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PRIMARY MATHEMATICS POLICY
Whilst the acquisition of knowledge, skills and facts and the ability to perform mathematical processes are patently important aims for mathematics education, we believe that it is equally important to develop an appreciation of the nature of mathematics and of being mathematical, to develop an understanding of the underlying concepts to develop powers of reasoning and to encourage creativity and free thinking.
We believe that learning is a very personal process and that children will acquire mathematical understanding in many different ways. Our aim is to assist the children to develop and refine their thinking and deepen their understanding in order to empower their control over the efficient use of mathematics.
These beliefs determine our aims and objectives.
Values and Aims
The provision for mathematics throughout the school will reflect the following aims:
* that the curriculum should be designed in such a way as to secure
for all children their entitlement to the full range of learning experiences
encompassed by the attainment targets set out in the National Curriculum.
* that the acquisition and consolidation of knowledge and skills appropriate
to the child's mathematical abilities goes hand in hand with a deepening
understanding of the underlying concepts.
* that all children should be enabled to employ their mathematical abilities
with confidence and accuracy.
* that the learning of mathematics should be a satisfying and enjoyable
activity, conferring a sense of self-esteem and achievement.
* that all children should be enabled to develop an appreciation of
mathematics in the fullest sense as a form of communication, in its aesthetic
sense, as a way of making sense and explaining, in its utilitarian form both
within the 'real world' and in its applications within other areas of the
curriculum. The value placed on mathematics will be reflected in displays of
mathematical work throughout the school.
* that the learning experiences should provide differentiation to
enable each child to make his or her own sense of the ideas and
processes involved in mathematics and mathematical working.
* that the learning experiences should encourage fascination,
curiosity, questioning and the desire to challenge and be challenged.
* that the children should be fully involved in all aspects of their learning,
including the recognition and assessment of their achievements.
* that the children should find themselves in an environment that supports
and encourages learning, both through its resources and its attitudes.
* that all children should be enabled to develop fully their mathematical
potential regardless of gender, ethnic origin, disability or social/educational
deprivation and be able to recognise the relevance of mathematics to every
day life.
OBJECTIVES
Learning
We believe that children learn mathematics:
* in ways that are individual and personal to each child.
* by building on the understandings that they already have.
* through experiencing challenges to these understandings.
* by developing an increasing range of knowledge and facts upon
which they can draw.
* through experiences that assist the development of their feelings,
images and ideas.
* through modelling ideas and mathematical situations.
* through interaction with other people.
* through interaction with mathematics in a wide range of contexts.
* through discussion and debate.
* through reflection.
* through consolidation
* through practice
* through the application of their skills and/or knowledge in
relevant contexts
and that learning will take place:
* in a climate that encourages exploration and experimentation,
but acknowledges the security offered by a sound knowledge of
mathematical processes.
* in a climate that makes it explicit that thoughts and ideas are not
just valued but desired.
* in an environment that has resources that support the learning.
* that values ordered, careful thinking.
Teaching
We believe that, in order to enable an understanding of mathematics and an acquisition of associated knowledge and facts, all teachers need to employ.
* exposition and demonstration
* exploration and investigation
* discussion and debate
* concrete experiences
* abstract experiences
and to provide opportunities for
* consolidation
* practice
* explanation and reasoning
* application of acquired skills and/or knowledge.
Exposition and demonstration
It is necessary for a teacher to convey facts, offer their views and show possible ways of performing some aspects of mathematics.
Children need to see what a mathematical model, a mathematical explanation and a mathematical method can look like. This is not only to develop their understanding of the mathematics but also to enable them to create their own models, explanations and methods. Teachers need to convey facts, share knowledge and discuss mathematical conventions. Exposition and demonstration provide such opportunities.
We believe that exposition and demonstration should not mean a passive experience for children, but one that encourages their questioning, challenges their understanding and excites their curiosity.
Exploration and Investigation
Exploration and investigation in mathematics are vital to developing not only an understanding of mathematics itself but also to enable children to realize that the knowledge they already possess can have the power of making sense of ideas that are new to them.
Exploration and investigation also encourage creativity and the development of personal methods that can be used flexibly, with confidence and understanding.
Exploration and investigative working can occur in many ways - during free play, focused play, discussion, debate, mental activity, child or teacher initiated activities and enquiries.
Discussion and Debate
Discussion and debate offer the opportunity to develop mathematical meanings and mathematical language, to consider how mathematics can be represented and interpreted, to consider mathematical conventions and to develop a view of being mathematical. This may take place when children are considering strategies in group work or discussing outcomes of work with their teacher.
Discussion and debate offer the children the opportunity to consider their understanding and ideas:
* by describing their current view of a situation.
* through considering the views of others (teaching, children, conventions)
* by questioning and commenting on these views.
* by exploring and testing their ideas in light of all views of the situation.
* by reflecting on their findings and evaluating their view of the situation.
* through explaining their reasons for their view of the situation
* through seeking conviction and proof.
Concrete experiences
We believe that children of all ages need to experience mathematics:
* through physical participation in mathematicsl situations.
* through modelling situations
* by considering other people's (teacher's and children's) models of a
situation.
We follow the CPA approach in Maths. The CPA method involves using actual objects for children to add, subtract, multiply or divide. They then progress to using pictorial representations of the object, and ultimately, abstract symbols. Children often find maths difficult because it is abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way.
Concrete experiences offer children opportunities to consider, to develop images, of the mathematics and to make sense of the mathematics. They are the foundations which support the abstractions of mathematics.
Concrete experiences also help the children to recognise mathematics as it exists in the real world. This supports them in applying their mathematical knowledge in 'real life' situations.
Abstract experiences can take many forms - imagining, playing with mental images, seeking underlying patterns and/or similarities, predicting, generalising, proving.
We believe that mental arithmetic is an important component of the child's abstract experience. This is the reason why fluency feeder is an important aspect of our day as fluency feeder activities provide opportunities for pupils to intelligently rehearse facts and strategies. Fluency is developed through strong conceptual understanding (use of manipulatives, regular fluency feeders, strategy exploration and explanation).
As new work is introduced children need time and practice to develop their proficiency. They should be encouraged to apply new processes in a variety of situation.
Mastery Approach
Using the core content from the Programmes of Study, we aim to provide children with deeper knowledge and understanding of mathematical procedures and related concepts. As such the school has identified the key learning for each year group/age range and supports teachers to plan to secure these. Learning sequences are developmental and, depending on the concept, a good proportion of time will be spent securing key learning. Teachers will use their judgement about when it is the right time to move on. As we secure this approach, it is envisaged that the large majority of pupils will progress through the curriculum content at broadly the same pace.
Explanation and Reasoning
Explanation and reasoning are at the heart of being mathematical. Children need to be constantly encouraged to look beyond the 'what is happening' to the 'why and/or how is it happening?'
From the very start, children should be asked what they have noticed, how they have done things, why they did them that way, what they are thinking and why they think that might be.
Reflection and the seeking of explanation should assist the deepening of mathematical understanding and lead to some conviction and proof of the mathematics involved.
Through reaching some conviction, the mathematics involved becomes 'owned by' and part of the child.
Application of Acquired Skills and Knowledge
Acquired knowledge and skills should be directed to 'real life' situations and within mathematics itself.
Application of mathematics can:
* contribute to the children's sense of purpose of mathematics
* strengthen their mathematical images and understanding
* help them recognise mathematics in the 'real world' and therefore
develop their problem solving abilities.
* sometimes lead the children into an area of mathematics they have
not previously considered.
Planning
Planning should ensure that the mathematical experiences provided for the children are contributing both to the school's overall aims and beliefs about the teaching of mathematics and to the development of the child's mathematical knowledge, skills and understanding and should be based on our knowledge of the children's previous achievements.
A scheme of work for KS1 and KS2 is in preparation to fall in line with the new areas of the New National Curriculum which need to be addressed using other resources that are in school.
Therefore planning should ensure:
1. Continuity, through providing a consistent approach to the
teaching and learning.
2. That all planning should aim at a high degree of pupil involvement.
3. Progression, through providing learning experiences that build on
previously acquired knowledge and skills.
4. Provision of an environment that supports and stimulates learning.
5. Balance across the new mathematics curriculum.
6. Coverage of the aims and attainment targets of each key stage.
Children's Mathematical Thinking
In recognition of the personal nature of mathematics, the National Curriculum states that children should:
Develop their own mathematical strategies
Develop different mathematical approaches
Develop flexible and effective methods of computation and recording.
We believe that it is important for children to know that their personal methods are valid, and not things to be hidden away. However the provision of standard approaches or strategies is vital as children must appreciate that mathematics is a form of communication subject to its own conventions. The learning of these conventions enhances and speeds mathematical communication.
For this to happen the teaching needs not just to take into account but actively to encourage children's own methods in order to gain understnding of the conventions we might meet and need.
Given the great emphasis on 'flexibility' and 'range of methods' stated in the Number Attainment Target, it is particularly important that a school considers its approach to calculation.
Our beliefs about teaching and learning and our objectives set out in the school scheme of work are the basis and structure that should guide the use of any resources. Therefore, we believe that:
* if a commercial scheme is used, there must be explanation of how
it is used to support the development of the children's mathematics.
* if there is no commercial scheme in use, there must be explanation
of how any textual resources that are used support the development of the
children's mathematics.
* it is not sufficient to simply state which scheme or texts are utilised
with each year group.
Management and Co-ordination
The 'Framework for a Subject Policy Statement' suggests the following considerations for managing and evaluating the curriculum area.
* role of the co-ordinator (leadership, resource management).
* monitoring of practice and standards of achievement (e.g.
through agreement trailing, observation, review).
* evaluation of policy and practice
* INSET programme
* termly review and overview by deputy headteacher
These would form the basis for co-ordination of any area of the curriculum. Within mathematics, there may be some aspects that might need consideration.
* keeping colleagues updated abut current issues and requirements.
* raising teachers' own confidence with and understanding of
mathematics.
* developing a view of mathematics teaching and learning that may not be
held by all colleagues.
* helping teachers develop their picture of what Mastery 'looks like' in practice.
Therefore planning should ensure:
1. High degree of pupil involvement in learning experiences, continuity,
through providing a consistent approach to the teaching and learning
appropriate.
2. The consistent use of core manipulatives and representations to support
ability to access learning and to deepen childrens understanding.
3. Rehearsal of core facts and strategies through the development of frequent
intelligent rehearsal (Fluency Feeders)
4. Progression through providing learning experiences that build on
previously acquired knowledge and skills.
5. Provision of an environment that supports and stimulates learning.
6. Balance across the mathematics curriculum
7. The knowledge and skills they aim to teach.
Planning decisions will include
* how particular experiences will be presented to the children - as a
separate subject, within a wider topic or theme, within existing
classroom or school activities and procedures.
* what outcomes might be expected - discussion, explanation, presentation
models, sketches, written;
The Use of IT
The school needs to consider its use of computers. These considerations should describe the contribution IT can make to the overall aims and objectives for mathematics. The acquisition of IT capability, whilst it might occur during mathematical experiences, is no longer a requirement of the Mathematics National Curriculum.
Computers can be used to:
* assist recording and explanation (word processor)
* explore spatial aspects, LOGO and Roamer (floor turtle)
* explore data and graphical representation.
* provide models and simulations
* provide investigative situations
Organisation
Any organisation that is employed has to take into account the full range of the children, the purpose of the learning experience and the extent to which the children will be involved in the organisation of the learning.
Choices or organisation for working might include:
* whole class
* small groups
* large groups
* individuals
* ability groups
* interest groups
Differentiation
Differentiation should ensure appropriate learning experiences for all children. This might be achieved by differentiated provision or by differentiated outcomes from a common provision.
At times, the purpose of the learning experience might determine the approach to differentiation - for instance, a practice situation might need a range of suitable exercises whereas an investigative situation might differentiate through outcomes.
Whatever form of differentiation is employed (and particularly with differentiation by provision), it is important that teachers do not restrict a child from reaching his or her personal best. Thus more able children should be given activities that fully stretch them.
It is recognised that children will progress further in some aspects of mathematics than others. While not neglecting areas where a child is making slower progress, encouragement should be given to move ahead in those aspects for which particular aptitude is shown. This needs to be reflected in the planning and provision. Equally, provision needs to be made for the aspects which are progressing more slowly.
Assessment, Recording and Reporting
The 'Framework for a Subject Policy Statement' suggests the following considerations for responding to and sharing children's work.
* our immediate response which will include the setting of
individual targets.
* our marking policy and/or correction procedures
* response to miscues/virtuous errors (e.g. as a learning opportunity)
* assessment strategies, including child's own assessment and review.
* next steps marking
* record keeping
* Teachers assessment in line with the new assessment criteria.
* contributions to child's record of achievement
* moderation of childrens work
* involvement of parents at consultation evenings and in the
annual report
Many of these targets for mathematical progress will be set by the school's Assessment Policy, but within mathematics we feel it is important to consider them in light of the following:
* mathematics can frequently appear to have specific outcomes and
these can tend to overshadow the processes involved in reaching the
outcomes. Whilst being able to reach an outcome is often desirable,
it is equally important to develop mathematical processes and reasoning.
Credit should be given for using an appropriate process systematically
even when the answer is incorrect.
* Will the outcome always be written? If not, what evidence do we have of
achievement? Anecdotal notes of childrens' responses in oral work are
of value.
Resources
Core Scheme
Although we have access to a commercial scheme we feel the opportunities for thematic approaches offered by it give adequate scope for differentiation. Each teacher has the Rising Stars textbooks, workbooks and Teacher's Resource books in their classroom. Teachers also have access to the IT programmes: Testbase, Espresso and Rising Stars.
Other Texts and Materials
There are also other photocopiable resources and games available in all class rooms. There are worksheets available of Staff Resources.
Classroom Resources
There are suitable resources for learning within all classrooms. All classes have access to the core manipulatives in line with the new curriculum. Within Y5/Y6's classroom are large stocks of compasses, set squares, mirrors and protractors which are available for general use..
Each class room has a quantity of the mathematical resources at its disposal. Teachers are free to use any resources available in the school. All classes have a basic set of core manipulatives.
Children will know that they are free to make use of whatever materials assists their learning.
Future Resourcing
Making further provision for mathematical equipment will be met from the Mathematics Budget which is held by the Maths Co-ordiantor. The level of this budget is set to meet the needs of the School Development Plan. Requests for equipment will be prioritised by the Maths Co-ordinator in consultation with the Head.
The Role of the co-ordinator
The Co-ordinator shall be responsible for the following:
* Having an overview of long and medium term planning.
* Monitoring of practice and levels of achievement
* Management of resources and budget.
* Monitoring of the above.
* Overview of provision for SEN.
* keeping staff informed of Inset needs.
* keeping colleagues updated about current issues
and requirements.
* raising teachers' own confidence with and
understanding of mathematics.
Work sampling
* developing a view of mathematics teaching and
learning that may not be held by all colleagues.
Cross Curricular Issues
We fully endorse the sentiments expressed in the Hertfordshire Curriculum Guidelines which state:
'Mathematical ideas and opportunities for mathematical thinking exist with the full school curriculum. The teacher in the Primary school is particularly well placed to seize natural opportunities for mathematics to emerge as an integral part of broad cross-curricular themes. Mathematics has obvious connections with areas such as science and geography. It supports others in more subtle ways. For example, time signatures, symmetry and structure in the composition and performance of music, proportion, ratio and measure in technology. Physical education and movement develop a feel for shape while history helps to establish a sense of the passage of time. A cross-curricular topic such as, for example, 'Our Food' will need to embody mathematics in its use of measures and of calculation, in its statistical analysis and its diagrammatic representation. The natural amalgamation of various subject disciplines in this way acts to counter the artificial boundaries erected by subject headings.'
June 2017
Review June 2019
PAGE12
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