Research-based guidance and classroom activities for teachers of mathematics

Functions as mathematical entities

Functions as mathematical entities is a theme within functional relations between variables. Links to relevant activities and resources are on the right hand side of this page. 

Objects in their own right

Eventually learners need to see functions as objects in their own right that can be transformed, combined, classified and categorised according to their characteristics, and used as inputs for more complex ideas and actions.

It is also helpful for learners to develop a repertoire of functions that can be used for conjecturing about relationships, and for modelling purposes. Typically, learners end up with a limited collection of continuous, differentiable, monotonic or symmetrical, calculable functions unless they have had to transform them to look unfamiliar, and have also experienced functions which do not behave in those ways.

Without this breadth, learners can base their assumptions on a limited class of functions and hence find further mathematics (especially real analysis) rather mysterious.