In maths, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content.
Understanding is where students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and when they interpret mathematical information.
Fluency develops skills which allow students to calculate answers efficiently, recognise robust ways of answering questions, choose appropriate methods and approximations, and recall definitions and regularly use facts.
In problem-solving students formulate and solve problems using mathematics to represent unfamiliar or meaningful situations, they design investigations and plan approaches using existing and developing strategies.
Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.