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Maths at KLT
KLT Maths Vision
For KLT pupils to develop a deep conceptual understanding of mathematics, which they are able to apply to their everyday life and accurately communicate.
KLT Maths Aims
We want KLT pupils to:
- foster a positive attitude towards mathematical concepts and be keen to explore and apply their knowledge and understanding;
- develop their knowledge of how mathematics is used in the wider world and make rich and varied real life connections;
- think logically, work systematically and be able to explain their reasoning;
- become accurate mathematicians, using precise mathematical vocabulary;
- be able to communicate their mathematical thinking both verbally and in written form.
Five Big Ideas in Teaching for Mastery
Children’s chances of mathematical success are maximised if they develop deep and lasting understanding of procedures and concepts.
The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Mastering maths means pupils acquiring a deep, long-term, secure and adaptable understanding of the subject. Achieving mastery means acquiring a solid enough understanding of the maths that has been taught to enable pupils to move on to more advanced material.
As promoted by the National Centre for Excellence in the Teaching of Mathematics (NCETM), Five Big Ideas, drawn from research evidence, underpin the teaching for mastery of mathematics.
Coherence
Lessons are broken down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.
Representation and Structure
Representations used in lessons expose the mathematical structure being taught, the aim being that pupils can do the maths without recourse to the representation.
Mathematical Thinking
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the pupil: thought about, reasoned with and discussed with others.
Fluency
Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics
Variation
Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
By applying the Five Big Ideas, pupils’ progress through the following stages, to develop a deep and lasting understanding of mathematical concepts, as illustrated below.
Use of Power Maths to deliver a Mastery approach
The Power Maths scheme is employed at KLT from Foundation Stage to Year 6 as a vehicle to ensure consistency throughout the school. A whole-class, mastery approach is promoted through Power Maths, in which pupils are encouraged to develop the depth and breadth of their knowledge and understanding before moving their learning forward. Aligned to White Rose Maths progression, Power Maths ensures that learning is carefully planned through each year group, to build upon prior learning.
Power Maths
Year Group Overviews
Year group overviews outline the learning for each term, indicating the units and how these correlates to the National Curriculum objectives for each year group.
Unit Overviews: Developing pedagogical understanding
As the mastery approach is underpinned by small connected steps that gradually unfold the concept, it is vital that teaching staff have sound pedagogical knowledge. At the start of each unit the following information is provided to ensure accuracy of teaching;
- Why is this unit important;
- Where this unit fits;
- Assessing mastery: common misconceptions, strengthening understanding, going deeper;
- Ways of working;
- Structure and representations; and
- Key language.
In addition, the Calculation policies for Key Stage 1, Lower Key Stage 2 and Upper Key Stage 2 ensure that all staff have a clear understanding of prior, current and future learning for all four operations, and the progression within pupil’s learning to support and further develop pupils’ learning.
Key Learning Elements
Within Power Maths, the ‘discover, share, think together, practice, reflect’ sequence is adopted to deliver each learning outcome. The following elements should be in place in each lesson.
1.Representation and structure
Mathematics is an abstract subject; representations and structure have the potential to provide access for pupils and to develop their understanding.
The ‘Concrete – Pictorial – Abstract’ model is used to support pupils within Power Maths lessons, with pupils having access to both concrete apparatus and visual representations.
Concrete – children have the opportunity to use concrete objects and manipulatives, to help them to understand what they are doing. This is the “doing” stage, using concrete objects to model problems.
Pictorial – alongside concrete objects, pupils should use pictorial representations. These can then be used to help reason and solve problems. This is the “seeing” stage, using representations of the objects to model problems.
Abstract – both concrete and pictorial representations should support children’s understanding of abstract methods. In this stage, the teacher models the mathematical concept at a symbolic level, using only numbers, notation, and mathematical symbols to represent the number of circles or groups of circles. The teacher uses operation symbols (+, –, x, /) to indicate addition, multiplication, or division. This is the “symbolic” stage, where students are able to use abstract symbols to model problems.
Key Language
Key language for a unit is introduced at the start of a sequence of lessons and displayed throughout the unit on the maths display board. This is a vital reference tool, which teachers utilise throughout each lesson, providing pupils with the vocabulary to accurately explain their thinking. Throughout all stages of a lesson, pupils are given frequent opportunities to discuss their mathematical thinking and to share this with different audiences (their partner, group, or whole class). This is a vital skill which enables pupils to make sense of their learning and to allow them to make connections.
Fluency
Following the “I do, we do, you do” approach, pupils begin to apply the strategies they have been taught to their independent work. The “I do” element of this approach plays an important role, allowing the class teacher to verbalise the strategy they are adopting and explaining why this this (‘thinking out loud’), to enable pupils to understand why some strategies are more suitable than others. The “we do, you do” questions then allow pupils to experiment with different strategies to enable them to identify the most appropriate and efficient method to solve calculations.
Mathematical Reasoning
Reasoning in maths is the process of applying logical thinking to a situation to derive the correct problem-solving strategy for a given question, and using this method to develop and describe a solution. Mathematical reasoning is the bridge between fluency and problem solving. It allows pupils to use the former to accurately carry out the latter.
Problem Solving
Problem solving in maths is finding a way to apply knowledge and skills to answer unfamiliar types of problems.
A problem is something that pupils do not immediately know how to solve. There is a gap between where they are and getting started on a path to a solution. This means that the children require the opportunity to think and play with the problem. They need to test out ideas, to go up ‘dead ends’ and adjust their thinking in the light of what they learn from this, discuss ideas with others and be comfortable to take risks. When the children are confident to behave in these ways they are then able to step into problems independently.
As teachers we can support our children to develop the skills they need to tackle problems by the
classroom culture we create. It needs to be one where questioning and deep thinking are valued, mistakes are seen as useful, all children contribute and their suggestions are valued, being stuck is seen as positive and children learn from shared discussion with the teacher, support staff and peers.
The following stages are used to support pupils in their approach towards problem solving:
- Understanding the problem: discussing with a partner; drawing a picture; using concrete apparatus to model the problem; ‘acting out’ the situation
- Devising a strategy for solving it: considering known strategies and which may best support tackling the problem (trial and improvement; working systematically; identifying patterns; working backwards)
- Carrying out the strategy: choosing one of the identified strategies to solve the problem
- Checking the result: using another, different method to solve the problem – is the same answer calculated?