Defining moments in the graphing calculator solution of a cubic function task

A case study investigated cognitive, mathematical, and technological processes undertaken by senior secondary students as they searched for a complete graph of a difficult cubic function using a graphing calculator. Intensive qualitative macroanalysis identified several defining moments in the solution process. Those related to use of scale marks and identification of key function features are presented. Students’ understanding of scale marks varied and this impacted on the efficiency and elegance of their solution. A range of calculator features was used in identifying key feature coordinates. These were not always used successfully or with an understanding of the mathematics underpinning their operation.