The proficiencies of Understanding, Fluency, Problem Solving and Reasoning are fundamental to learning mathematics and working mathematically and are applied across all three strands Number and Algebra, Measurement and Geometry, and Statistics and Probability. Understanding refers to students building a robust knowledge of adaptable and transferable mathematical concepts and structures. Students make connections between related concepts and progressively apply the familiar to develop new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Students build understanding when they:
connect related ideas
represent concepts in different ways
identify commonalities and differences between aspects of content
describe their thinking mathematically
interpret mathematical information.
Fluency describes students developing skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they:
make reasonable estimates
calculate answers efficiently
recognise robust ways of answering questions
choose appropriate methods and approximations
recall definitions and regularly use facts,
can manipulate expressions and equations to find solutions.
Problem-solving is the ability of students to make choices, interpret, formulate, model and investigate problem situations, select and use technological functions and communicate solutions effectively. Students pose and solve problems when they:
use mathematics to represent unfamiliar or meaningful situations
design investigations and plan their approaches
apply their existing strategies to seek solutions
verify that their answers are reasonable.
Reasoning refers to students developing an increasingly sophisticated capacity for logical, statistical and probabilistic thinking and actions, such as conjecturing, hypothesising, analysing, proving, evaluating, explaining, inferring, justifying, refuting, abstracting and generalising. Students are reasoning mathematically when they:
explain their thinking
deduce and justify strategies used and conclusions reached
adapt the known to the unknown
transfer learning from one context to another
prove that something is true or false
make inferences about data or the likelihood of events
compare and contrast related ideas and explain their choices.
Information Communication Technologies and Mathematics Information Communication Technologies (ICT) are powerful tools that can support student learning. Students can develop and demonstrate their understanding of concepts and content in Mathematics using a range of ICT tools. It is also important that students know how to use these ICT efficiently and responsibly, as well as learning how to protect themselves and secure their data.