Using Dynamic Sketches to Enhance Preservice Secondary Mathematics Teachers' Understanding of Limits of Sequences

This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in the contexts of various sequences, coupled with answering carefully chosen questions and completing interview tasks before, during, and after technology-enhanced instruction, gave the participants opportunities to investigate and reflect on their own concept image as they compared their understandings to the results of the actions they performed on the sketch. The participants modified their conceptions of limit and strengthened their understandings of formal limit ideas as they integrated the visual representation with the symbolic definition.