Mathematics

‘Pure mathematics is, in its way, the poetry of logical ideas’ – Albert Einstein

What do we want for our children?

Through our mathematics curriculum children at Preston Park become fluent in mathematics, are able both to solve problems and to reason mathematically. Mathematics provides a foundation for understanding the world and giving children the ability to think in abstract ways. We strongly believe it is vital that our children are equipped with the tools and knowledge to succeed in life and with this in mind, mathematics is an integral and daily part of the Preston Park curriculum. Through a Teaching for Mastery approach, we encourage our children to articulate their understanding  of mathematical concepts clearly and confidently whilst making connections to help them problem solve creatively and efficiently.

Since 2019, we have been following a teaching for mastery curriculum. Promoted by mathematics professionals and the Department for Education since 2015, this is largely based around employing approaches that help children to develop a deep and secure knowledge and understanding of mathematics so that by the end of each year they have acquired mastery of mathematical facts and concepts they have been taught[1] [2].

The mastery approach, as well as the National Curriculum, places emphasis on children becoming fluent in the fundamentals of mathematics so they can rapidly recall facts and answer problems. With this in mind, fluency is a core part of mathematics teaching at Preston Park and features in every lesson to ensure that children are best equipped to succeed at mathematics when they transition to secondary school.

Our Mathematics Leader trained with the NCETM in 2018 to become a Primary Maths Specialist working with the London Central and West Maths Hub in supporting local London schools in developing their pedagogical understanding of the teaching for mastery approach. Through their training, they are kept abreast of changes in curriculum or guidance. Our teachers take part in regular professional development sessions to ensure they are confident at delivering our mathematics curriculum effectively. 

How do we deliver this effectively?

 At Preston Park, we are always updating and tailoring our curriculum to ensure we are teaching the relevant strategies to support our pupils understanding of mathematical concepts. We currently follow the NCETM materials for teaching place value, the four operations and fractions and the MyMastery curriculum for shape, measurement and statistics units.

Our curriculum is underpinned by the ‘5 Big Ideas’ for Teaching for Mastery.[3]

 The 5 Big Ideas underpin our curriculum and allow us to ensure we building pupils understanding of mathematical concepts whilst allowing them to make connections to support their mathematical thinking.

 A Teaching for Mastery approach is simple and allows pupils to use concrete, pictorial and abstract (CPA approach] representations to develop their understanding of mathematical concepts. This is influenced by the work of Constructivist Psychologist, Jerome Bruner who developed work on the enactive, iconic and symbolic stages of learning. [4] [5]

Enactive is the representation of knowledge through actions.

Iconic is the visual summarization of images.

Symbolic is the use of words and other symbols to describe experiences.

At Preston Park, we have developed upon the CPA to CCPA, by building in the importance of context.

When children have a context to relate the maths to, then the manipulatives have meaning and their visualisation and experience will be stronger. In the symbolic stage, pupils are describing their experiences therefore talk and language is important to make those connections. At this stage, accurate use of mathematical vocabulary and sentence stems are crucial to help children reach the abstract stage of their learning.

There is a strong emphasis on the use of mathematical manipulatives and representations to develop understanding of different concepts. There has been a shift in pedagogy that manipulatives are for all learners to encourage discussion about mathematical structures of concepts. We encourage our children to use a variety of concrete objects such as Base 10 blocks and Ten-Frames to build a foundation of understanding in mathematics in all years, before deepening and consolidating through the use of written calculations and problems. [6]

It is noted that the key feature of dynamic mathematical activities is the hierarchical levels of knowledge and skills. These kind of levels can be shown as a series of learning steps, or as certain strategy or experience. “It is certain that this teaching approach of progressively unfolding mathematics is of course not rote learning.” (Professor Gu, 2018).

Our curriculum is designed to enable more time to be spent on topics to enable teachers to teach small steps to allow our children to master a concept and build connections to other topics where possible. 

We have an inclusive approach which supports children with SEND. At Preston Park, teachers adapt and tailor their lessons to meet both the learning and physical needs of all children. Each class has a mathematics display with key vocabulary and models of mathematical concepts for visual learners. We practise the concrete – pictorial – abstract approach to teaching mathematics and this multi-sensory method is well suited to children with SEND. Each classroom has concrete resources such as Base 10, Numicon and bead strings and pupils are encouraged to use these to enhance their understanding. Some activities and tasks are adapted to enable access and ensure the correct level of challenge.  At other times, pupils with SEND might work on a parallel activity towards a specific personalised outcome with adult support.

What does this look for our children?

Children begin every year by consolidating concepts from the previous year with a focus on Place Value and Number. A large emphasis is placed on number skills to ensure children can add, subtract, multiply and divide using mental and written methods. Children are encouraged from year one to learn vital multiplication and division facts. Evolving from this, we develop children’s mathematical thinking and reasoning skills through problem-solving and context-driven teaching.

Early Years Foundation Stage (EYFS including our 2 Year Old Provision)

Children will work towards the Department for Education’s non-statutory Early Learning Goals [7] through short mathematics sessions to ensure children are best-set for the demands of the National Curriculum. These are separated into ‘Numbers’ and ‘Shape, Space and Measures’. The Early Learning Goals are outlined in our ‘Progression of Skills and Understanding’ document.

Although there are short daily mathematics sessions led by the teacher and follow up adult led activities, often mathematics is taught discretely through play and child-led activities. Learning opportunities for mathematics are planned for both inside and outside the classroom, and these link where possible to the weekly learning intentions as well as the children’s interests. These could include counting how many scoops of water are needed to fill different size containers, writing numerals in large scale using chalk or solving problems through play such as which container fits the most farm animals to transport them around the farm.

Teaching staff in the EYFS have a strong understanding of effective strategies for the teaching of early mathematics. The mathematics curriculum is designed to help children embed their learning in order to integrate new knowledge and larger concepts. Teaching staff are trained in checking children’s learning and understanding, through questioning and formative assessment methods. Through this engagement with children, all staff are then able to provide suitable scaffolding or extension to support children in consolidating their learning of key mathematical concepts or challenging them further so that they reach their individual potential. At this stage recording mathematical thinking is encouraged whether this is pictorial, with numbers or more formal written methods. At all times mathematical language and new vocabulary is prioritised.

Key Stage One (Years One and Two)

Fluency is a vital component of Key Stage One mathematics. Children work with number and the main four operations to ensure that they become confident with number facts and calculations. Teaching uses a range of concrete, pictorial and abstract approaches to build children’s understanding to a point where they can use mathematics skills to independently approach a range of context-driven problems.

Lower Key Stage Two (Years Three and Four)

Fluency is still at the heart of mathematics teaching in Lower Key Stage Two, ensuring children can quickly recall facts and work out problems involving number and the four main operations. Children will develop efficient written and mental methods and be able to calculate accurately with large whole numbers.

Upper Key Stage Two (Years Five and Six)

This is a period of consolidation and extension of concepts children will have mastered in previous years. Children will develop an understanding of connection between numbers and concepts not only with multiplication, division and whole numbers but also with decimals, fractions, ratio and percentage. Emphasis is placed through reasoning on multi-step words problems and strategies to break these down and work them out.

Progression in Skills and Understanding

Consistent progression in mathematics is essential and our ‘Progression of Skills and Understanding’ document clearly outlines how children will develop year-on-year.

How does our Mathematics curriculum contribute to and develop our 21st Century learner?

In the first national Multiplication Test Check in Summer 2022, 71% of our year 4 pupils achieved full marks.

We strive to ensure that all children meet the ‘Expected Standard’ at the end of Key Stage 2.

Research

 Research frames our thinking in what we teach and how we deliver it to our children to ensure teaching and learning has maximum impact.

Please see references to the research linked above:

[1] https://schoolsweek.co.uk/what-is-teaching-for-mastery-in-maths/

[2] https://teaching.blog.gov.uk/2019/09/27/boosting-confidence-in-maths-our-teaching-for-mastery-journey/

[3] https://www.ncetm.org.uk/teaching-for-mastery/mastery-explained/five-big-ideas-in-teaching-for-mastery/

[4] The Validity of Enactive Iconic Symbolic Problem Based Learning Model (PBMENIKSI) for Elementary School

[5] https://mathsnoproblem.com/blog/teaching-tips/jerome-bruner-theories-put-into-practice

[6] EEF Guidance Report on ‘Improving Mathematics in Key Stage 2 and 3’

[7] https://www.foundationyears.org.uk/files/2012/03/Early_Years_Outcomes.pdf