The function concept: Making connections within and between representations

Year: 1994

Author: Ryan, Julie

Type of paper: Abstract refereed

The function concept is a crucial one in secondary school mathematics. It can be seen as a unifying idea throughout the algebra curriculum, yet its potential for creating a structured learning environment has not been fully examined. Students have difficulties with various representations for function: set-theoretic, tabular, algebraic and geometric representations. It is the nature of the connections within and between representations that is worth investigation.

A learned dependence also on one or other representation may be a reason for student difficulties with the translation process between representations. It is a common experience for teachers to see their students floundering with the algebraic form when the graphical form presents a more efficient problem-solving strategy.

Current practice in Australian schools most usually develops the intuitive base for function with tabular representation or input- output values (e.g., "Guess my rule"). The subsequent attempts to link symbolic and geometric representations through graphical work may assume that each representation is without its own difficulties. This study considers student difficulties with the various representations and attempts to identify levels of learning with a view to providing a developmental sequence for classroom use.