Using drawings and generating information in mathematical problem solving processes

Abstract

The purpose of this paper is to investigate how drawings can contribute to generating new information when solvers use drawings in solving mathematical problems. For this purpose, two episodes, in which drawings enabled a solver to find ideas useful for his solutions, were qualitatively and closely analyzed, especially focusing on what roles drawings could play when the solver found new information about the problem situations. The analysis demonstrates the following aspects of use of drawings: (a) drawings can contribute to information generation by producing unexpected combinations or configurations of elements solvers identified in the problem situations previously, which led the solver to recognizing emergent patterns; (b) the use of drawings includes cyclic processes, through which the solver's understanding of the problem situations and his way of interacting with drawings varied each other. Implications for instruction will be also discussed on the basis of such aspects. Copyright © 2006 by Moment.