AbstractMultiple representation software was used here as the core of the algebra curriculum of eighth graders (age 14 years) learning algebraic functions and graphs. The connection between the symbolic representation of functions and their graphs received special emphasis. Thirty‐five students met 20 times over a 3‐month period in computer‐facilitated lessons. Data was gathered through observations of class work and the results of five paper‐and‐pencil tasks. Three aspects of student perceptions of the concept of function were examined: identification and classification of families of functions, identification of the connections between inclination and slope of graphs, and the distinction between the properties of a function and its picture. Results of student performance on the tasks were analyzed primarily in terms of the type of arguments they used—either standard algebraic computation techniques, visual considerations, or a combination of both. Findings indicated that although the software and the method of teaching both promoted student inventiveness—i.e. original and unexpected conjectures—and enhanced their understanding of the three aspects of function examined, connection between the algebraic manipulations and visual representation did not occu