Curriculum aims
Learning and undertaking activities in mathematics contribute to achievement
of the curriculum aims for 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.
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
both personal and public decision-making. Mathematics is fundamental to national
prosperity in providing tools, for understanding of science, engineering and
technology, and for participation in the knowledge economy. The language of
mathematics is international. The subject transcends cultural boundaries and
its importance is universally recognised.
Mathematics equips pupils with uniquely powerful ways to describe, analyse
and change the world. Pupils who are functional in mathematics and financially
capable are able to think independently in applied and abstract ways, to reason,
solve problems and assess risk.
Mathematics is a creative discipline. 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.
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.
Competence in mathematical procedures
- Applying mathematical processes and algorithms accurately to a widening
range of familiar and unfamiliar contexts within the classroom and beyond
including managing money and other everyday uses of mathematics. (IE3 explore issues, events or problems from different perspectives)
- Making choices about effective ways to communicate mathematical understanding. (IE4 analyse and evaluate information, judging its relevance and value)
- Using mathematical terminology and ideas accurately and coherently in
spoken and written forms. (IE4 analyse and evaluate information, judging its relevance and value)
- Reading and understanding texts with mathematical content.
Creativity
- Making connections between different areas of mathematics and between
mathematical techniques and problems or situations.
- Using existing mathematical knowledge to create solutions to unfamiliar
problems.
- Posing questions and developing appropriate lines of enquiry (IE2 plan and carry out research, appreciating the consequences of decisions).
Appreciation of mathematics
- Understanding that mathematics is both a tool for solving problems and
a discipline with distinct structure.
- Gaining a sense of the history of mathematics and exploring how the mathematics
of different cultures is present in modern mathematics (IE3 explore issues, events or problems from different perspectives).
- Being aware of some current applications of mathematics.
- Appreciating mathematics as an interesting and enjoyable activity in itself.
Critical understanding in using mathematics
- Recognising that a situation or problem can be represented using mathematics,
that it can be represented in different ways and making connections between
these representations.
- Using mathematical ideas and models to explore real world issues and problems,
recognising that solutions may need to take account of wider factors (IE3 explore issues, events or problems from different perspectives).
- Using deductive reasoning as a tool for solving problems.
- Questioning, analysing and evaluating mathematical solutions.
Key processes
These are the essential skills and processes in mathematics that pupils need
to learn to make progress.
Representing
Pupils should be able to:
- identify the mathematical aspects of the situation or problem (IE1 identify questions to answer and problems to resolve)
- 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 (IE4 analyse and evaluate information, judging its relevance and value).
Analysing
Use mathematical reasoning
Pupils should be able to:
- make connections within mathematics
- use knowledge of related problems
- visualise and work with dynamic images
- look for and examine patterns and classify
- make and begin to justify conjectures and generalisations, considering
special cases and counter examples (IE6 support conclusions, using reasoned arguments and evidence)
- explore the effects of varying values and look for invariance
- 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, using a calculator when 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.
Interpreting and evaluating
Pupils should be able to:
- form convincing arguments based on findings and make general statements (IE6 support conclusions, using reasoned arguments and evidence)
- consider the assumptions made and the appropriateness and accuracy of
results and conclusions
- be aware of strength of empirical evidence and appreciate the difference
between evidence and proof (IE4 analyse and evaluate information, judging its relevance and value)
- 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 (IE3 explore issues, events or problems from different perspectives)
- consider whether alternative strategies may have helped or been better.
Communicating and reflecting
Pupils should be able to:
- communicate findings in a range of forms
- 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 ones
they have met before.
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:
Number and algebra
- rational numbers and their different representations
- rules of arithmetic applied to calculations and manipulations with rational
numbers
- applications of ratio and proportion
- accuracy and rounding
- algebraic expressions, formulae, equations, inequalities and identities
including index notation and the use of brackets to indicate precedence
- simultaneous linear equations in algebraic and graphical forms
- sequences, including those arising from rules, in a variety of contexts
- graphs of polynomial functions and their properties
Geometry and measures
- properties of 2D and 3D shapes and their applications, including constructions,
loci and bearings, deductive reasoning and Pythagoras' theorem
- transformations, similarity and congruence including the use of scale
- points, lines and shapes in 2D coordinate systems
- units, compound measures and conversions
- perimeters, areas, surface areas and volumes
Statistics
- 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
- applying statistics to enable comparisons.
Curriculum opportunities
During the key stage pupils should be offered the following opportunities,
which 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:
- 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 pupils 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 mathematical content,
involving use of several of the key processes, or require using the handling
data cycle (IE4 analyse and evaluate information, judging its relevance and value)
- work collaboratively as well as independently to solve mathematical problems
in a range of contexts, evaluating their own and others' work and responding
constructively
- use a variety of resources when solving problems or carrying out mathematical
procedures.