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Constructionism: Intrinsic and extrinsic perspectives

Chronis Kynigos

 

 

In this paper we report findings of a classroom research aiming at shedding light on 12 year-old students’ construction processes as they worked with a 3d Logo / Turtle Geometry environment which we call ‘MachineLab Turtleworlds’ (MaLt). Illustrative examples of students’ work are provided trying to examine in particular: a) the way the students used the software’s functionalities of changing viewing angles throughout the construction processes, b) the interplay between the turtle metaphor and space visualisation through various viewing angles, c) the interplay between the perception of figures considered in relation to different viewpoints and in relation to their geometric properties. The analysis of the results brings in the foreground the dialectic relationship between the way the available viewing angle manipulation tools were used and the construction strategies followed, within the framework of particular tasks. It seems that the 3d space was experienced by the students through two distinct perspectives: an intrinsic and an extrinsic one. When the students were focusing on navigating and orientating the turtle, the 3d space was experienced through an intrinsic perspective, according to which the simulated space was viewed from inside, through the turtle’s viewpoint. In this case the use of the body-syntonic metaphor was critical but yet not the same as conventional 2d turtle geometry. In contrast, when the focus was shifted from the management of the turtle’s spatial movements to the construction of a graphic object, the 3d space was experienced through an extrinsic perspective, from the view point of an external observer who looked at the figural results of turtle’s movement.

 


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