Aims of the Curriculum

Aims of the curriculum

Education influences and reflects the values of society, and the kind of society we want to be. It is important, therefore, to recognise a broad set of common purposes, values and aims that underpin the school curriculum and the work of schools.

Clear aims that focus on the qualities and skills learners need to succeed in school and beyond should be the starting point for the curriculum. These aims should inform all aspects of curriculum planning and teaching and learning at whole-school and subject levels.

The curriculum should enable all young people to become:

successful learners who enjoy learning, make progress and achieve
confident individuals who are able to live safe, healthy and fulfilling lives
responsible citizens who make a positive contribution to society.

Purposes of the curriculum

The Education Act (2002) requires that all maintained schools provide a balanced and broadly based curriculum that:

promotes the spiritual, moral, cultural, mental and physical development of learners at the school and within society
prepares learners at the school for the opportunities, responsibilities and experiences of adult life.

The purpose of having a statutory core to the curriculum is:

to establish an entitlement. The national curriculum secures for all pupils, irrespective of social background, culture, race, gender, differences in ability and disabilities, an entitlement to a number of areas of learning and to develop knowledge, understanding, skills and attitudes necessary for their self-fulfilment and development as active and responsible citizens.
to establish standards. The national curriculum makes expectations for learning and attainment explicit to pupils, parents, teachers, governors, employers and the public and establishes national standards for the performance of all pupils in the subjects it includes.
to promote continuity and coherence. The national curriculum contributes to a coherent national framework that promotes curriculum continuity and is sufficiently flexible to ensure progression in pupils’ learning. It facilitates the transition of pupils between schools and phases of education and provides a foundation for lifelong learning.
to promote public understanding. The national curriculum increases public understanding of, and confidence in, the work of schools and in the learning and achievements resulting from compulsory education. It provides a common basis for discussion of education issues among lay and professional groups, including pupils, parents, teachers, governors and employers.

In particular the curriculum should:

raise attainment, particularly in English, mathematics, science and ICT
ensure entitlement for all learners to a broad, balanced and relevant curriculum that offers continuity and coherence and secures high standards
induct learners into the essential knowledge, skills and discourse of subject disciplines and to develop specialisms appropriate to aptitude
prepare young people for the world of employment and further and higher education
make learners more aware of, and engaged with, their local, national and international communities
encourage learners to take responsibility for their own health and safety, and appreciate the benefits and risks of the choices they make
contribute to community cohesion
acknowledge, promote and pass on the core knowledge and skills valued by society to the next generation.

Values underpinning the curriculum

Education should reflect the enduring values that contribute to personal development and equality of opportunity for all, a healthy and just democracy, a productive economy, and sustainable development. These include values relating to:

the self, recognising that we are unique human beings capable of spiritual, moral, intellectual and physical growth and development
relationships as fundamental to the development and fulfilment of ourselves and others, and to the good of the community. We value others for themselves, not only for what they have or what they can do for us
the diversityin our society, where truth, freedom, justice, human rights, the rule of law and collective effort are valued for the common good. We value families, including families of different kinds, as sources of love and support for all their members, and as the basis of a society in which people care for others. We also value the contributions made to our society by a diverse range of people, cultures and heritages
the environment, both natural and shaped by humanity, as the basis of life and a source of wonder and inspiration which needs to be protected.

At the same time, education must enable us to respond positively to the opportunities and challenges of the rapidly changing world in which we live and work. In particular, we need to be prepared to engage as individuals, parents, workers and citizens with economic, social and cultural change, including the continued globalisation of the economy and society, with new work and leisure patterns and with the rapid expansion of communications technologies.

Mathematics Key Stage 3

The importance of mathematics

Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy.

Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all pupils when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Pupils who are functional in mathematics and financially capable are able to think independently in applied and abstract ways, and can reason, solve problems and assess risk.

Mathematics is a creative discipline. The language of mathematics is international. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.

1. Key concepts

There are a number of key concepts that underpin the study of mathematics. Pupils need to understand these concepts in order to deepen and broaden their knowledge, skills and understanding.

1.1 Competence

Applying suitable mathematics accurately within the classroom and beyond.
Communicating mathematics effectively.
Selecting appropriate mathematical tools and methods, including ICT.
Creativity

Combining understanding, experiences, imagination and reasoningto construct new knowledge.
Using existing mathematical knowledge to create solutions to unfamiliar problems.
Posing questions and developing convincing arguments.

1.3 Applications and implications of mathematics

Knowing that mathematics is a rigorous, coherent discipline.
Understanding that mathematics is used as a tool in a wide range of contexts.
Recognising the rich historical and cultural roots of mathematics.
Engaging in mathematics as an interesting and worthwhile activity.
Critical understanding

Knowing that mathematics is essentially abstract and can be used tomodel, interpret or represent situations.
Recognising the limitations and scope of a model or representation.

2. Key processes

These are the essential skills and processes in mathematics that pupils need to learn to make progress.

2.1 Representing

Pupils should be able to:

identify the mathematical aspects of a situation or problem
choose between representations
simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models
select mathematical information, methods and tools to use.

2.2 Analysing

Use mathematical reasoning

Pupils should be able to:

make connections within mathematics
use knowledge of related problems
visualise and work with dynamic images
identify and classify patterns
make and begin to justify conjectures and generalisations, considering special cases and counter-examples
explore the effects of varying values and look for invariance and covariance
take account of feedback and learn from mistakes
work logically towards results and solutions, recognising the impact of constraints and assumptions
appreciate that there are a number of different techniques that can be used to analyse a situation
reason inductively and deduce.

Use appropriate mathematical procedures

Pupils should be able to:

make accurate mathematical diagrams, graphs and constructions on paper and on screen
calculate accurately, selecting mental methods or calculating devicesas appropriate
manipulate numbers, algebraic expressions and equations and apply routine algorithms
use accurate notation, including correct syntax when using ICT
record methods, solutions and conclusions
estimate, approximate and check working.

2.3 Interpreting and evaluating

Pupils should be able to:

form convincing arguments based on findings and make general statements
consider the assumptions made and the appropriateness and accuracy of results and conclusions
be aware of the strength of empirical evidence and appreciate the difference between evidence and proof
look at data to find patterns and exceptions
relate findings to the original context, identifying whether they support or refute conjectures
engage with someone else’s mathematical reasoning in the context of a problem or particular situation
consider the effectiveness of alternative strategies.

2.4 Communicating and reflecting

Pupils should be able to:

communicate findings effectively
engage in mathematical discussion of results
consider the elegance and efficiency of alternative solutions
look for equivalence in relation to both the different approaches to the problem and different problems with similar structures
make connections between the current situation and outcomes, and situations and outcomes they have already encountered.

3. Range and content

This section outlines the breadth of the subject on which teachers should draw when teaching the key concepts and key processes.

The study of mathematics should enable pupils to apply their knowledge, skills and understanding to relevant real-world situations.

The study of mathematics should include:

3.1 Number and algebra

rational numbers, their properties and their different representations
rules of arithmetic applied to calculations and manipulations with rational numbers
applications of ratio and proportion
accuracy and rounding
algebra as generalised arithmetic
linear equations, formulae, expressions and identities
analytical, graphical and numerical methods for solving equations
polynomial graphs, sequences and functions

3.2 Geometry and measures

properties of 2D and 3D shapes
constructions, loci and bearings
Pythagoras’ theorem
transformations
similarity, including the use of scale
points, lines and shapes in 2D coordinate systems
units, compound measures and conversions
perimeters, areas, surface areas and volumes

3.3 Statistics

the handling data cycle
presentation and analysis of grouped and ungrouped data, including time series and lines of best fit
measures of central tendency and spread
experimental and theoretical probabilities, including those based on equally likely outcomes

Curriculum opportunities

During the key stagestudents should be offered the following opportunities that are integral to their learning and enhance their engagement with the concepts, processes and content of the subject.

The curriculum should provide opportunities for pupils to:

develop confidence in an increasing range of methods and techniques
work on sequences of tasks that involve using the same mathematics in increasingly difficult or unfamiliar contexts, or increasingly demanding mathematics in similar contexts
work on open and closed tasks in a variety of real and abstract contexts that allow them to select the mathematics to use
work on problems that arise in other subjects and in contexts beyond the school
work on tasks that bring together different aspects of concepts, processes and mathematical content
work collaboratively as well as independently in a range of contexts
become familiar with a range of resources, including ICT, so that they can select appropriately.

Mathematics and the national curriculum aims

Mathematics has a distinctive contribution to make to the aims of the national curriculum. The mathematics programme of study provides opportunities to plan sequences of work, learning outcomes and teaching approaches that develop:

Successful learners

The curriculum aim – developing successful learners who are numerate, creative and enquiring and able to solve problems – is at the heart of the mathematics programme of study. The key concepts of applications and implications of mathematics and critical understanding enable pupils to find out about mathematical ideas that shape our world.

The mathematics programme of study develops pupils with enquiring minds who think for themselves, which is essential to being a successful learner. It provides opportunities for pupils to tackle problems with more than one approach and to solve open-ended problems. Pupils are given the opportunity to consider errors and misconceptions, which helps them to understand how they learn, as well as to learn from their mistakes. Communication and critical understanding encourage pupils to reason and evaluate, both independently and with others.

Confident individuals

The mathematics curriculum provides opportunities for pupils to develop confidence in an increasing range of methods and techniques. Pupils are given the opportunity to express their ideas using strategies they are familiar and secure with. This helps them communicate confidently and encourages them to believe in themselves. Peer and self-assessment opportunities allow pupils to consider where they are and how to move on, thus becoming increasingly confident and independent. Sharing feedback also allows them to express their ideas and suggestions and relate well to others. The mathematics programme of study encourages pupils to enjoy the challenge of trying new things and justifying their own views with evidence, through discussing different interpretations of ideas.

Responsible citizens

Pupils are able to prepare for life and work through the mathematics programme of study. It contributes the underpinning skills for financial capability that will prepare individuals to live safe, responsible and healthy lives. Similarly, the emphasis on analysing and justifying conclusions in mathematical situations helps prepare pupils for taking critical and analytical approaches to real-life situations.

An open mind and an appreciation of how different cultures have influenced society are important in understanding what it means to be a responsible citizen. The mathematics programme of study takes into account the rich historical and cultural roots of mathematics, encouraging pupils to appreciate the diverse nature of mathematics and recognise the role of mathematics in modern society. Through exploring real data pupils are able to investigate real-life issues and problems related to social justice, globalisation and environmental changes.

Mathematics, personal development and Every Child Matters

Personal development is a vital part of the key stage 3 curriculum and mathematics has a distinctive contribution to make in this area. The mathematics programme of study provides opportunities to plan sequences of work, learning outcomes and teaching approaches that support personal development through the five Every Child Matters outcomes.

Enjoy and achieve

Mathematics can be enjoyed as a worthwhile activity for its own sake and as a powerful tool in a wide range of applications. Enjoyment stems from the creative and investigative aspects of mathematics, from developing mathematical ways of perceiving the world and recognising underlying structures and connections between mathematical ideas.

Mathematics is a subject that empowers pupils to prove results. Pupils develop their problem-solving, decision-making and reasoning skills through working on a range of tasks.

Be healthy

Mathematics enables pupils to understand the numerical data related to becoming and staying healthy. Monitoring nutritional intake, blood sugar levels and cardiovascular health are all examples where mathematics assists understanding and can lead to making healthy decisions. By becoming financially capable, young people are able to exert greater control over factors affecting their health such as housing and money management. Strategy games and logic puzzles are an important part of maintaining mental health.

Stay safe

Understanding risk through the study of probability is a key aspect of staying safe and making balanced risk decisions. Pupils learn to understand the probability scale and use it as a way of communicating risk factors. They develop an understanding of how data leads to risk estimates. By understanding probability and risk factors young people are able to make informed choices about investments, loans and gambling.

Achieve economic wellbeing

An understanding of mathematics, and confidence in using a variety of mathematical skills, are both key to young people’s ability to play their part in modern society. The skills of reasoning with numbers, interpreting graphs and diagrams and communicating mathematical information are vital in enabling individuals to make sound economic decisions in their daily lives. Mathematics skills and habits of mind are highly prized by many employers and mathematics is a gatekeeper to many careers and professions.

Make a positive contribution

Having confidence and capability in mathematics allows pupils to develop their ability to contribute to arguments using logic, data and generalisations with increasing precision. This in turn allows pupils to take a greater part in a democratic society. Becoming skilled in mathematical reasoning means pupils learn to apply a range of mathematical tools in familiar and unfamiliar contexts

Developing personal, learning and thinking skills in mathematics

What are we trying to achieve?

The new secondary curriculum focuses on developing the skills and qualities that learners need to succeed in school and the broader community. The development of personal, learning and thinking skills (PLTS) is essential to meeting the three national curriculum aims of becoming successful learners, confident individuals and responsible citizens.

The individual subjects, which make up the curriculum, provide the essential range of activities, learning opportunities and contexts essential for the effective development of these skills (PLTS).

The framework comprises of six PLTS: