The disposition, confidence and capability to use mathematics for life, learning and work
Students at this level are willing to have a go at using mathematics they are familiar with to understand situations.
They are beginning to identify mathematical ideas within their interest areas. With prompting, they will consider whether mathematics might help in tackling a problem. They are willing to follow familiar mathematical steps to solve problems or tackle practical tasks. They regularly check their working and that their answers are accurate and make sense.
Students at this level reliably use the mathematics they know to help solve problems they are working through.
They can identify and describe when mathematics is used in a situation, task or problem. They look for mathematical solutions. They can identify and organise mathematical information and use mathematical techniques unprompted. They will respond to mathematical claims made by others and seek help to make sense of them.
Students at this level make use of their growing repertoire of mathematical strategies to explore unfamiliar situations.
They appreciate that mathematics has application in their lives so they look to see if mathematics might help. They can systematically restate a familiar problem type in mathematical terms. They select and sequence the mathematical steps they intend to use. They explain their working and where necessary will look for another way to solve the problem. When presented with claims that use mathematics they will check to see if the mathematics makes sense.
Students at this level are competent and confident users of mathematics in their lives.
They appreciate mathematics is helpful in making sense of the world and can explain how seeing the world mathematically opens up new possibilities. They understand that a mathematical model is a simplified representation of phenomenon. They can interpret unfamiliar formulae, transform mathematical information from one form to another, and explain and justify their decisions as they work. They persist when the problems are challenging and are willing to ask for help when they don’t understand the mathematics. They analyse the mathematics they or others choose to use. They are learning to deal with the constraints of a situation and specifications built into a task.
Students at this level understand the systematic nature of mathematics and the power of it in modelling the physical or social environment.
At this level students show persistence, autonomy and flexibility in using mathematics to help with understanding situations, solving problems or completing practical tasks. They can question the assumptions of a mathematical model and its suitability in a given situation. They can generalise from one situation to another and rethink problem conditions and constraints. They have the motivation to look for how mathematics might help – even when it is not immediately obvious that it will. They recognise that there are limits to mathematics in understanding and explaining situations and look to identify its misuse by others. They use rigorous mathematical arguments to support their methods and conclusions and their critique of other’s mathematical claims.