The Shape of Fairness

Abstract

Shape and form are often used as mathematical models of situations. For example, teachers explain that light travels in a line or that the shadow cast by a person is related by similar triangles to that cast by a flagpole. Yet despite the common use of mathematical models in the sciences and in design professions, children rarely have the opportunity to participate in this form of mathematical thinking. In this article, we describe how first and second graders modeled a “fair” playing space in a game of tag called “Mother, may I?” The children modeled the playing space by using a succession of different forms, such as lines and squares, to represent a fair game, discovering along the way the properties of each of the forms that made them less-than-ideal models of fairness. Participation in the game gave the children many opportunities to think about important concepts in measuring length and the idea of using form to model a situation.