Mathematics

Intent: Introduction, Vision and Philosophy 

The purpose of this document is to clarify the how, why and what of maths teaching at Harris Junior Academy Carshalton. This is to be used by staff to clarify expectations, highlight the resources that we have access to, and to ensure that a high-quality maths curriculum is being taught to all pupils in our academy.

At HJAC, we want our children to be confident, fluent mathematicians, as well as problem solvers. We teach maths for mastery. This means that we are teaching our children to have a deep conceptual understanding as opposed to teaching children to answer correctly. Being able to explain how they got an answer, why that answer is correct, and what might happen if a particular variable was changed are the hallmarks of a mathematician – simply getting the correct answer ought to be a given. 

We emphasise: 

Retrieval practice - Knowing more- remembering more! Daily retrieval practice to consolidate prior learning and practice. 

Language – communicating ideas, proof, clarity and development of mathematical concepts. 

Thinking – questioning and task design to promote mathematical thinking. 

Understanding – using the concrete, pictorial and abstract approach to deepen conceptual understanding and making connections to previous learning, to other subjects. 

Problem Solving – to be mathematical is to solve mathematical problems. Problem solving is both why and how we learn mathematics. 

Implementation: 

What does maths look like at HJAC? 

At HJAC we teach maths in units, usually for a couple of weeks per unit. We aim to develop children’s understanding from the Concrete (actual physical manifestation of the maths), on to the Pictorial (being able to approach maths using pictures rather than physical resources), and finally onto the Abstract (being able to approach mathematics without the physical or pictorial resources). A typical two-week unit might have 2-4 concrete, practical lessons (photo recorded with follow-up questions) as well as 6-8 lessons focussing more on the pictorial and abstract (recorded using stickers followed by further extension sticker where necessary). 

HJAC has opted for the White Rose Maths scheme of learning from Year 3 to Year 6 to ensure a robust, comprehensive, and high-quality approach to the teaching and learning of mathematics. The decision to adapt this scheme was guided by a desire to foster maths mastery, improve conceptual understanding, and to align with Ofsted's standards for effective teaching and learning.

White Rose Maths adheres to the concrete, pictorial, abstract (CPA) approach, a three-step pedagogical strategy that aids in developing a deep and sustainable understanding of maths. Beginning with 'concrete' experiences, where pupils engage with physical, manipulatives, learners are then introduced to 'pictorial' representations, followed by 'abstract' symbols. This gradual approach aids pupils in visualising mathematical concepts and contextualising abstract ideas, thereby nurturing mastery learning.

The systematic nature of the White Rose Maths scheme underscores the importance of conceptual understanding. Rather than rushing to provide quick fixes or rote learning methods, White Rose allows our pupils to understand the ‘why’ and ‘how’ of mathematical concepts. This aligns with Ofsted's emphasis on deep learning, wherein pupils should understand and apply the underlying principles and connections within their learning.

Each White Rose Maths unit provides a 'small steps' progression framework, ensuring a pedagogically sound sequence of mathematical learning that we at HJAC have adapted to best fit the needs of our pupils. This approach allows concepts to be broken down into manageable chunks, giving learners the opportunity to fully grasp each new skill or concept before moving on. This fits within Ofsted's recommendation that schools offer a curriculum with appropriate sequencing, which provides a strong foundation for cumulative learning.

The White Rose Maths scheme comprehensively covers the breadth of the national curriculum. It provides a coherent, structured and detailed scheme of learning that ensures all necessary topics are covered systematically. This aligns with Ofsted's requirement that the school curriculum should be broad, balanced and provide the requisite knowledge and skills for future learning and employment.

The White Rose scheme is a progressive model that consolidates, builds upon and extends our children's maths learning. It provides a carefully crafted journey, where children continuously build on their previous learning, ensuring readiness for the next steps in their mathematical education. This complies with Ofsted’s expectations of effective progression and curriculum planning, helping pupils to deepen their knowledge and understanding over time.

By adapting the White Rose Maths scheme, HJAC demonstrates a commitment to a high-quality mathematics education that is personalised for the needs of all our pupils. White Rose equips our pupils with the necessary mathematical skills, knowledge and understanding to excel in their future academic and personal endeavours and develop a love of mathematics.

When planning a unit, teachers will have access to a range of different resources and areas to support the lessons that are outlined in our teaching overview. Generally, teachers will follow the recommended progression delivered in staff CPD sessions as well as the order of the slideshows in White Rose. However, additional slides are added to promote vocabulary, timestables and partner practice. If a specific teaching tool or representation is not available on White Rose, then teachers have the freedom to make their own resource to best suit the needs of their class.

Teaching staff recognise the difference between performance and learning and understand that pupil performance in the lesson today does not necessarily translate into the type of learning that will be evident tomorrow. As a result, the use of low stakes tests (in the form of spaced retrieval practice) enable staff to regularly assess what learning has been retained by pupils over longer periods of time. This also provides pupils with the regular opportunity of retrieving information from memory, which consequently facilitates learning. 

This includes: 

· Assessment of learning 

· Pupil voice (WIL about maths) 

· Challenge tasks 

· End of unit assessment (Low Stakes Testing) 

· Standards of learning in books 

· Spaced retrieval practice (see below) 

· WIL