Mathematics and Numeracy
The development of mathematics has always gone hand in hand with the development of civilisation itself. A truly international discipline, it surrounds us and underpins so many aspects of our daily lives, such as architecture, art, music, money and engineering. And while it is creative and beautiful, both in its own right and in its applications, it is also essential for progress in other areas of learning and experience.
What is more, numeracy the application of mathematics to solve problems in real-world contexts plays a critical part in our everyday lives, and in the economic health of the nation. It is imperative, therefore, that mathematics and numeracy experiences are as engaging, exciting and accessible as possible for learners, and that these experiences are geared towards ensuring that learners develop mathematical resilience.
In the early years, play forms an important part in the development of mathematics and numeracy, enabling learners to solve problems, explore ideas, establish connections and collaborate with others. In later years, learners need to have opportunities to work both independently and collaboratively to build on the foundations established in the early years.
What matters in this Area has been expressed in four statements which support and complement one another and should not be viewed in isolation. Together they contribute to realising the four purposes of the curriculum.
What Matters Statements
- The number system is used to represent and compare relationships between numbers and quantities
Numbers are the symbol system for describing and comparing quantities. This will be the first abstract concept that learners meet in mathematics, and it helps to establish the principles of logical reasoning. In mathematics the number system provides learners with a basis for algebraic, statistical, probabilistic and geometrical reasoning, as well as for financial calculation and decision-making.
- Algebra uses symbol systems to express the structure of mathematical relationships
Algebra is the study of structures abstracted from computations and relations, and provides a way to make generalisations. Algebraic thinking moves away from context to structure and relationships. This powerful approach provides learners with the means to abstract important features and to detect and express mathematical structures of situations in order to solve problems. Algebra is a unifying thread running through the fabric of mathematics.
Algebraic thinking is essential for reasoning, modelling and solving problems in mathematics and in a wide range of real-world contexts, including technology and finance. Making connections between arithmetic and algebra develops skills for abstract reasoning from an early age.
- Geometry focuses on relationships involving shape, space and position, and measurement focuses on quantifying phenomena in the physical world
Geometry involves playing with, manipulating, comparing, naming and classifying shapes and structures. The study of geometry encourages the development and use of conjecture, deductive reasoning and proof. Measurement allows the magnitude of spatial and abstract features to be quantified, using a variety of standard and non-standard units. It can also support the development of numerical reasoning.
Reasoning about the sizes and properties of shapes and their surrounding spaces helps learners to make sense of the physical world and the world of mathematical shapes. Geometry and measurement have applications in many fields, including art, construction, science and technology, engineering, and astronomy.
- Statistics represent data, probability models chance, and both support informed inferences and decisions
Statistics is the practice of collecting, manipulating and analysing data, allowing representation and generalisation of information. Probability is the mathematical study of chance, enabling predictions of the likelihood of events occurring. Statistics and probability rely on the application and manipulation of number and algebra.
Managing data and representing information effectively provide learners with the means to test hypotheses, draw conclusions and make predictions. The process of reasoning with statistics and probability, and evaluating their reliability, develops critical thinking and analytical skills that are fundamental to enabling learners to make ethical and informed decisions.