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 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 students with uniquely powerful ways to describe, analyse
and change the world. Students who are functional in mathematics and financially
capable are able to think independently in applied and abstract ways, to
reason, to solve problems and to assess risk.
Mathematics is a creative discipline. It can stimulate moments of pleasure
and wonder for all students 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.
Students 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.
- 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 and proof as a tool for solving problems.
- Questioning, analysing and evaluating mathematical solutions.
Key processes
These are the essential skills and processes in mathematics that students
need to learn to make progress.
Representing
Students should be able to:
- identify the mathematical aspects of the
situation or problem (IE1 identify questions to answer and problems to
resolve)
- compare and evaluate representations of a situation before making a
choice
- simplify the situation or problem in order to represent it mathematically
using appropriate variables, symbols and diagrams and models
- select mathematical information methods,
tools and models to use (IE4 analyse and evaluate information, judging
its relevance and value).
Analysing
Use mathematical reasoning
Students 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 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
- identify a range of techniques that could be used to tackle a problem,
appreciating that more than one approach may be necessary
- reason inductively and deduce.
Use appropriate mathematical procedures
Students 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
Students should be able to:
- form convincing arguments to justify findings
and general statements (IE6 support conclusions, using reasoned arguments
and evidence)
- consider the assumptions made and the appropriateness and accuracy of
results and conclusions
- appreciate the strength of empirical evidence
and distinguish between evidence and proof (IE4 analyse and evaluate information,
judging its relevance and value).
- look at data to find patterns and exceptions
- relate their findings to original question or conjecture, and indicate
reliability
- make sense of someone else's findings and
judge their value in the light of the evidence they present (IE3 explore
issues, events or problems from different perspectives)
- critically examine strategies adopted.
Communicating and reflecting
Students should be able to:
- use a range of forms to communicate findings to different audiences
- 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 (IE3 explore issues, events or problems from different perspectives)
- give examples of similar contexts met previously
and identify how they differed from or were similar to the current situation
and how and why the same, or different, strategies were used (IE6 support
conclusions, using reasoned argument and evidence).
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 students to apply their knowledge,
skills and understanding to relevant real-world situations.
The study of mathematics should include:
Number and algebra
- real numbers and their different representations
- rules of arithmetic applied to calculations and manipulations with real
numbers including standard index form and surds
- proportional reasoning, direct and inverseproportion, proportional change
and exponential growth
- upper and lower bounds
- linear and quadratic equations in one unknown
- simultaneous equations
- graphs of exponential and trigonometric functions
- transformation of functions
- graphs of simple loci
Geometry and measures
- properties of 2D and 3D shapes, and their applications including constructions,
loci, geometric proof, Pythagoras' theorem, circle theorems and trigonometrical
relationships
- properties and combinations of transformations including enlargements
with negative scale factors
- 3D coordinate systems
- vectors in 2 dimensions
- conversions between measures and compound measures
- perimeters, areas, surface areas and volumes including those associated
with parts of a circle
Statistics
- presentation and analysis of large sets of grouped and ungrouped data
including box plots and histograms, lines of best fit and their interpretation
- measures of central tendency and spread
- experimental and theoretical probabilities of single and combined events
- applying statistics to enable comparisons and give evidence for associations
and relationships.
Curriculum opportunities
During the key stage students 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 students 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 students 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
- 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. (IE2 plan and carry
out research, appreciating the consequences of decisions)
