The Essential Summary (links may not work as this is a copy of a 2010 set of Information, now archived
Importance of Mathematics key stage 3
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.
Key concepts of Mathematics key stage 3
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.
Applying suitable mathematics accurately within the classroom and beyond.
Communicating mathematics effectively.
Combining understanding, experiences, imagination and reasoning
to 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.
1.4 Critical understanding
Knowing that mathematics is essentially abstract and can be used to
model, interpret or represent situations.
Recognising the limitations and scope of a model or representation.
Study of mathematics: This is concerned with the learning processes for mathematics.
Applying suitable mathematics: This requires fluency and confidence in a range of mathematical techniques and processes that can be applied in a widening range of familiar and unfamiliar contexts, including managing money, assessing risk, problem-solving and decision-making.
Communicating mathematics: Pupils should be familiar with and confident about mathematical notation and conventions and be able to select the most appropriate way to communicate mathematics, both orally and in writing. They should also be able to understand and interpret mathematics presented in a range of forms.
Mathematical tools: Pupils should be familiar with a range of resources and tools, including graphic calculators, dynamic geometry and spreadsheets, which can be used to work on mathematics.
Mathematical methods: At the heart of mathematics are the concepts of equivalence, proportional thinking, algebraic structure, relationships, axiomatic systems, symbolic representation, proof, operations and their inverses.
Posing questions: This involves pupils adopting a questioning approach to mathematical activity, asking questions such as ‘How true?’ and ‘What if…?’
Mathematics is used as a tool: This includes using mathematics as a tool for making financial decisions in personal life and for solving problems in fields such as building, plumbing, engineering and geography. Current applications of mathematics in everyday life include internet security, weather forecasting, modelling changes in society and the environment, and managing risk (eg insurance, investments and pensions). Mathematics can be used as a way of perceiving the world, for example the symmetry in architecture and nature and the geometry of clothing.
Historical and cultural roots of mathematics: Mathematics has a rich and fascinating history and has been developed across the world to solve problems and for its own sake. Pupils should learn about problems from the past that led to the development of particular areas of mathematics, appreciate that pure mathematical findings sometimes precede practical applications, and understand that mathematics continues to develop and evolve.
Limitations and scope: Mathematics equips pupils with the tools to model and understand the world around them. This enables them to engage with complex issues, such as those involving financial capability or environmental dilemmas. For example, mathematical skills are needed to compare different methods of borrowing and paying back money, but the final decision may include other dimensions, such as comparing the merits of using a credit card that promotes a particular charity with one offering the lowest overall cost. The mathematical model or representation may have properties that are not relevant to the situation.