Characterizing Practices Associated with Functions in Middle School Textbooks: An Empirical Approach

Exercises and problems about functions found in 24 middle-school textbooks from 15 countries were analysed using an adaptation of Balacheff's theory of conceptions and Biehler's notion of the prototypical domain of application of concepts in order to describe the practices associated with the notion of function. The analysis yielded five different practices — symbolic rule, ordered pair, social data, physical phenomena, and controlling image — that were present both across and within the textbooks analysed. The existence of different practices might help to explain the compartmentalised and sometimes contradictory notions that students and teachers have about functions and might shed light on the processes of designing curriculum and instruction on functions.