effective

Most Effective

Peer Tutoring

Tutoring by Adults

Self-Instruction

Co-operative Learning

Heuristics

Feedback to Teachers

Feedback to Pupils

Computer-Aided Instruciton

Representatives

Manipulatives

Click to learn more about this study

Drag them into the order you think they were found to be most effective.

In this study by Hodgen et al. 12 teaching strategies and approaches were identified that can be put in place to address pupils' low attainment.

Prior attainment

01

1. Explicit & Direct Instruction

12. Student- Centred Approach

Least Effective

Most Effective

5.Peer Tutoring

4. Tutoring by Adults

10. Self-Instruction

11. Co-operative Learning

6. Heuristics

9. Feedback to Teachers

7. Feedback to Pupils

2. Computer-Aided Instruciton

8. Representations

3. Manipulatives

Click to learn more about this study

Here is the order that the study found had the most impact on LPA students, compare them to your answers.

Prior attainment

01

The study found that good explicit & direct instruction had the biggest impact on supporting LPA students.

During this training we will be exploring how we adapt lessons for the success of all students.This will include how you will plan to run lesson tasks.

• What you will say
• What you expect students to do

1. Explicit & Direct Instruction

Prior attainment

01

In this chapter you focused on the importance of the language used to describe students. The trajectory for different students and strategies to support high expectations for all students were examined.

Understanding Students with Lower Prior Attainment

• Ability is often considered innate and therefore use of the word can imply that it is fixed.

• Attainment can improve and thereore use of the word can lead to higher expectations for all students.

• Students' attainment can improve or decrease over time.

• High expectations for all students will also support students with higher prior attainment who are at risk of worsening outcomes.

• There are a number of evidence based strategies that can support this.

Attainment is not fixed

Chapter 1Review

Key Takeaways:

01

Next

Not all LPA students are students with SEND and not all students with SEND are students with lower prior attainment. This chapter examines what this means for teaching.

Chapter 2

Distinguishing between LPA and SEND students

• Learning of mathematics

• Classroom norms
• LPA needs
• SEND

Write your ideas in the box below, these might include;

Think of some ideas why students might be unsuccessful when attempting this task?

Look at the Develop Learning task below (click to enlarge).

Barriers to success

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Think about a HPA student that also has SEND needs.What do you do to support them?

Low Prior Attaining

Barriers to success

Visual impairment

Dyslexia

Gaps in learning through teacher absence

Anxiety or depression

Frequent absence from school

SEND

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https://educationendowmentfoundation.org.uk/news/five-evidence-based-strategies-pupils-with-special-educational-needs-send?utm_source=/news/five-evidence-based-strategies-pupils-with-special-educational-needs-send&utm_medium=search&utm_campaign=site_search&search_term=send

Explicit instruction

Cognitive & Metacognitive Strategies

Scaffolding

Flexible Grouping

Using Technology

'...good teaching for pupils with SEND is good teaching for all.'

Click on each of the five strategies recommended by the EEF to support students with SEND

EEF SEND Recommendations

In this chapter you examined some of the many barriers that can exist for a student which prevent success. Many of these can be overcome through planning to allow appropriate entry points for students

Distinguishing between students with LPA and students with SEND

SEND and LPA needs are often conflated but it is important to remember that not all SEND students are students with lower prior attainment and should be planned for according to their need.

SEND and LPA

Chapter 2 Review

Key Takeaways:

01

The lesson slide decks always start with a unit overview slide containing the learning objectives for each lesson. In this chapter we will examine using the learning objectives to meet the needs of all students whilst maintaining high expectations for all. We will be looking at Year 7 Unit 11 Lesson 1.

Next

Chapter 3

Knowing the Learning Objectives

What do you use Learning Objectives for?Look at the statements below, and sort them from most to least important to you.There are no right or wrong answers.

Before you begin planning your lesson it is vital that the aims of the lesson are clear

Learning Objectives

The Unit Overview is the first point of call for finding the Learning Objectives for each unit and lesson within it.Click on the buttons below to explore the Learning Objectives.

Finding the Learning Objectives

There are multiple places that exemplify what students should know.Two examples of this are the Start of Unit Quiz and the Exit Ticket. Click on eack of them to see how they can be used.

Exemplifying Knowledge Expectations

Where can you see the Learning Objectives in each lesson task?

• Talk Task
• New Learning
• Develop Learning

You may not see every objective in each task

Learning Objectives: Lesson 1 - Describing Perimeter

• Be able to work out perimeters of different shapes.
• Understand perimeter as a measure of length expressed in appropriate units.
• Experience connecting perimeter calculations to shapes using axioms of number and algebra.

Click on the tasks to enlarge them. Answer the questions alongside them.

05:00

Learning Objectives

Click on each lesson task to see where we found the learning objectives.

Learning Objectives

You have students that might struggle to get started with this task. What will you say, or do to help them?eg. Giving sentence starters, giving additional examples, questioning prompts, or explaining in a different way

Look at this Talk Task, click on it to enlarge

05:00

Planning with Learning Objectives in Mind

Here are the accompanying notes from the Notes and Guidance page in the slide deck. Read through and compare with your previous answers.

2. You have students that might struggle to get started with this task. What will you say, or do to help them?eg. Giving sentence starters, giving additional examples, questioning prompts, or explaining in a different way

1. What is a good answer to this Talk Task?Think about key terminology, full sentences, exemplifying and explaining why

Look at this Talk Task, click on it to enlarge

Planning with Learning Objectives in Mind

Here is an example of an adapted Talk Task.Click on each adaptation for more context.

Planning with Learning Objectives in Mind

Learning Objectives can inform adaptations by:

• Guiding the key concepts of the lesson
• Ensuring you know the minimum that all students should know by the end of the lesson
• Help you understand the purpose of each lesson task

No student should lose out from the adaptions made

Adaptations for Success

In this chapter you have explored how examining the learning objectives can aid planning for success for all students without anyone losing out.

Knowing the Learning Objectives

The plenary and Start of Unit Quiz can also be used to exemplify skills students will need before starting the unit, and the skills all students will have acheived by the end of the lesson.

• The objectives for each lesson can be found in the unit overview slide

• The goals for each task can be found in the Notes and Guidance slide (Year 7)

Learning objectives

Chapter 3 Review

The objectives for each lesson should be fulfilled, which will often require you to adapt slides maybe to move more slowly through the material, or by adding in alternative examples and explicit modelling.

No-one should lose out when adaptations are made

Key Takeaways:

01

Next

In this chapter you will plan and adapt a New Learning and Develop Learning slide to ensure success for all your learners

Chapter 4

Planning for Success for All

Look at this New Learning slide (click to enlarge),and answer the questions on the right.

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New Learning

1. What is the key learning from this slide?Think back to the Learning Objectives

2. Write down two ways you would adapt this task for LPA studentsWill you use additional examples? What will you say? Do you need to plan for accessability?

In Chapter 2 you saw the importance that Explicit & Direct Instruction had on the success of LPA studentsWatch the video below to see how this task could be modelled

New Learning

Complete these questions individually,then feedback as a team

1. What is one answer you want to see from your students in this task?

You have already explored this task using the Dimensions of Depth.Now we will look at how to adapt it.

Develop Learning

2. How will you introduce this slide?Will you talk through the first example?Do you need to add in an additional example?

Use the Notes & Guidance slides to support your adaptations, especially when thinking about teacher exposition and prompting questions.

Your exposition and modelling are key strategies for supporting LPA students.

Modelling

In this chapter you have examined two lesson tasks and how they might be adapted to support success for all students, including students with LPA and SEND.

Planning for Success for All

Chapter 4 Review

Key Takeaways:

Chapter 5

Quiz and Evaluation

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Next

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Evaluation & Quiz

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• support pupils to recall previously learned content, before they move on to new content?
• help pupils to organise their thinking by ‘chunking’ the content into smaller steps?
• ask metacognitive questions that support pupils to plan, monitor and evaluate their own learning?

2. Cognitive & Metacognitive Strategies

This section states the intention of the New Learning from each lesson of the week

Definitions

Having clear definitions on the board for key terms you will be revisiting throughout the lesson will help students remember them You could also get the students to write this into their books, chant as a whole class, or print and stick this slide into their books

Students may start to make their own conjectures about how they form the shortest and longest perimeters. If they don't, ask them questions that may encourage this. Physical manipulatives will support students in trying this out. Ask students to try to justify why the shape with the longest perimeter will be formed from joining the shortest edges.

Mathematical Thinking

Talk task

By using both straight and curved lines, the talk task emphasises perimeter as a linear measurement supporting students to understand perimeter as a measure of length.

Building up gradually

You may want to consider starting the task with a similar question that encompasses the same learning objectives. Here I want to draw the attention to the difference in lengths between a straight and curved boundary, before moving on to a more challenging example.

Through this purposeful practice task of calculating perimeter, as students rearrange the rectangles to form different compound shapes they will discover that the perimeter changes. They may also recognise that althought the perimeter changes, the area remains the same.

Click here to link to the Unit 11 Area and Perimeter of 2D shapes overview video

Conceptual Understanding

Key Words

Displaying key words on the board can help minimise the cognitive load for students who might struggle to recall prior tems easily. They can also help guide students to use the correct mathematical language during class discussions

Prompts on the slide

Adding prompts that come up on the slide can also help with cognitive load, and act as a reminder for students when attempting the next examples

Teachers have high expectations for every single learner, rooted in a belief that anyone can become an excellent mathematician. Teachers reinforce this attitude to build confidence and resilience. Helen Drury

https://helendrury.com/2021/09/02/origins/

Maths Mastery is built with success in mind

• use clear and succinct language when explaining things to pupils, checking their understanding frequently?
• use dual coding (i.e. diagrams, images or tables on a mini-whiteboard) to aid students’ understanding of new content?
• model how to complete a task before expecting pupils to work independently?

1. Explicit Instruction

Definitions & Key Terms

Are there any words your students might struggle with? Explaining definitions before beginning a task can help make sure it runs smoothly.

Clear learning objectives enable teachers and departments to create consistent learning environments, aligning the aims for each lesson.

They set student expectations, guide their learning processes, and help them focus their study time.

Learning Objectives

They form the basis for developing high-quality assessments for formative and summative purposes.

Building Up Gradually

If you want to check that your students are ready for the New Learning question, you may want to add some additional examples that build up gradually to it. This is a good time to look at the prio knowledge students need from the Start of Unit Quiz These wouldn't necessarily be on the slide all at once, they could be animated to show up one by one, or you may prefer to draw them on a whiteboard to save planning time creating them in powerpoint

In the Notes and Guidance slide for this Develop Learning we suggest that you offer students different prompt questions to encourage their thinking: “Compare the number of edges on the inside/outside of your shapes.” “Compare the number of long/short rectangle sides on the outside of your shape” “Can you form two different shapes with the same perimeter?' Encourage students to answer these questions in full sentences.

Language & Communication

What are YOU going to say?

Having prompts for students can ensure that they are boing pointed in the right direction, that they are noticing the important parts of this task.

This section goes through the objectives for each lesson

They are showed alongside the tasks that accompany each lesson. The lesson objectives can be found in each task, although every task may not encompass every one. By completing the lesson students will have been exposed to all the objectives.

Exit Ticket

When planning your lessons, the Exit Ticket can provide key information about the learning objectives. By the end of the lesson students should have the neccessary skills and understanding to complete these questions.

https://www.gov.uk/government/publications/subject-report-series-maths/coordinating-mathematical-success-the-mathematics-subject-report

i.e. the practice of using prior attainment data informs decisions about curriculum choices for year 11 from year 9 data.

The Ofsted subject review report of June 2023 evaluated the common strengths and weaknesses of mathematics in the schools inspected and considers the challenges that mathematics education faces. In paragraph 69 they found that

Coordinating mathematical success: the mathematics subject report

• utilise technology as part of the delivery of interventions?
• support pupils to use technology to record their learning, i.e. through speech-to-text software?

5. Using Technology

New Learning

The New Learning slide is an opportunity to explicitly model calculating a perimeter so that students are able to work out the perimeter of different shapes.In this task they will also experience being aware of the sides of the square and triangle that are not a part of the perimeter of this compound shape. For some students, modelling the calculation using the distributive property of arithmetic would also be appropriate allowing students to experience connecting perimeter calculations to shapes using the axioms of number and algebra.

These are only our recommened discussion points, but there may be other areas where you might wish to pause and come together to discuss.

We recommend that everyone opens the training on their own individual laptops/ computers, with the ML facilitating the discussions and pace. There are discussion opportunities throughout this training, these are signposted by the icon in the bottom left corner. Colleagues may want to input their own responses separately, or you may like to summarise your team discussions in the response boxes. We have included timings to help you keep this training to 1 hour.

Running this training as a team...

Throughout this training there are opportunities to submit your thoughts. Mathematics Mastery will be able to see your responses and they will be connected to the name you entered at the start of the training which ensures your anonymitiy if that is your preference. It is not currently possible for you to download your responses but you could take screenshots as a reminder should you wish. Your responses will be invaluable in informing the future development of the programme.

These set out the overarching objectives for the whole week of lessons

• use scaffolds (visual, verbal, and written) that support pupils to access the learning?
• use scaffolding in a way that reduces pupils’ reliance on adult support, lessening scaffolds over time?
• provide scaffolds in a non-stigmatising way (i.e. providing them for a small group or pair, rather than only for 1 pupil)?

3. Scaffolding

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Key Words

Having key words written on the slide can help minimise cognitive load, but also prompt student discussion in the right direction.

Adapting the Question

Think about breaking the question down into smaller chunks. You may want to scaffold the question to make it more accessible.

Plenary

Students continue to demonstrate their undersanding of what they are able to do within this task and what they have understood about perimeter. This lovely task gives students an opportunity to develop their language in reasoning as they explain why Xavier is correct.

See section 4: https://www.gov.uk/government/publications/national-curriculum-in-england-framework-for-key-stages-1-to-4/the-national-curriculum-in-england-framework-for-key-stages-1-to-4

High Expectations

The National Curriculum Inclusion Statement states that teachers should set high expectations for every pupil, whatever their prior attainment.

achievement gap: The impact of between-class attainment grouping on pupil attainment and educational equity over time https://bera-journals.onlinelibrary.wiley.com/doi/10.1002/berj.3838

Althought the term 'ability grouping' is frequently applied in the United Kingdom, in their report on The Achievement Gap, Hodgen et al say: 'We avoid this terminology, which suggests a perception of ‘ability’ as fixed. We refer instead to ‘attainment grouping’.'

Ability is not fixed

• work with several different pupils, forming temporary groups when several pupils have the same current difficulty?
• promote peer tutoring, facilitating pupils learning from one another?

4. Flexible Grouping

Start of Unit Quiz

The start of unit quiz can identify some key prior knowledge that students will need when accessing this unit. If you think students might need additional support with some of the aspects of this unit, ask your Mastery Lead to refer to the PL4 training module on Interventions.

Develop Learning

In this Low Threshold, High Ceiling purposeful practice, all students can practise calculating the perimeter of different compound shapes and some students can continue to practise and experience the axioms within their calculations. This task also lends itself to Mathematical Thinking as some students start to conjecture as to how they may make the longest and shortest perimeters.

Questioning Prompts

Planning your own questioning prompts will ensure that you are working with the Learning Objectives in mind. You will be able to guide students to the desired outcome of the task. You may want to include prompts that scaffold, such as 'What do you already know about the side lengths of squares?' and ones that challenge, 'Can you find multiple calculationsto work out the perimeter? '