Maths

At Monkwick Infant and Nursery School, we believe that learning is a change in the working Memory.

We aim to ensure that our children experience a wide breadth of study and have, by the end of each key stage, long-term memory of an ambitious body of procedural and semantic knowledge. Our curriculum drivers shape our curriculum breadth. They are derived from an exploration of the backgrounds of our children, our beliefs about high quality education and our values. They are used to ensure that we give our children appropriate and ambitious curriculum opportunities. 

Cultural capital gives our children the vital background knowledge required to be informed and thoughtful members of our community who understand and believe in British Values.Curriculum breadth is shaped by our drivers, cultural capital, subject topics and our ambition for our children to study the best of what is thought and said.

Our curriculum distinguishes between subject topics and ‘threshold concepts’. Subject topics are the specific aspects of subjects that are studied. The threshold concepts tie together the subject into a meaningful schema. The same concepts are explored in a wide breadth of topics. Through this ‘forwards and backwards engineering’ of the curriculum allows our children to return to the same concepts over and over again and gradually build an understanding of them. 

The retrieval of knowledge helps students related each topic to previously studied topics and form a strong, meaningful schema. We know that working memory is limited and that cognitive load is too high if children are rushed through content. This limits the acquisition of long term memory. Cognitive science also tells us that for children to become creative thinkers, or to have a greater depth of understanding that they must first master the basics, which takes time.

During KS1, children gradually progress in their procedural fluency and semantic strength through three cognitive domains which we call; remembering, knowing and reasoning. The aim is that by the end of KS1, our children can display sustained mastery. Children will secure knowledge, facts, and concepts and will have the ability to apply, analyse, evaluate and prove.

 

Our curriculum design is based on evidence from cognition science, three main principles underpin it:

• Learning is most effective with spaced repetition.

• Interleaving helps our children to discriminate between topics and aids long term retention

• Retrieval of previous learned content is frequent and regular, which increases both storage and retrieval strength. 

In addition to the three principles we also understand that learning is invisible in the short term memory and that sustained mastery takes time. Our content is subject specific. We make intra-curriculum links to strengthen schema wherever possible. Continuous provision, in the form of daily routines, replaces the teaching of some aspects of the curriculum and, in other cases, provides the retrieval practice for previously learned content. 

Because learning is a change in the long term memory it is impossible to see impact in the short term. We do, however, use probabilistic assessment based on deliberate practice. This means that we look at the practices taking place to determine whether they are appropriate, related to our goals and likely to produce results in the long run. We use comparative judgement in two ways: in the end outcomes of a unit of work and in comparing a child’s work over time.

We use lesson observations to see if the pedagogical style matches our depth expectations and pupil voice to quality assure what the children have been taught. 

 

Threshold concepts

 

• Know and use numbers

This concept involves understanding the number system and how they are used in a wide variety of mathematical ways.

 

• Add and subtract

This concept involves understanding both the concepts and processes of addition and subtraction.

 

• Multiply and divide

This concept involves understanding both the concepts and processes of multiplication and division.

 

• Use fractions

This concept involves understanding the concept of part and whole and ways of calculating using it.

 

• Understand the properties of shape

This concept involves recognising the names and properties of shape and angles.

Describe position, direction and movement

This concept involves recognising various types of mathematical movements

 

• Use measures

This concept involves becoming familiar with a range of measures and devices used for measuring and calculations.

 

• Use statistics

This concept involves interpreting, manipulating and presenting data in various ways.

 

EYFS: breadth of study 

Developing a strong grounding in numbers is essential so that all children develop the necessary building blocks to excel mathematically. 

Children should be able to count confidently and develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. By providing frequent and varied opportunities to build and apply this understanding—such as using manipulatives, including small pebbles and tens frames for organising counting—children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built. In addition, it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics, including shape, space and measures. It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes. (Statutory framework for EYFS.). Setting the standards for learning development and care for children from birth to 5. March 2021)

ELG 

 

Number 

Children at the expected level of development will: 

- Have a deep understanding of number to 10, including the composition of each number;  

- Subitise (recognise quantities without counting) up to 5; 

- Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts. 

 

Numerical Patterns 

Children at the expected level of development will: 

- Verbally count beyond 20, recognising the pattern of the counting system; 

- Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity; 

- Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally. 

 

Early years follow the NCETM Mastering Number as their daily maths sessions. Below is the overview:

 

KS1 

 

• Count and calculate in a range of practical contexts.

• Use and apply mathematics in everyday activities and across the curriculum.

• Repeat key concepts in many different practical ways to secure retention.

• Explore numbers and place value up to at least 100.

• Add and subtract using mental and formal written methods in practical contexts.

• Multiply and divide using mental and formal written methods in practical contexts.

• Explore the properties of shapes.

• Use language to describe position, direction and movement.

• Use and apply in practical contexts a range of measures, including time.

• Handle data in practical contexts.

 

To help our children become excellent mathematicians, we have designed a mathematics curriculum that includes cross-curricular links and builds on previously taught skills. We carefully selected topics that our children are interested in and that they have some prior knowledge of. We have designed a curriculum that will provide inspiring and successful learning opportunities for all students. A curriculum that broadens children's knowledge and equips them with the necessary skills to become aspirational mathematicians