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NSW Syllabuses

Working Mathematically

Working Mathematically is integral to the learning process in mathematics. It provides students with the opportunity to engage in genuine mathematical activity and develop the skills to become flexible, critical and creative users of mathematics. In this syllabus, Working Mathematically builds on the skills developed in Stage 5, and encompasses six interrelated aspects which form the focus of the syllabus:

The Working Mathematically diagram shows a central circle labelled Working Mathematically. This is surrounded by six overlapping circles representing the six aspects of Working Mathematically. The aspects are: Fluency –  Recall factual knowledge and concepts, and select and apply appropriate procedures flexibly, accurately and efficiently; Understanding – Make connections between experiences and related concepts, and progressively expand and develop ideas; Justification – Justify strategies and strategic thinking used, conclusions reached and explain the reasonableness of findings, proving results where appropriate; Problem Solving – Interpret, formulate, investigate, model and solve problems, using mathematics in simple and complex, familiar and unfamiliar situations; Reasoning – Analyse, evaluate, explain, infer, generalise, deduce and reach conclusions; Communicating – Describe, represent, formulate, express and explain mathematical situations, concepts, methods and solutions to problems using a variety of presentations utilising appropriate language, notation or diagrams.

These six aspects of Working Mathematically are embedded across the range of syllabus objectives, outcomes and topics. Teachers extend students' level of proficiency in Working Mathematically by creating opportunities for development through a range of teaching and learning activities. 

The two key components of assessment are created from these aspects:

Understanding, Fluency and Communicating
Problem Solving, Reasoning and Justification