2. Key processes
These are the essential skills and processes in mathematics that pupils need to learn to make progress.
2.1 Representing
Pupils should be able to:
 identify the mathematical aspects of a situation or problem
 choose between representations
 simplify the situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models
 select mathematical information, methods and tools to use.
2.2 Analysing
(Use mathematical reasoning
Pupils should be able to:
 make connections within mathematics
 use knowledge of related problems
 visualise and work with dynamic images
 identify and classify patterns
 make and begin to justify conjectures and generalisations, considering special cases and counterexamples
 explore the effects of varying values and look for invariance and covariance
 take account of feedback and learn from mistakes
 work logically towards results and solutions, recognising the impact of constraints and assumptions
 appreciate that there are a number of different techniques that can be used to analyse a situation
 reason inductively and deduce.
Use appropriate mathematical procedures Pupils should be able to:
 make accurate mathematical diagrams, graphs and constructions on paper and on screen
 calculate accurately, selecting mental methods or calculating devices as appropriate
 manipulate numbers, algebraic expressions and equations and apply routine algorithms
 use accurate notation, including correct syntax when using ICT
 record methods, solutions and conclusions
 estimate, approximate and check working.
2.3 Interpreting and evaluating
Pupils should be able to:
 form convincing arguments based on findings and make general statements
 consider the assumptions made and the appropriateness and accuracy of results and conclusions
 be aware of the strength of empirical evidence and appreciate the difference between evidence and proof
 look at data to find patterns and exceptions
 relate findings to the original context, identifying whether they support or refute conjectures
 engage with someone else’s mathematical reasoning in the context of a problem or particular situation
 consider the effectiveness of alternative strategies.
2.4 Communicating and reflecting
Pupils should be able to:
 communicate findings effectively
 engage in mathematical discussion of results
 consider the elegance and efficiency of alternative solutions
 look for equivalence in relation to both the different approaches to the problem and different problems with similar structures
 make connections between the current situation and outcomes, and situations and outcomes they have already encountered.
