Maths progression across the school

Maths manipulatives are very important in maths as they help students visualise and internalise different concepts. Children need to hold maths in their hands before they can hold maths in their minds. Virtual maths manipulatives that simulate the physical manipulatives and more, are very useful with the new reality of virtual learning.

Lower key stage 2

Older pupils progress to holding a range of mathematical 'tools' in the heads - number facts, times tables and mathematical fluency all serve to help them calculate more efficiently. In class, pupils support one another in peer work, small groups are supported in their learning by teachers and learning is extended to deepen mastery and offer challenge where needed.

Mathematics Curriculum Statement
Intent

Our Maths curriculum at Whitstone aims to give pupils real and memorable mathematical learning experiences. We have a belief that children learn best by having opportunities to explore concepts from a variety of approaches. In Maths, lessons are sequenced to build knowledge, skills and vocabulary where we recognise prior learning and build on it with memorable learning experiences and provide targeted support where necessary. Each lesson is planned to include the development of quick recall of number facts underpinned by strong basic skills and an in-depth focused mastery lesson developing knowledge of concepts and procedures. We aim to provide a high-quality mathematics education with a mastery approach so that all children:

• become fluent in the fundamentals of mathematics.
• reason mathematically.
• can solve problems by applying their mathematics knowledge and skills.
• can become confident, curious, happy, resilient and proactive learners.
• can reach their full potential

We believe the teaching of mathematics is underpinned by the following aims:

• Children can enjoy maths and realise that everyone can succeed in this subject.
• Basic number facts are learnt so children can work quickly and accurately. To develop conceptual understanding by using models, pictorials and concrete resources so that children understand the mathematics that they are learning.
• To highlight and utilise relationships between concepts and procedures.
• To encourage mathematical reasoning by following lines of enquiry, generalising and justifying using mathematical language
• To apply mathematical understanding to problem solving by breaking down problems into simpler steps and persevering in seeking solutions using a range of strategies
• To develop resilient children who are confident and enthused about mathematics who understand that mistakes are part of learning.
• To provide ‘purposeful maths’ through application of mathematical skills and knowledge to the world around them.
• To recognise prior learning and build on it with memorable learning experiences, providing targeted support where necessary.

Implementation

Our approach to Maths follows established methodology of taking pupils from the concrete to the abstract in a series of steps –

Concrete       Pictorial       Abstract     (C.P.A)

It also aligns with the Connective Model of Maths:

The Connective Model

Understanding mathematics involves identifying and understanding connections between mathematical ideas. Haylock and Cockburn (1989) suggested that effective learning in mathematics takes place when the learner makes cognitive connections. Teaching and learning of mathematics should therefore focus on making such connections. The connective model helps to make explicit the connections between different mathematical representations: symbols, mathematically structured images, language and contexts.

Learning mathematics and demonstrating understanding of mathematics involves connecting real experiences, contexts, mathematical images/pictures, language and symbols.

A pupil really understands a mathematical concept, idea or technique if he or she can:

• Describe it in his or her own words.
• Represent it in a variety of ways (e.g. using concrete materials, pictures and symbols)
• Explain it to someone else.
• Make up his or her own examples (and non-examples) of it.
• See connections between it and other facts or ideas.
• Recognise it in new situations and contexts.
• Make use of it in various ways, including new situations.

There is evidence from brain research that shows that connecting different representations of mathematics leads to more powerful learning. When students work with symbols, such as numbers, they are using a different area of the brain than when they work with visual and spatial information, such as an array of dots. Joonkoo Park & Elizabeth Brannon (2013) found that mathematics learning and performance was optimized when the two areas of the brain were communicating. Additionally, they found that training students through visual representations improved students’ maths performance significantly, even on numerical questions, and that visual training helped the students more than numerical training.   Reference:  Derek Haylock and Anne Cockburn (1989), Understanding Early Years Mathematics, pp 2-4.

Guided Maths in the Classroom

Guided maths is a fantastic classroom routine that allows for a more differentiated approach to classroom maths instruction and gives pupils more equal exposure to the 4 areas of the Connective model. After a whole-class mini teacher instructed lesson, students break into groups (ability or mixed ability) to complete a variety of different activities. These rotational activities include a guided maths session with the teacher.

What’s more, guided maths sessions allow the teacher the opportunity to monitor and assess how students are progressing along the maths continuum. This, in turn, helps the planning of further maths teacher instruction.

Teachers plan their weekly maths with a series of rotation stations as follows.

• M is for Maths with a friend – these are partner based activities. Pupils are given carefully chosen activities which give them a real context for using mathematical language. Activities have a real purpose and pupils support each other whilst communicating with new vocabulary.
• A is for At work on your own – this is more of an independent activity, often focusing on fluency. The activities are differentiated by ability with options of additional challenge activities for the more able pupils.
• T is for Teacher Table– this is for giving additional challenge, problem solving and deepening understanding. Teachers plan and teach in the moment, in response to need and ability. These sessions are key for assessment, moving pupils on and allowing for misconceptions to be addressed promptly. With low ability pupils these sessions can be used as immediate interventions.
• H is for Hands-On Activities – this is for hands-on, practical activities, using real-life examples and manipulatives. This is essential for allowing pupils to see the maths in action and to gain a deeper , more concrete understanding of mathematical concepts.
• S is for Speed Maths – this is usually for quick and fast maths mentals work.

Within an hour’s lesson, each pupil will visit two or three  15-min stations thus exploring learning objectives more deeply in every lesson.

Impact

The desired impact of our curriculum is that children:

• Will develop a greater love of maths.
• Will become fluent, competent and efficient mathematicians.
• Develop the ability to reason and problem solve, often using more than one approach.
• Will become competent and well-versed in explaining their reasoning with a wide mathematical vocabulary.
• Develop skills to use maths in real life.
• Gain knowledge and quick retrieval of basic number facts.
• Are able to learn from mistakes and are resilient .
• Develop a responsibility for making choices and decisions.
• Make good or better progress.

Breadth       Depth       Engagement        Progression