Representing numbers and figures in problem-solving activities in mathematics

JOSÉ GUSTAVO MORALES; MATÍAS A. SARACHO

Río de Janeiro

Workshop; Shapes 2.0: The Shape of Things. Workshop at 4th World Congress on Universal Logic; 2013

Department of Computer Science, University of Bremen, Germany & San Pablo University, Brasil.

In our paper we will rely on research by Grosholz (2007) considering her thesis of the irreducibility of iconic representation in mathematics. Against this background, our aim will be to discuss the epistemic value of “shape” or iconicity in diagrammatic representations in geometry. We show that iconic aspects of diagrams reveal structural relations underlying the method to solve quadrature problems developed by Leibniz (1675/76). As a concluding remark, we shall argue that in retrieving the information embedded in a diagram the reader must establish a meaningful relationship between the information supplied by the diagram and the relevant background knowledge which often remains implicit.