Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships. The symbolic nature of Mathematics provides a powerful, precise and concise means of communication.
Mathematical ideas have evolved across all cultures over thousands of years and are constantly developing. Digital technologies facilitate this expansion of ideas, providing access to new tools for continuing mathematical exploration and invention. Mathematics is integral to scientific and technological advances in many fields of endeavour. In addition to its practical applications, the study of Mathematics is a valuable pursuit in its own right, providing opportunities for originality, challenge and leisure.
Mathematics in K–10 provides students with knowledge, skills and understanding in Number and Algebra, Measurement and Geometry, and Statistics and Probability. It focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, communication, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing strategies to make informed decisions and solve problems relevant to their further education and everyday lives.
The ability to make informed decisions and to interpret and apply Mathematics in a variety of contexts is an essential component of students' preparation for life in the 21st century. To participate fully in society, students need to develop the capacity to critically evaluate ideas and arguments that involve mathematical concepts or that are presented in mathematical form.
The Mathematics curriculum makes clear the links between its various components, as well as the relationship between Mathematics and other disciplines. Students learn to apply their mathematical knowledge, skills and understanding in a broad range of contexts beyond the Mathematics classroom, including in such core learning areas as Science, Geography, History and English.
The study of Mathematics provides opportunities for students to appreciate the elegance and power of mathematical reasoning and to apply mathematical understanding creatively and efficiently. The study of the subject enables students to develop a positive self-concept and become self-motivated learners through inquiry and active participation in challenging and engaging experiences.
The aim of Mathematics in K–10 is for students to:
- be confident, creative users and communicators of the subject, able to investigate, represent and interpret situations in their personal and work lives and as active citizens
- develop an increasingly sophisticated understanding of mathematical concepts and fluency with mathematical processes, and be able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability
- recognise connections between Mathematics and other disciplines and appreciate Mathematics as an accessible, enjoyable discipline to study, and an important aspect of lifelong learning.
Knowledge, skills and understanding
- develop understanding and fluency in Mathematics through inquiry, exploring and connecting concepts, choosing and applying problem-solving skills and techniques, communication and reasoning
Number and Algebra
- develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation
Measurement and Geometry
- identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems
Statistics and Probability
- collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgments.
Values and attitudes
- appreciate Mathematics as an essential and relevant part of life, recognising that its cross-cultural development has been largely in response to human needs
- demonstrate interest, enjoyment and confidence in the pursuit and application of mathematical knowledge, skills and understanding to solve everyday problems
- develop and demonstrate perseverance in undertaking mathematical challenges.
The continuum of learning in Mathematics K–10 table is an overview of the sub-strands, objectives and outcomes in each of the content strands.
The concepts in each of these strands are developed across the stages to show that understanding in the early years must precede understanding in later years. In this way, the continuum of learning table provides an overview of the sequence of learning for particular concepts in Mathematics. It links content typically taught in primary Mathematics classrooms with content typically taught in secondary Mathematics classrooms. It illustrates assumptions about prior learning and indicates pathways for further learning.
In this syllabus, it is generally the case that content is not repeated. This is intentional and is not meant to suggest that review and consolidation are not necessary. When programming, it will be necessary for teachers to determine the level of achievement of outcomes in previous stages before planning new teaching and learning experiences. Students may be operating at different stages for different strands of the continuum of learning. For example, a student may be working on Stage 4 content in the Number and Algebra strand but be working on Stage 3 content in the Measurement and Geometry strand.
It is not intended that the continuum of learning table be used as a checklist of teaching ideas. Rather, a variety of learning experiences need to be planned and presented to students to maximise opportunities for achievement of outcomes. Students need appropriate time to explore, experiment and engage with the underpinning concepts and principles of what they are to learn.