Spatial Structuring in 1st Grade: from local structuring to global structuring

Abstract In this paper, we aim to understand how 1st grade students develop their spatial structuring of 2D figures composed by squares (pentominoes) by analyzing students' strategies to compose pentominoes, to determine the congruency between pentominoes and to anticipate composites, and the importance of drawing the constructions. Data was collected during the implementation of the first sequence of tasks, from cycle two, of a design-based research. Results show that, at first, students build pentominoes by manipulating squares individually and by trial and error, which is a strategy associated to local structuring. Gradually, students evolve in their capacity of coordinating components and composites, stimulated by the relationships they stablish and reflect upon between manipulatives and drawings. As they stablish more complex relationships, based on the coordination of components and composites, they start to be able to build with anticipation. Building with anticipation, based on mental images, suggests the use of integration operation, which is associated with global structuring. Students use movements as rotating and flipping, at first, with manipulatives and later mentally to determine the congruency between two pentominoes and to anticipate the result of pentominoes manipulation.