Flexibility and coordination among acts of visualization and analysis in a pattern generalization activity

This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students’ attempt to reach a general formula for a three-dimensional pattern generalizing task.The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate the number of blocks in a three-dimensional tower of different heights. The students’ activity was video- and audio-taped, fully transcribed and lasted for 50 min.The analysis discloses several instances of how the students were linking acts of visualization and analysis to reach a general formula. However, regarding flexibility, we found that it was more natural for the students to change visual format than to change analytical position and direction in their attempts to generalize the three-dimensional pattern of the task in a closed formula.

► We study flexibility and coordination of visualization and analysis in a generalizing task.
► A case study of the work of two 15-year-old students is conducted.
► The Visualization/analysis model is used as an analytical lens.
► Hard to analytical, mathematical position.
► Easier to change visual format.