The use of visualization for learning and teaching mathematics

In this article, based on Dissection-Motion-Operations, DMO (decomposing a figure into several pieces and composing the resulting pieces into a new figure of equal area), a set of visual representations (models) of mathematical concepts will be introduced. The visual models are producible through manipulation and computer GSP/Cabri software. They are based on the van Hiele’s Levels (van Hiele, 1989) of Thought Development; in particular, Level 2 (Informal Deductive Reasoning) and level 3 (Deductive Reasoning). The basic theme for these models has been visual learning and understanding through manipulatives and computer representations of mathematical concepts vs. rote learning and memorization. The three geometric transformations or motions: Translation, Rotation, Reflection and their possible combinations were used; they are illustrated in several texts. As well, a set of three commonly used dissections or decompositions (Eves, 1972) of objects was utilized