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Since 2014, The NCETM and Maths Hubs have been working together to develop approaches to teaching for mastery within primary mathematics. This has been partly informed by the teaching of mathematics in high performing South East Asian jurisdictions. In 2015, the NCETM and Maths Hubs recruited 140 teachers (4 per Maths Hub) to participate in a Mastery Specialists development programme. During this academic year, the teachers have been developing teaching for mastery approaches in their own school as well as working with interested schools through pilot Teacher Research Groups (TRG).

 

classroom 1Teaching for Mastery Work Groups

In 2016-17, all Maths Hubs will be running 4 primary mathematics Teaching for Mastery Work Groups. Each Work Group will be led by one of the current Maths Hub’s Mastery Specialists and involve six primary schools. During the year, they will work closely together to introduce and develop approaches to teaching for mastery.

We are now seeking to recruit 24 schools across the Surrey Plus Maths Hub region to participate in this important project.

This project is an exciting opportunity to develop Teaching for Mastery in your school and as such, the teachers involved will require a minimum of 10 days (per pair) release time.

There is no charge for participating in this work group, and a generous grant of £1000 will be given to each participating school to help subsidise teacher release time.

What is involved?

The Work Group activity will include:

  • Each school identifying two teachers to lead developments within their school.
  • The two teachers working together with the Mastery Specialist and teachers from the other Work Group schools in half-termly TRG meetings and through an online community.
  • Each school receiving a termly support visit from the Mastery Specialist to observe teaching, support in-school TRGs, and work with the lead teachers and head teacher.
  • The head teacher working with the Maths Hub’s leadership and other Work Group school head teachers to develop whole school policies and structures to support teaching for mastery.
  • The lead teachers, supported by the head teacher, working with colleagues to develop teaching for mastery approaches in the classroom, supported by professional development activity including Teacher Research Group methods.

Commitment of the School

Schools chosen to participate in the Work Group commit to the following expectations:

  • The lead teachers will participate in the half-termly, cross-school Work Group meetings with the Mastery Specialist (half-days) and contribute to the online community.
  • The lead teachers will receive a minimum of 10 (combined) days release time for development work including the above meetings.
  • The head teacher will meet with the Mastery Specialist and the Maths Hub’s leadership as well as working with the other Work Group school head teachers.
  • The school will seek to introduce teaching for mastery approaches across the school and establish TRG professional development models to support teacher development.
  • The school will provide any reports required by the Maths Hub and participate in any evaluation processes required.

Commitment of the Two Teachersclassroom 3

  • Be able to attend 6 separate half-day TRGs, once per half term.
  • Be full-time (or nearly full-time) class teachers.
  • Have strong and secure subject and pedagogical knowledge.
  • Have good experience of teaching Primary Mathematics.
  • Be prepared to change their pedagogy and practice based on lessons learnt.
  • Be enthusiastic and motivated.
  • Have some experience of leading CPD within their school.
  • Be willing to work collaboratively with colleagues from other schools.
  • Be prepared to disseminate ideas and strategies to colleagues at their school.

Benefits for your school and staff

Participating in the Work Group will provide the following benefits:

  • Teachers will gain a stronger understanding of the principals of Teaching for Mastery.
  • High quality support for teacher professional development for the lead teachers, facilitated by the Mastery Specialists.
  • Support for the head teacher in addressing leadership issues related to teaching for mastery from the Mastery Specialist and the Maths Hub’s leadership.
  • Opportunity to work closely with other teachers and schools also develop- ing Teaching for Mastery.
  • No charge for participation and a grant of £1000 to help subsidise teacher release time.

Who can apply?

The Work Groups are intended for schools that are already committed to using Teaching for Mastery approaches for primary mathematics. Schools should also have the capacity for engaging in significant development work during 2016-17.

Schools that have already begun to engage with teaching for mastery are more likely to be prioritised by the Maths Hub.

Next Steps? How to get involved

Schools interested in applying to be part of a Work Group in 2016-17 should complete the application form attached and submit to your Maths Hub by Wednesday 8th June.

The Maths Hub will then make contact with you with more details about the selection process.

 

You can download this information here – Full details TRG Schools 2016-17

You can download the application form here – Teaching for Mastery Work Group Application 2016-17

TC 2

Depth NOT acceleration

TC 1The old national curriculum, measured in terms of levels, encouraged undue pace. Children were accelerated onto more complex concepts before really mastering earlier ones. Imagine the cubes to the left represent the building blocks of maths. As you move on swiftly from one topic to the next the tower gets taller and taller, until eventually it comes crashing down. By moving on before a child is ready, before they fully understand the concept, you are helping them build a tall tower, which at some point will become unstable.

TC 2

The new national curriculum encourages the study of fewer skills in greater depth in order to achieve mastery. By taking the same cubes and arranging them differently, the tower remains standing.

So by ensuring that the foundations are solid before moving on, children develop a more stable platform from which to build.

 

Curriculum: Sprial vs Linear

Many primary schools are still following a spiral curriculum where topics get revisited each term. The nature of this is that you have to move on quite quickly from one topic to the next, often spending only one week on something and not really having time to ensure that the children have properly and deeply undersood the concepts being taught. This suited the old national curriculum as it was content heavy and didn’t require any depth of understanding.

An alternative to this approach is following a linear curriculum in which topics are blocked together and covered only once in the year. Doing so allows more time for children to gain a deeper understanding of the key topics as there is less pressure to move on before they are ready. Evidence shows that children who have a deeper understanding of number and an enhanced ability to reason mathematically can progress through other topics more quickly.

TC 3

This is an example of how a linear curriculum might be structured. Note the emphasis that is placed on number in the first two terms. It is important to note that just because the curriculum is linear, it does not mean that the skills learnt in one block are not revisited again throughout the year as research clearly shows that interleaving ideas and revisting them aids long term retention. For example in the scheme above, during the geometry in the spring term you might look at perimeter and in doing so revisit addition and subtraction.

It is important at this stage in the year that schools consider whether the scheme they are following really provides their children with the most solid foundations.

There are many schemes availble on the market to suppot teaching for mastery (two of which we review in Textbooks: Compare and contrast). In addition to these, there is a FREE scheme that has been created by the White Rose Maths Hub, which provides an excellent starting point for any primary school wishing to adopt a new approach. We are currently working with the White Rose Maths Hub to further enhance these resources, details of what we are adding and expected timelines can be found here.

Depth is achieved through variation

There are three elements that are critical on the journey towards mastery in maths and that we need to develop in our children. Fluency, reasoning and problem solving. Without one, the next cannot follow and it is only by developing these three skills that children can move towards mastery.

TC 7

This flow of learning was first seen in Shanghai by the teachers who went on the exchange trip. Children must first gain fluency in whatever topic they are studying before they move on to reason mathematically and then begin to solve a variety of different problems which probe and challenge their depth of understanding.

Here’s a few examples to help illustrate how this development might look.

Example 1:

Fluency:

TC 8

Reasoning:

TC 9

Problem Solving:

TC 10

Example 2:

Fluency:

TC 4

Reasoning:

TC 6

Problem Solving:

TC 5

Can you see how each task builds on the previous one? The skills required are the same but the depth of understanding required is very different. When these activities are put in the context of whole-class, mixed-ability teaching where the aim is for all children to develop the skills of fluency, reasoning and problem solving at the same time, the slow progression through these three elements is even more critical. More will be written on this blog shortly regarding whole-class, mixed-ability teaching and how it can and does work.

Intelligent Practice

Variation is a phrase which has been banded about all too often since the first teachers returned from the Shanghai exchange visit. It think it has taken us a very long time to fully appreciate what is meany by variation…

Variation is NOT:

  • more of the same thing but a bit harder.
  • the same as variety!

When using intelligent practice, all tasks are selected and sequenced carefully with purpose, offering appropriate variation so that when viewed together they reveal something about the underlying mathematical structure, concept or process. Put simply, variation reveals concepts.

Variation is an approach to teaching. It is the art of sequencing similar but increasingly complex problems to “generate disturbance of some sort for the learner” Festinger (1957)

Consider the following example:

23 + 10 = [   ]

23 + 11 = [   ]

23 + 12 = [   ]

 

23 + 9 = [   ]

23 + 8 = [   ]

23 + 7 = [   ]

By changing just one small element at a time children are given the chance to develop their understanding of a concept rather than just learning a process to get the right answers. However, it is not as simple as just finding patterns. Care must be taken to ensure the structural concept is understood; not just a superficial procedure found, as it is this deep conceptual understanding that leads to mastery.

If you just rearrange the questions a little you can quickly see how big a difference the order the questions are in can make to the development of a child’s understanding.

23 + 9 = [   ]

23 + 12 = [   ]

10 + 23 = [   ]

23 + 7 = [   ]

23 + 11 = [   ]

8 + 23 = [   ]

It is this intelligent practice, the appropriate selection and sequencing of questions, that can make a fundamental difference to a child’s conceptual understanding.

Conceptual understanding leads to mastery

It is critical that children are taught maths in a way the develops a deep conceptual understanding as this is the only way of securing solid foundations. One way in which we can help children to do this is by using the concrete-pictorial-abstract (CPA) approach. This is based on research by psychologist Jerome Bruner, which suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

CPAConcrete

In this stage a student is first introduced to an idea or a skill by acting it out with real objects. In division, for example, this might be done by separating balls into groups of red ones and green ones or by sharing 10 biscuits among 5 children. This is a ‘hands on’ component using real objects and it is the foundation for conceptual understanding.

Pictorial

In this stage a student has sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. In the case of a division exercise this could be the action of circling objects.

Abstract

In this symbolic stage a student is now capable of representing problems by using mathematical notation, for example: 10 ÷ 2 = 5 Students only use abstract numbers and figures when they have enough context to understand what they mean This is the ‘final’ and most challenging of the three stages.

Example:

The following example demonstrates the principles of CPA. It starts with a pictorial representation of the problem using a clear diagram (the use of counters is important for any child still at the concrete stage), but it then builds the abstract alongside, so that the child can make that leap between the pictorial and the abstract as and when they are comfortable in doing so.

TC 11

Example:

In this second example the concrete is used as a starting point for the question. Two oranges are divided up into quarters, three of them are circled from each which leaves six quarters which are then put back together to make one and a half oranges. The pictorial stage sees the introduction of circles instead of oranges and then the final stage is the introduction of the abstract, the numerical calculation. By putting all three alongside each other students can see the progression and when they are ready, they will naturally make the transition from concrete to pictorial to abstract.

TC 12

In Summary…

  1. Teach fewer concepts in greater depth
  2. Intelligent practice gives children a rich appreciation of the concepts through variation
  3. If you help children unlock this depth of learning then, over time, whole class, mixed ability teaching will become even more successful.

 

Many of the ideas in this post have been adapted from ideas seen in Tom Collin’s session at the spring conference. Click here to download the powerpoint Session 1 – Teaching for Mastery

Textbooks 2

This project is being conducted by Goldsworth Park Primary, Cranborne Primary and Uplands Primary.

Background

Cranborne and Uplands

  • Started using the OUP Inspire Maths books with year 1 in Jan 2015 as part of the Maths Hub national project
  • Staffing changes/issues as well as some challenges associated with a mid-year start meant that it wasn’t adopted overly successfully last year, however both schools have been using it in year 1 since September.

Goldsworth Park

  • Opted to use the Maths No Problem with year 1 as part of the second phased of the Maths Hub national project

We are fortunate to be trialling both textbooks in the region and are therefore in a unique position to comment on both.

You can read the individual summaies of the two textbooks here:

Maths No Problem

OUP Inspire Maths

 

Compare and contrast

  • Both use a Singapore approach, however Maths No Problem! covers everything in the NC whereas Inspire doesn’t.
  • Inspire’s package included assessment materials and a teacher guide. Maths No Problem! has no teacher guide so more thinking is required of staff.
  • Inspire teacher book is overloaded whereas Maths No Problem! lessons only go over 2-3 pages.
  • The lesson approach is different: Maths No Problem! have an exploration task to start every lesson where Inspire follows a more traditional approach using teacher input.
  • Both have good variation within the tasks and the questions.
  • Thought needs to be put into the children with barriers to Maths for both schemes.
  • Inspire does challenge the fast graspers through acceleration. Thought needs to be put into challenge activities for more able in Maths No Problem! but it sticks within the end of year expectations.
  • Students love both schemes.
  • Inspire assessment materials are not great – sometimes not linked to what they been doing. Maths No Problem! assessments are in a similar format to the textbooks and follow them directly
  • Training experiences were mixed with Inspire – some key aspects of the programme were held back. Maths No Problem! training was excellent.

 

 

 

Textbooks 6

This project is being carried out by Cranborne Primary and Uplands.

Background

  • The books is based on the Singapore approach ‘My Pals are Here!’.
  • Used by over 80% of primary schools in Singapore.
  • Highly scaffolded learning framework with problem solving at the core.
  • Concrete-Pictorial-Abstract (CPA) methods are throughout.

What does it consist of?

  • 2 Teacher guidesTextbooks 6
  • 4 Student practice books (A, B, C, D)
  • 2 Textbooks (A, B)
  • Assessment book
  • Online support

 

Links to the UK curriculum

  • Based on the Singapore curriculum and so does not directly match the UK NC.
  • A correlation chart is available to map missing objectives, however this can cause difficulties with both resourcing and standardised testing.
  • Aspirational program as Year 1 covers both Year 1 and some Year 2 NC objectives.

Ease of use for teachers?

  • 5 days of teacher training provided as part of the program are essential.
  • Teachers planning guides are easy to follow but trying to fit each ‘session’ into a typical 1 hour lesson is challenging.
  • Resources are provided, saving lots of time!
  • Good variety of activities in books.
  • It is tricky to map the objectives to the UK curriculum and it definitely requires professional judgement and experience as well as flexibility in approach.

Ease of use for pupils?

  • Children need to be trained to use the books, including switching between textbooks and practise books (this is possible!)
  • Children love the books; they are bright and the layout is clear
  • Challenging for less able readers – particularly at the start of the year
  • Large volume of written work means that sometimes the less able do not reach the investigative activities (4 pages per lesson) which means they aren’t all learning the same thing.

Is there sufficient challenge?

  • Good for more able children who quickly grasp concepts due to the CPA activities.
  • Fast graspers have up to 4 pages of activities to complete per lesson, but sometimes need additional challenge.
  • Lower attainers need to be supported, particularly for reading the tasks.
  • Need to build in lesson time for lower attainers to access the high expectations.

Classroom practice

  • Strong focus on verbalising thinking into full sentences and giving clear explanations has had a hugely positive impact on the children’s learning.
  • Children need to be provided with a range of resources that can be accessed throughout the lesson which has led to greater independence.

Assessment

  • The assessment book included contained multiple choice questions which the younger children struggled with.
  • The format is very different from any other part of the program and doesn’t always link to the textbooks.
  • After the first assessment, we decided to discontinue using these.

Are we going to continue?

  • Yes – we have bought into the scheme for Year 1 again next year, but not yet rolling out across the whole school.
  • Would tweak a few aspects- timings, practice books, move some to Reception.
  • Cost is a barrier that we need to try and overcome if we are going to move it into Year 2 and beyond.

 

 

Textbooks 1

This is being trialled in Goldsworth Park school with year 1.

What does the programme consist of?

  • Two textbooks per year group which cover the English National Curriculum.
  • There are two workbooks which align with the textbooks.
  • Online element with training videos and parent support videos.

How are lessons compiled?

The ‘In Focus’ section is always a very open task that leads them to explore ideas and start to think about what they already know and how it can be used (it very much links in with the idea of letting the kite fly and then reeling it in!)

Textbooks 1

The ‘Let’s Learn’ section focuses on the key mothods.

Textbooks 2

There is then a ‘Guided Practice’ question and a ‘Mind Workout’ which are designed to be some variation activities.

 

Why are the lessons compiled like this?

During the training course we received insight into the research and thinking of 5 people… The Maths No Problem series is underpinned by their theories:

  • Jean Piaget – ample processing time (exploration)
  • Zoltan Dienes – ideas looked at informally before formal teaching
  • Lev Vygotsky – cooperative learning
  • Richard Skemp – relational understanding (links and relationships between concepts) not just instrumental (learning rules or by rote)
  • Jerome Bruner – CPA approach

 

Training

We were fortunate enough to go on a 6 day training course provided as part of this research project. This was highly valuable training and gave us the opportunity to talk to other teachers across the country doing the same.

If you buy into Maths No Problem you can buy training blocks from them depending on your needs.

 

Examples

Below are some examples of the work being produced by our children.

Textbooks 3Textbooks 4

Textbooks 5

 

Positives

  • Amazing methodology; children’s understanding is at a much higher level than in previous years.
  • The lessons are planned carefully in small steps allowing most children to keep up.
  • The textbooks have great visual representations which the children find easy to use.
  • The variation of tasks lead to a certain level of differentiation.
  • Online resource is useful for planning and the training videos are great.
  • Access to parent videos which can be placed on your website.
  • Training was excellent with Professor Yeap Ban Har.

Negatives

  • Expensive!
  • Still need to differentiate for the more able, especially at the start of the year, so suitable depth was being reached.
  • Textbooks mean that levels of literacy can hold children back.
  • Workbooks need to be bought to purchase the scheme and we have not been able to build them into the work we’ve done.
  • Planning can take a little more time when splitting the lessons up – needs professional dialogue, but this is actually a huge positive too!
  • You still need to provide for the children that have barriers to their learning as you would with any scheme.

 

Next steps

  • YES!
  • We think it is having massive impact and we have found a way of making it work costs wise.
  • CPD of staff will be highly important in this and we will only be introducing it one year group at a time.

 

Things to consider

  • If you can’t afford to buy into the whole scheme then it is worthwhile purchasing a copy for each teacher just to help them see the progression and get ideas from the ‘In Focus’ sections.

 

classroom 1

Back in February I was heard Jane Jones @JaneJonesHMI speak at the Maths Hub Forum… Ofsted’s response to ‘teaching for mastery’ is something that many of our schools were interested to hear.  Here are a few of the key messages:

First a bit of background.

Ofsted expect…

… teachers to use their subject and pedagogical expertise to provide high quality teaching and curricular experiences in order to secure the best possible learning and outcomes for their pupils (taken directly from the Sept 2015 handbook).

The NC: A Mastery Curriculum

  • An expectation that all pupils can and will achieve.
  • The large majority of pupils progress through the curriculum content at the same pace. Differentiation emphasises deep knowledge and individual support/intervention.
  • Teaching is underpinned by methodical curriculum design, with units of work that focus in depth on key topics. Lessons and resources are crafted carefully to foster deep conceptual and procedural knowledge.
  • Practice and consolidation play a central role. Well-designed variation builds fluency and understanding of underlying mathematical concepts in tandem.
  • Teachers use precise questioning to check conceptual and procedural knowledge. They assess in lessons to identify who requires intervention so that all pupils keep up.
  • A mastery curriculum often involves whole-class teaching, with all pupils being taught the same concepts at the same time. Small-group work typically involves challenge through greater depth for the ‘rapid graspers’ and support with grasping concepts and methods for pupils who have more difficulty.
  • ‘Intelligent practice’ through tasks and exercises usually concentrates on the same topic/method/concept but varies in how the questions are presented, often in ways that expose the underlying concept or mathematical structure, and makes pupils think deeply for themselves.

Taken directly from the NCETM Developing Mastery in Mathematics Document Oct 2014 which can be found here

There is a lot of further information developing mastery on the NCETM website here

What do you think inspectors expect to see in relation to mathematics teaching?

… would it be different where schools are teaching for mastery?

Below is a snipped from the framework on ‘Inspecting the Impact of the teaching of mathematics’ which can be downloaded here

ofsted 1

Something that Jane Jones asked us back in February was “Are there any of the points in conflict with teaching for mastery?” and the answer is simply no! This was a very positive message from Jane Jones and one that the Maths Hub Leads were very pleased to hear.

“It’s brilliant that acceleration in maths is out and depth is in!”

Opportunties

We need to start seeing the changes to the national curriculum as a positive and start to embrace the opportunities that it affords us. The new National Curriculum:

  • captures, in its aims, the best mathematical education for all pupils;
  • represents greater ambition for all pupils, especially the lower attainers;
  • emphasises depth over acceleration;
  • gives us the chance to think afresh about progression, the wider aims and conceptual links;
  • provides a context for teachers and schools to learn from each other and together.

 

Challenges

“Acknowledge the challenges then set about overcoming them.”

The following challenges were highlighted to us in February by Jane Jones. I believe these were the result of the 2014-15 primary subject survey that was carried out by Ofsted. It’s positive that Ofsted are aware of the challenges faced by school leadership teams and teachers.

  • Teachers’ subject expertise:
    • ‘new’ mathematics content
    • the NC aims: how to teach reasoning, problem solving for all/the ‘rapid graspers’; the meaning of fluency
  • Expectations and progression:
    • gaps between where pupils are now and the programme of study they are learning/due to learn
    • higher demand, especially for lower attainers and SEN
    • differentiation; challenge for the ‘rapid graspers’
  • Teachers’ worries about demonstrating pupils’ progress:
    • in lessons
    • for performance management/inspection
  • Assessment without NC levels, and the quality of national assessments
  • Transition between: schools, key stages, one year to the next, one lesson to the next, one mathematical idea to the next, …
  • Capacity:
    • recruitment and retention of suitably qualified staff and subject leaders
    • availability of local/in-school expert help

 

 

Differentiation

“In the past differentiation was often achieved by a teacher preparing different activities or worksheets for different groups of pupils. Now there are other ways, consistent with the new curriculum and a mastery approach, of catering for different attainment levels within a classroom.”

Critically the message that was given to us is that Ofsted want to see challenge through depth and support through intervention.

It’s no longer about five different groups in the class all learning and doing different things based on their ability… There is huge scope for saving time here and by saving time, teachers can spend time planning great lessons!

 

Marking

”We need to get workload in proportion. Teachers are spending time marking when they should be planning quality lessons.”

This was a revalation to many at the forum back in February! Jane told us a story about her daughter or niece(?) either way the crux of it was – it’s such a waste of time highlighting childrens work in rainbow colours, you marking in red, expecting them to respond in green etc. TEACHERS SHOULD BE PLANNING GREAT LESSONS NOT WASTING TIME MARKING!! That said, she highlighted to us what it says in the Ofsted handbook…

Ofsted recognises that marking and feedback to pupils, both written and oral, are important aspects of assessment. However, Ofsted does not expect to see any specific frequency, type or volume of marking and feedback; these are for the school to decide through its assessment policy. Marking and feedback should be consistent with that policy, which may cater for different subjects and different age groups of pupils in different ways, in order to be effective and efficient in promoting learning.

In other words, if the school policy says ‘highlight in rainbow colours’ and ‘children respond to a learning question in green’ then Ofsted must check that is what the teachers and students are doing.

The NCETM have just published some useful guidance on marking in maths which can be downloaded here NCETM Primary Marking Guidance April 2016

So… maybe it’s time schools reviewed their marking policies!! There’s only so much time in the day, and it’s important that the precious time teachers do have is spent doing what is going to make the biggest difference to their students.

This was the final quote from Jane Jones at the forum back in February – so true!!

”If it’s not useful, don’t do it… definitely don’t do it for Ofsted!”

Click here to download the powerpoint from the spring conference Session 1 – AD Ofsted

classroom 3

This project was conducted by The Dawnay Primary School (Kayleigh Hewitt-Lee) and St Thomas of Canterbury Primary School (Mary Petley).

Scope of the project

  • Students will be sat in mixed ability groups to assess the impact of more confident students being able to support those less confident (thus prevent a gap from opening).
  • Students will also be sat in rows in order to ensure their focus throughout the lesson is on the teacher at the front of the classroom.
  • The research project will be trialed with at least 1 class for a minimum of 1 term.
  • A case study produced to reflect on the project with specific examples and evidence (and research where possible).

 

Background

St Thomas of Canterbury

  • Initially undertaken in a Year 6 class and two year 5 classes for the first term.
  • Extended to include two Year 4 classes and a Year 2 class for a second term.
  • Prior to the start of the project St. Thomas’ was not using setting for maths but there was ability grouping within some classes.

The Dawnay

  • Initially involved four classes in this project. These classes are: Year 1, a Lower Junior class (mixed Year 3 and 4) and two Year 6 classes
  • Prior to the start of the project The Dawnay were setting for maths in KS2 but not in KS1.

 

Monitoring Impact

The effects of this project have been monitored through drop in visits, lesson observations, work sampling and pupil and staff surveys.

Unfortunately, due to the removal of levels and the requirements of the new NC it has been difficult to compare the outcomes of mixed ability teaching with stream maths lessons, this is because we do not have a cohort to compare them with. We also felt that it was difficult to compare the results of St Thomas and The Dawnay as the two schools have different catchment areas and therefore a different entry point for pupils.

 

What we found

Within the year 1 classroom the children are used to being taught in mixed ability groups. The teacher immediately found that whole class teaching suited the children in her class as they enjoy working together and helping one another. During an observation it was noted that the mixed ability teaching was helping to bridge the gap between the more able and the least able children in the class.

classroom 4Throughout the project the children within the year one classroom were very positive about their learning experience within mathematics. During one of the student surveys one of the children noted that it was fun to work together. Another children who found maths more difficult said that working with other people was helpful as they had two brains to use.

The Lower Junior teacher who participated in the project was in favour of the approach in September however at the start of the term he found it a challenge to teach the children in a mixed ability layout as the spread of ability was extreme. He felt that the core and less able pupils were supported well within his lessons but the more able children were not being extended, especially in relation to the new NC requirements.

classroom 3In addition to this some of the children within the lower junior classes found the change from streamed maths to mixed ability maths a challenge. The more able children, in particular, perceived that their learning was not being challenged and some found that the learning was repetitive. During our first student survey some of the more able children in this class they also make comments that reflected the same feelings of the teacher. One of the comments for a child stated that she could do the maths being taught and although she didn’t always get every answer correct she didn’t feel it was challenging. As the project has advanced the children are now more positive about their experience of mixed ability maths lessons and feel that their activities are now set at a challenging level. The Dawnay have found that assessment materials from NCETM have provided them with activities to deepen the children’s learning, in particular the more able, and as a result more children are accessing mastery level in mathematics. During our last student survey we took the same 8 more able pupils that we took in our first survey. Six out of eight children said that they now enjoyed their mathematics lessons. Two of the children said that they enjoyed sitting with other people. A different child said that they liked the challenge cards (NCETM Mastery Assessment Material) they were given as it meant that he had to think about the problem differently.

As the project progressed the teacher found that the mixed ability teaching has given him more flexibility with his class and more time is able to be focused towards the teaching of mathematics as children can be ‘drip fed’ their learning throughout the day. The teaching of mixed ability maths has developed the children’s collaboration skills and they are able to work together with their learning. This has particularly helped the children with their reasoning skills.

The project also ran in two upper junior classes at The Dawnay. Within one of the Upper Junior classes the teacher found the classroom layout a barrier to the children’s learning as the classroom’s space was limited. She found it difficult to set up and deliver her lessons using this model due to the lack of space. The teacher tried many different classroom layouts and found that the seating needed to be adapted. Pupil discussions show that the children very positive about mixed ability seating and observations show that there was an increase in pupil support and engagement within lessons. Now the teacher knows the children better, she feels that if she were to reintroduce the rows, it would be more successful and this is something that will be tried this term.

In the year 5 classes at St. Thomas’ the children were used to working in table groups, but now the majority prefer sitting in rows as they recognize it makes it easier to both see and hear the teacher. This was also supported by the class teachers and through observations. The children were very comfortable discussing their work in mixed ability pairs and saw asking a learning partner as an alternative step to waiting for a teacher to help when they are stuck on a question. Although the children did not recognize it, this method of working benefitted both learners. While supporting a less able child, the more able was using and developing their mathematical language and their ability to explain how to problem solve. In areas of Maths, such as ‘Time’, different children can struggle or excel; the mixed ability teaching has made it easier to match the level of challenge for each child in the different areas.

In the year 6 class at St. Thomas’ the teacher tried out several classroom layouts. She found the main benefit of being in rows facing the board was that the pupils were more focussed and involved in discussing problems and ways of solving them. However, the difference of ability within her class was very wide and this kind of layout did not make best use of adult support within her class. She adapted the design so it could include a small cluster of tables to be used for a focus group for the least able children when a teaching assistant was available. This is what she feels works best with her class and she is keen to take it forwards. Pupils are confident about mixed ability teaching and choosing the correct level of challenge for themselves.

 

Key Advantages

classroom 1

We have seen significant improvements in:

  • Behaviour
  • Concentration
  • Noise level
  • Independent work
  • Confidence in discussing learning, using mathematical vocabulary

There have also been some improvement in:

  • Contribution to discussion, especially from the less able.
  • Learning partner work

 

Key Challenges

We have encountered some challenges with:

  • Space
  • Furniture
  • Manipulatives
  • Teacher organisation

 

Pupil Voice

All children in Years 2, 4, 5 and 6 were asked to complete a survey at the end of the Easter term, including the classes that were still sitting in groups.

84% of children at St Thomas of Canterbury and 92% at The Dawnay felt that facing the board helped them follow the lesson better.

Here’s the results of some further questions:

classroom 10 - pupil voice

classroom 11 - pupil voice

 

Teacher Voice

classroom 7 - staff voiceclassroom 8 - staff voiceclassroom 9 - pupil voice

 

Next Steps

The Dawnay:

classroom 5 classroom 6

After a successful first time that has seen positive responses from pupils and staff The Dawnay will be continuing with mixed ability teaching for mathematics. The staff at The Dawnay have enjoyed participating in the project and feel that the mixed ability teaching benefits the ethos and learning environment of the school. Through the research the school has found out that the schools in Shanghai have a much different learning environment to their school in terms of displays. As their next steps the school is interested in finding out whether the displays in the classrooms affect the learning of the children.

 

St Thomas of Canterbury:

After the positive response seen in the top two years at St. Thomas’ we would like to develop this project further by introducing it to classes in the Lower Juniors and KS1. We feel we need more time to share our findings and compare the effectiveness of this teaching style at different stages of learning.

Display was mentioned by several children as something you can use to help you when you don’t understand. It would be useful to find out more about which displays, if any, are best at supporting Mathematics.

 

Click here to download the powerpoint from the spring conference Session 2 – classroom design

This project was undertaken by Thorpe Church of England Primary School and led by Mandy Ambridge.

Scope of project

  • Adopting a two part lesson approach, teachers will begin with an input phase (35 minutes) followed by a more independent practice phase (25 minutes). During the input phase, teachers will be able to identify students who may need extra support and those who are comfortable with the content. The practice phase can then be used to allow those who are comfortable to consolidate their learning. Intervention would be provided for those less confident students to enable them to reach the required level.
  • The research project will be trialled with at least 1 class for a minimum of 1 term.
  • A short evaluation will be completed at least twice (once per half term) during the course of the project; an evaluation template will be provided by SJB.
  • A case study produced to reflect on the project with specific examples and evidence (and research where possible).
  • Showcase the results of the research project at the next primary conference (Spring 2016)
  • Share the results of the project and work collaboratively to implement in at least 4 other schools.

 

Background

Thorpe Church of England Primary School is a growing Primary school with 165 on role at present from 4 to 10 years (EYFS to year 5). It is a one form entry school growing by one year group yearly until September 2016.

The project was initially to take place in year 3, 4 and 5 but due to staffing and the needs of the children it was implemented in year 5 consistently with year 3 and 4 dipping in when possible.

 

Research completed

Previous experience of intervention in our school has been it is most effective when it is short term and is targeted and measurable ie First class @ Number

Alice Hansen in ‘Children errors in Mathematics’ (2013) says:

‘Misconceptions are a natural part of a child’s conceptual development and consequently greater time in mathematical lessons should be given to encourage children to make connections between aspects of mathematical learning and their own meanings’

The Williams review (2008) quotes research from Every child counts development group ‘ Intervention was more successful when carried out by a qualified teacher with secure mathematics who assessed the child’s learning needs accurately and used resources and activities flexibly’

The Williams review (2008) suggests that the ‘Essential characteristics of intervention’ include:

  • Assessment – accurate identify children who need intervention
  • Timing – once the weakness is identified it must be addressed before the child’s long term confidence is eroded. (this refers to addressing the issue in KS 1 but can be linked to early intervention)
  • Teacher led intervention
  • Need for Coherence between intervention strategy and whole class activities

 

Data collection

Prior to and after project – Rising Stars Number and Place Value assessment

After project – pupil attitudinal survey, pupil interviews, teacher and teaching assistant interviews.

 

Resources Developed

Planning sheet to reflect needs of lesson structure. Also include possible misconceptions.

Collection of ‘going deeper’ challenges.

Daily assessment sheet.

 

 

Implementing the same day intervention

 

First half Autumn Term 2015 (September 2015)

In September we had daily maths lessons from 9.00 till 9.45 followed by time to mark and review whilst the children worked on SPAG with a TA. Then we had a second session from 10.05 till 10.25 when we provided deeper tasks for the TA to complete with the majority of the class whilst we intervened with those who had not achieved the learning objective to address their misconceptions.

Issues and Barriers

  • Timings – With new complex content it took time to do the whole class input and therefore there was little time to practice and decide who was on track.
  • ‘Marking time’ – is often rushed for teacher and difficult to resource valuable activity for the class to complete. TA delivers SPAG in this time currently not sure this is effective.
  • Consolidation activities –need a bank of resources!
  • TA has to explain the consolidation task– needs to be quick to explain TA needs to understand the task!? (TA in year 5 currently doing Maths Hub training)
  • What mark and when? – assume from first session who got it then double check those not sure of and decide who in which group for follow up?

 

Second half Autumn Term 2015 (October 2015)

In October 2015 we changed our timetable to suit the needs of the case study and the children. We had a Maths session 9 till 10 every morning, at around 9.50 we peer or self mark and the children also self assess using red/amber or green. They place their Maths books or work in 3 boxes as well red/amber/green to reflect how they feel about their progress that day. During the rest of the morning and lunchtime we look at the books and how the children feel and decide which group best suits their needs for the second session. We have a second maths session from 1 till 1.30 in the afternoon during which the teacher introduces the task for the Green and Amber group and then works with the Red group.

Issues and Barriers

  • Format change – this addressed many of the issues from September.
  • Time – longer spent on Maths now impact on other subjects but easier to input maths content.
  • Time to mark and assess work –still ongoing issue.
  • TA on sick leave- no TA for either of the Maths sessions to support learning.
  • Building up ideas for easy to explain but valuable ‘ going deeper’ tasks

 

Impact so far

  • One term is too short and one class too limited to have any real definitive proof of impact, however it is useful to be able to identify and target immediately those children who are struggling to understand concepts introduced. Also when questioned, all the children in the class had a positive attitude towards maths and the same day interventions.

“If I don’t get it in the morning I get it in the afternoon”

“I like doing it on the same day, it helps me understand more than I did.”

“I like doing it twice you can sort out your mistakes.”

  • Intervention is very targeted as works on the concepts introduced that day unlike other interventions ie snap and first class which follow their own programs. Resulting in improved understanding.
  • Children are also becoming more capable at self- assessment using the coloured boxes and taking ownership of their own learning.
  • Class generally very supportive of each other in terms of making mistakes and learning from each other-no stigma attached to putting work into the red box- fluid as to who puts their book in there.
  • High quality intervention as delivered by a teacher. This teacher has also marked the work so fully understands the nature of the errors and misconceptions.

 

Observations/children’s progress

It is difficult to assess the children’s progress over and above what would be normal progress however children were assessed on the Rising Stars diagnostic test on entry and at Christmas and 92% children have made progress. There is no way of knowing at this time whether this would be better or worse without the same day intervention.

Looking at the data and from classroom observations and discussions with the children, same day intervention does seem to suit girls, who on entry to year 5 lacked confidence, as the progress they have made is very good.

Results of pupil attitudinal survey show significant improvement in how children feel about maths.

  • 13% more children consider themselves good at maths and 23% more consider themselves very good at maths;
  • Half as many children now rate themselves as ‘in the middle/average’ after the first term of SDI.

See below:

 

How would you rate yourself in the class?

 

Very good Good In the Middle Not so good
Before SDI 0% 28% 71.5% 0.5%
After SDI 23% 41% 35.5% 0.5%

 

  • A large increase can be seen in the enjoyment of maths;
  • Significant decrease in children considering maths to be ok.

 

See below:

 

How much do you enjoy maths?

 

I really like it I like it It is ok I do not like it
Before SDI 31.5% 18% 50% 0.5%
After SDI 31.5% 45% 23% 0.5%

 

All the above shows the children have become more resilient, are more motivated within lessons and feel a sense of empowerment through higher ownership of their own learning

 

Considerations for further implementation

A need for more ‘going deeper’ tasks is required to further consolidate the learning of the children who grasp the concepts from first session.

The provision for children who are SEND and are significantly behind ( 2 years or more) needs to be addressed.

Time available to assess and mark work and prepare resources for intervention.

Impact on other subjects due to time allocated to maths.

 

Quotes from children interviews

“I enjoy the challenge of the afternoon activities.” (more able child)

“I am very confident with maths and enjoy the afternoon activities they are fun.”

“I feel more confident this year.”

“Things make more sense than before. The challenge in the afternoon helps me”

“Maths is fun”

“I feel good and confident.”

“Maths is my favourite subject. I understand more now and after lunch makes sure that I understand. It’s good I can improve what I have done.”

“Fresher in my mind than doing it the next day.”

 

Teacher quotes

“It is very satisfying knowing that I am addressing the children’s learning needs immediately.”

“I feel more in control of the children’s learning. From my experience of other interventions they are most successful when they are short term and focussed which SDI definitely is”

“I enjoy working alongside the teacher in the classroom instead of withdrawing children to work with. I feel better placed to help the children progress and can ask the teacher for advice immediately.”

 

Click here to download the powerpoint from the spring conference Session 2 – Intervention

Screen Shot 2016-04-14 at 16.42.26

It’s just over a year since we held the ‘Shanghai Primary Maths Conference’ where we first started to learn about teaching for mastery, Miss Sarah taught two live demonstration lessons and we launched four research projects (same-day intervention, daily homework, classroom design and curriculum planning)…

In that time schools and individual teachers have been hard at work trialling ideas, developing their understanding of ‘teaching for mastery’ and creating resources so it was fantastic for us to have the opportunity today for them to come together and share their experiences and learn from each other.

98 primary Heads, Deputies and Maths Leads from 62 different schools to come together to talk about how we can improve maths teaching – it’s so exciting to see that the work we have been doing of the last 18 months is really having a lasting impression on schools and individuals!

 

Here’s a quick summary of the day with links to posts on all the different sessions that went on.

 

Welcome

Screen Shot 2016-04-14 at 16.42.26This is Emily… She’s 11 months old and every day she surprises me! Every day she comes back from the childminders or Granny’s being able to do something new… She’s like a sponge! Like all children, she observes and soaks up every word, every phrase, every expression…

As a parent, I want the best for best for as all parents do. Yes I want her to happy and healthy, but I also want her to be curious and inquisitive and develop a love of learning. I want her to want to understand things, to want to learn everything and to grow in confidence…

Of course, that starts at home with the family and I know that Emily is very fortunate, but from day one at primary school there is another group of adults that will influence who she becomes… the way she thinks… what she loves… what she hates… what she is confident in doing… and what she struggles with.

I want my daughter and her peers and generations to come to develop vondience in maths and to enjoy solving problems and reasoning – skills that stretch far beyond knowing her times tables and being able to add fractions…

I tried out a new hair dresser over Easter and as we started to chat she ask me, “What do you do?” to which I replied, “Teacher”. She followed on by asking me, “What do you teach?” to which I replied, “Maths”… The response was a look of horror closely followed by “I was never any good at maths!”. Although I haven’t ever kept track of the exact number, I would have to guess that at least 9 times out of 10 that is the response that I get! That makes me sad…

In a recent INSET day we ran for an alliance of primary schools we asked the teachers and teaching assistants to raise their hands if they would be one of those who reacted by saying “I was never any good at maths!”… Over three quarters of them put their hands up… Was I shocked? No. Was I sadened? Yes.

It’s time for that perception, that attitude to change… As a Maths Hub we want to work on changing the mind set of all those teachers so that when Emily and her friends go to school they are met with confident maths teachers who are able to develop her curiosity and her understanding of maths so that in 20 years time when Emily’s peers are asked that same question the response is “I loved maths at school!”

So that’s the journey we’re on… As a Maths Hub, we want to support teachers, particularly primary teachers, in improving the quality of maths teaching because if we get it right from day one in reception and slowly build each year then we will get there, we will change peoples perceptions.

GermanEurosThe German football team crashed out of the Euro 2000 finishing bottom of their group. This gave them the wake up call they needed to stop and reflect on why that was and make some significant changes. They decided that their approach to youth development needed a complete overhaul. They set about learning from the best across the world – The Netherlands football association, the New Zealand All Blacks… All the while considering, what is the difference that makes the difference? They borrowed methods and adapted ideas. They poured all their resources into producing greate players starting at grassroots level. They developed full time specialist youth coaches and began working closely with schools.

By 2014 they were back on top of the world, holding the World Cup.

PISAIn 2000, the UK was ranked 8th in the world for Maths in PISA, by 2009 this had fallen to 28th and then in 2012 we’d clawed back to 26th… I’m not a fan of PISA, it has many flaws, but one thing that you cannot argue with is the fact that we were no longer moving up.

It was time for a change. Maths Hubs were born and one of the first things we did was look to the best in the world, Shanghai and Singapore to see what made the difference for them… But like the German Bundesliga did in 2000, we need to borrow and adapt the best ideas and make them work here in England.

As a Maths Hub that’s what we’ve done. Over the last year schools have been trialling some of these ideas to see how we can make them work for us.

The question that every school leader needs to be asking is…

What CAN we do to ensure our children get the very best Maths education in the world?

 

Session 1

Session 2

Session 3

  • Live demonstration lesson – Year 6 St Joseph’s Primary School & Mr Collins