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The AusVELS curriculum is described by levels. This document provides advice on the nature of learners, by level and age and the relevant curriculum:
The ‘Towards Foundation Level AusVELS’ Levels A to D (Students with Disabilities) focusses on progressing students from a pre-intentional to intentional state, and are not associated with any set age or year level that links chronological age to cognitive progress.
These levels lay the foundation for learning mathematics. Students at this level can access powerful mathematical ideas relevant to their current lives and learn the language of mathematics, which is vital to future progression.
Children have the opportunity to access mathematical ideas by developing a sense of number, order, sequence and pattern; by understanding quantities and their representations; by learning about attributes of objects and collections, position, movement and direction, and by developing an awareness of the collection, presentation and variation of data and a capacity to make predictions about chance events.
Understanding and experiencing these concepts in the early levels provides a foundation for algebraic, statistical and numerical thinking, that will develop in subsequent levels. These foundations also enable children to pose basic mathematical questions about their world, to identify simple strategies to investigate solutions, and to strengthen their reasoning to solve personally meaningful problems.
These levels emphasise the importance of students studying coherent, meaningful and purposeful mathematics that is relevant to their lives. Students still require active experiences that allow them to construct key mathematical ideas, but also gradually move to using models, pictures and symbols to represent these ideas.
The curriculum develops key understandings by extending the number, measurement, geometric and statistical learning from the early levels; by building foundations for future studies through an emphasis on patterns that lead to generalisations; by describing relationships from data collected and represented; by making predictions; and by introducing topics that represent a key challenge in these levels, such as fractions and decimals.
In these levels of schooling, it is particularly important for students to develop a deep understanding of whole numbers to build reasoning in fractions and decimals and to develop a conceptual understanding of place value. These concepts allow students to develop proportional reasoning and flexibility with number through mental computation skills, and to extend their number sense and statistical fluency.
These levels of school mark a shift in mathematics learning to more abstract ideas. Through key activities such as the exploration, recognition and application of patterns, the capacity for abstract thought can be developed and the ways of thinking associated with abstract ideas can be illustrated.
The foundations built in previous levels prepare students for this change. Previously established mathematical ideas can be drawn upon in unfamiliar sequences and combinations to solve non-routine problems and to consequently develop more complex mathematical ideas. However, students of this age also need an understanding of the connections between mathematical concepts and their application in their world as a motivation to learn. This means using contexts directly related to topics of relevance and interest to this age group.
During these levels, students need to be able to represent numbers in a variety of ways; to develop an understanding of the benefits of algebra, through building algebraic models and applications and the various applications of geometry; to estimate and select appropriate units of measure; to explore ways of working with data to allow a variety of representations; and to make predictions about events based on their observations.
The intent of the curriculum is to encourage the development of important ideas in more depth, and to promote the interconnectedness of mathematical concepts. An obvious concern is the preparation of students intending to continue studying mathematics in the senior secondary levels. Teachers will, in implementing the curriculum, extend the more mathematically able students by using appropriate challenges and extensions within available topics. A deeper understanding of mathematics in the curriculum enhances a student’s potential to use this knowledge to solve non-routine problems, both at this level of study and at later stages.
Level 10A content descriptors indicate optional additional content suitable for development of student mathematical background in preparation for further study of functions, algebra, and calculus; as well as other additional content related to statistics and trigonometry.
Teachers can incorporate a selection of this and other additional content in Level 10 mathematics courses, as applicable for extension and enrichment purposes, and to prepare students for subsequent study of various implementations of General Mathematics Units 1 and 2 and/or Mathematical Methods (CAS) Units 1 and 2 in Level 11.
Where additional material is included in particular as preparation for subsequent study of Mathematical Methods (CAS) Units 1 and 2, content relating to an introductory treatment of logarithmic functions and circular functions (as functions of a real variable) will be helpful. This could include related algebra and solving simple equations, as well as some simple transformations of graphs, especially in modelling contexts. Students should also be familiar with corresponding work on sets, including relevant notation, that underpins the study of functions, algebra, calculus and probability; as well as the use of technology for numeric, graphic and symbolic computation.
The AusVELS - Mathematics Scope and Sequence chart is available from the VCAA website.