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