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1. Teachers have in depth subject knowledge and keep their learning up to date.
2. Teachers use a range of methods for assessment and questioning. Allowing their material to be accessed in various ways by all children.
3. Classroom climate - positive interactions between the teacher and children, safe learning environment provided.
4. Classroom management - teachers ensure they manage their time well through resources and use of extra staff and classroom space.
5. Teacher beliefs - implementing particular rules and boundaries in your classroom, having a high standard for all pupils to adhere to.
6. Professional behaviours - teachers reflect and develop their teaching strategies.

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Teachers in excellent and good schools appeared to set homework that was more meaningful and more directly linked to what the children were learning.

Classrooms in excellent schools were rated exceptionally highly on positive classroom climate.

Children in excellent schools spent the most time overall in collaborative learning situations.

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Emotional Support:
- Create a positive classroom environment based on respect, providing children with the opportunity to enjoy and be enthusiastic about learning.
- Teachers need to be aware and sensitive towards individual children's needs.
- An ability to understand and be aware of children's perspectives is key, for example having a respect for students autonomy, interests and motivations.
Classroom Organisation:
- Effectively manege students behaviour with clear rules that are consistently and appropriately enforced.
- Successful time management to provide opportunities for children to maximise their learning.
Instructional Support
- Use of effective and clear questioning
- Clear explanations to broaden children's knowledge and understanding of a topic.
- Progressively introducing new learning that is presented for all to access (scaffolding)

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-The maths curriculum was judged good or outstanding in less than half of the schools inspected (47%)
- In some schools,  teachers used a single scheme of work which was based on the needs of the average pupil (therefore not stretching or keeping the interest of the HAPs and both confusing and knocking the confidence of the LAPs).
-The variation of the pupils abilities in maths was vast in most schools and therefore a range of work needed to be set for each lesson.
-Short-term help is needed to support teachers, particularly nonspecialists, in the approaches and activities that best develop pupils’ skills and understanding.

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1. the focus is kept clearly on improving student outcomes.
2.Feedback is related to clear, specific  and challenging goals for the recipient.
3. Focus on the learning, not comparing one child to another. 4. Teachers are encouraged to be continual independent learners.
5. feedback is mediated by a mentor in an environment of trust and support.
6. An environment of learning is and support is promoted by the school's leadership.

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-Early Years-  teachers need to every opportunity for children to use mathematics in everyday activities (games, shapes, patterns,  construction sites and slowly using mathematic language).
-Transition between EYFS and KS1- some teachers found that by doing some whole class teaching in reception and some provision in KS1, it eased the transition and made it more manageable and natural.

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- Lessons begin with whole class engagement with a contextualized problem, Considerable use of concrete materials and dialogue around possible solutions. The tasks are carefully selected and there is an emphasis on mathematical variation and connections

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- A growth mindset is a belief that the harder you work, the smarter you get. It may be explained in an accessible way to learners by considering the brain to be a muscle, the more you exercise it, the stronger it becomes.

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-7 teachers within 7 primary schools
-Teachers looked through recorded lessons and saw what had gone well and what could be improved. They could compare their lessons with similar age ranges and learn from eachother.

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-Good quality lesson planning, teaching and intervention strategies helped to secure learning and progress within lessons, from lesson to lesson, and to close gaps.
- Instant recall of tables, and associated number facts, and good understanding of place value, become increasingly important as pupils move through primary school and are essential prerequisites to later success in multiplication.

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-Mindset Theory-  observation and test results identified some disadvantages for students in top sets as well as for those in bottom sets.
-Boaler addresses the issue of how to teach maths in mixed groups of children in such a way that students can be encouraged to take mathematics to different levels.

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- A recent review clarifies the position that overall, setting by prior attainment does not have a significant impact on levels of attainment except for a negative impact on lower sets.
- Seven key problems that may cause low attainment by students allocated to low sets:
1. Misallocation to groups.
2. Lack of fluidity of groups.
3. Quality of teaching for different groups.
4. Teacher expectations of pupils, 5. Pedagogy, curriculum and assessment applied to different groups.
6. Pupil perception and experiences of grouping by prior attainment, and the impact on their learner identities.
7. These different factors working together to cause a self-fulfilling prophecy.

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-Pupils were directly engaged in mathematics for a substantial portion of each lesson.
-They then had enough valuable time to tackle challenging, varied questions and mathematical problems that helped to deepen their understanding.
-In the very best schools, all lessons had a clear focus on thinking and understanding, for example, developing primary pupils' grasp of place value and the effect of multiplying or dividing by 10 as part of their ongoing conceptual understanding of structure and relationships in number.
- A further benefit of pupils working for sustained periods on suitability demanding exercises is that the teachers can devote more time to moving around the classroom, assessing each pupil's progress and understanding.

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Maths in English schools is defined in statute by the EYFS framework and the national curriculum.
The curricular documents have overlapping mathematical skills and content.
A factor that contributes heavily to the implementation of the maths curriculum is the significant emphasis on external assessments and related performance measures.
The National curriculum has a colour coded table, this represents the national expectations of a child through their school life. Most pupils stay within a colour brand as they advance through each key stage even though the graph indicates that progress through national curriculum level is smooth, pupils learning is uneven.

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-To enable a pupil's successful
framing of collaborative learning through exploration, relies
heavily on the textbooks. However, the lessons provided by the
textbook embed the pedagogical approach and in particular give
the teacher ‘permission’ to spend classroom time on collaborative
exploration of the anchor problem.
- This permission helps to
counteract contextual pressures to rush on with curriculum delivery
from an overloaded national curriculum, high stakes external
inspection, and the emphasis on test results and school league tables.
- The dependence on the textbooks and associated teacher guidance creates a worry, because it might be part of reducing teachers to a technician role of ‘delivering’ the curriculum.

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A great teacher must always be on top of planning. In maths it’s key to have your whole framework mapped out and have goals of what you want your pupils to achieve by a certain time. Good quality planning and teaching helps progress within lessons and helps to close gaps in children’s knowledge.
Despite this only few schools in a survey planned and taught maths in a strong progression over time. This reflected in the pupils depth of knowledge as there would be some gaps, and also the fluency in mathematical skills and problem solving skills.
The main hindrance to allow stronger progression in these schools was the lack of coherence in the way that topics are developed over time. Due to teachers teaching the same year group each year some became unaware of how topics fit together to benefit the pupils long term progression of that strand of mathematics.

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When teaching maths to younger students who are struggling with the work, it is essential to have key resources around the room and to ensure that the children know how and when to use them.
On the other hand for the higher achievers, have extensions available for the children to be getting on with if they have a grasp and want to expand their knowledge.

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Ways of challenging students in Maths ( year 2)

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Ways of challenging students in Maths ( year 2)

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A student on my placement was a high achiever, he would complete work before any other student in the class. Both myself and my class teacher would have printed off workbooks from Twinkl and other online resources. These would include challenges with division, multiplication and each challenge in the workbook equals a letter for the answer of the themed question in the front of the pack. The student in question would pick what theme he wanted to do that day and then complete it whenever he finished all of his work.

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-Children who are eligible for free school meals and pupil premium children seem to have lower attainment in maths.
- Schools tackle mathematically disadvantaged students through insight and determination, as well as using policies and procedures to ensure that the improvements put in place are consistent.
- Few schools provide their staff with curricular guidance, solidified by development of enhancing subject knowledge, helps to ensure that there is consistent implementation of approaches and policies

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4: Classroom Management
- Efficient use of lesson time.
- Co-ordinate classroom resources and space with topic of learning (relevance)
- Manage students behaviour with a range of strategies such as, consistent use of school rules and positive reinforcement.
- Ability to maximise children's learning and also presenting opportunities for children to discover and expand their own knowledge.
- Environmental factors are necessary for good learning.

5: Teacher Beliefs
- Theories about what learning is and how it happens.
- Conceptual models of the mature and role of teaching in the learning process are all important.

6: Professional Behaviours
- Reflecting on and developing professional practice is a teachers own responsibility.
-Participation in professional development (courses and conferences etc.)
- Supporting colleagues
- Liaising and communicating with parents is important.

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1: Pedagogical - content knowledge
- Have a deep knowledge of the subject they teach.
- When teachers knowledge falls below a certain level it is going to significantly impact students learning.
- Teachers must understand the way students think about the content they're learning.
- Ability to evaluate the thinking behind students own methods
- Ability to identify students common misconceptions.

2: Quality of Instruction
- Use of effective questioning and use of assessment by teachers
- Reviewing previous learning.
- Providing model responses for students.
- Giving adequate time for practice to embed skills securely.
- Progressively introducing new learning with accessible step by step explanations (scaffolding)

3: Classroom Climate
- Quality of interactions between teachers and students .
- Appropriate teacher expectations.
- Create a classroom environment that is always demanding more and appropriately challenging the children.
- Students self-worth is appreciated - resilience to failure is established (e.g. Circle time, JIGSAW)

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Primary schools should focus attention on:

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Primary schools should focus attention on:

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- Ensuring that they are improving on students progress from EYFS all the way through to year 2  to help to increase attainment of the most able students.
- Acting as soon as you notice gaps in attainment to secure the basic and essential knowledge of the least able students.

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Challenging Children that are below expected level in Maths (reception class)

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Challenging Children that are below expected level in Maths (reception class)

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I found that on placement my class engaged more with English and a large number lacked confidence with maths.
After a discussion with the class teacher and TA we believed that the best approach for the lower achievers would be smaller group work, providing them with more individual support.
Presenting them with the a wide range of concrete resources we gave them the opportunity to choose which resources they would like to work with which made the tasks more enjoyable, they then began to grow in confidence and therefore engage more with the learning taking place.

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it can be difficult to ensure that all of the children in the classroom are engaged. With maths specifically, if a child doesn't understand the work then they will disengage and become disruptive. In cases like this you need to ensure that you have fully explained what the expectations are for that day and have resources around. For the younger years the children will concentrate better if it is tailored to what they enjoy. For example, if the children in your class mainly love dinosaurs then you can edit the maths questions and this will ensure that the children are engaged and willing to learn.

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Mathematical learning is significantly different between reception and KS1.
A lot of learning in reception is through continuous provision where as in year one children will be in more routine classes where they’re expected to sit for longer periods of time.
As the usually primary pattern of whole class teaching for up to an hour at a time is a sharp contrast to the typical mix of play and focused activities in reception classes.

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Effective pedagogical strategies in Key Stage 2

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Effective pedagogical strategies in Key Stage 2

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Year 5 teachers in 'excellent' schools....
1: Have organisational skills:
- Share clear learning objectives with pupils.
- Ensure all pupils understand the objectives.
- Extremely well-organised resources.
- Well established classroom routines.
2: Establish a positive classroom climate:
- Relationships between the teachers and children and amongst the children is based on mutual respect.
- Classrooms are happy places.
- Children are less disruptive and behaviour management is handling sensitively.
3: Personalise their teaching:
- Teachers are sensitive to the needs and interests of their pupils.
- Provide a variety of resources to suit the individuals in their classes.
- Able to make explicit links between learning in the classroom and the world outside the classroom.
4: Use dialogic teaching and learning:
- Children work collaboratively.
- Take part in instruction conversation.
- Teachers use analysis and maths  discourse.
- Share maths authority with the children.
5: Make more frequent and better use of the plenary:
- Teachers in best schools = 2x more likely to use a plenary - use it to provide feedback and allow further discussion, exploration and extension

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Many schools in England are adopting mastery approaches to maths teaching influenced by South Asian approaches. The approaches vary somewhat but share some common characteristics. The whole class, of mixed prior attainment, moves at broadly the same pace through a maths curriculum that is not too content heavy.
My school used this scheme, I have mixed feelings about is as each topic varies in size and depth. I found it difficult moving onto the next topic when I knew there children who would have benefitted for more lessons on this particular topic.

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-Grouping, or moving away from in-class grouping based on prior attainment, and the associated belief in differentiation by task, is an important shift identified in this study.
-However, my school didn't always have this approach as they continued to group them based on their ability- especially in Maths.
-The pupils were sometimes put in their mixed ability threes while completing activities.
-I felt this worked really well, especially when summarising an activity in Maths.
-But the majority of the time the pupils worked and completed tasks based on their ability.

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-Teachers are reflecting both on their own mindset within the school subject of maths and on the 'situated' domain specific mindset of their students.
-They are seeing the subject of maths as being about collaborative problem-solving and deep-thinking, rather than focusing on speed and calculation to reach a single ideal solution.

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-IT (to enhance children’s understanding of maths eg interactive whiteboards)
-lots of resources (and teachers making the most of these resources)
-making the most of the teaching assistant and creating new resources
-regular assessment throughout lessons (in creative ways rather than just written work)
-assessment evidence can be hard but there are ways (pictures, notes, etc)
-teachers need to understand the difference between wrong method and wrong answer (eg child could have used algebra correctly but just done a simple sum (8-4) wrong)
-schools monitor teachers understanding of maths regularly and make sure it is at an ‘acceptable level’
-some schools get the teachers with mathematics related degrees to educate the other teachers in a Maths Development Programme

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-In my school, "Talking partners" was widely used for all subjects on a daily basis.
-It worked brilliantly for Maths, as it kept the children engaged and focused.
-They were able to interact with each other and form opinions based on questions like "Where's the Math in that?"
-The children were shown a picture of something e.g. shelves in a shop- prices, how many boxes etc...
-They had to discuss with their partner and voice their answer to the rest of the class.

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Overall, the teaching of children in primary is only 57% effective. This was judged on on achievement,  leadership, teaching and management.

Some early learning goals that  EYFS should reach are:
-Numbers as labels for counting
-Calculating
-Shape, space and measures. For children to be learning securely they have to score 6 or more in all 3 aspects. As a rule children in EYFS are better at counting than calculating, and girls seem to out perform boys in each aspect.

In Key Stage 1, National testing was  exchanged for assessments in 2005, this has supposedly caused a decrease in the proportion of children attaining a Level 3, due to not challenging the more-able students enough to develop their learning further enough to progress.

In Key Stage 2 ,2011, 82% of pupils had made 2 levels of expected progress by the ens of year 6. This was an increase of 4% over 3 years.