Forty Swedish elementary students, 7-12 years of age and working in pairs, constructed a series of bar graphs and pie charts using a graphing application software as an instructional tool under the guidance of the researcher. After successive withdrawal of help, each pair drew a small number of graphic displays manually at the end of the data collection period. Evidence is provided that children's engagement with the graphing application software enhanced their understanding of essential graphical ideas and that even the youngest students appropriated and talked insightfully about a number of critical aspects of graphing. The students' gradual mastering of different aspects of graphing is argued to be movements within their "zones of proximal development" towards a more competent use of graphs. (Contains 8 figures.)