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Anais do IHC'2001 - Departamento de Informática e Estatística - UFSC

Anais do IHC'2001 - Departamento de Informática e Estatística - UFSC

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<strong>Anais</strong> <strong>do</strong> IHC’2001 - IV Workshop sobre Fatores Humanos em Sistemas Computacionais 231<br />

changes the center of rotation and adjusting the endpoint changes the angle of rotation.<br />

Similarly, Sli<strong>de</strong> and Flip cause visual representations of geometrical concepts to appear and<br />

be available for manipulation. Translations are obtained by manipulating a directed<br />

resizable vector with three handles: head, center and tail. Manipulations of the head and tail<br />

alter the direction or the length of the vector, causing the ghost image of the object to shift<br />

its location, whereas manipulations of the center of the vector cause no changes to the<br />

ghost image. Reflection is obtained by manipulating an axis of reflection with two handles.<br />

One controls the location of the axis; the other controls the angle of reflection.<br />

Figure 2: A snapshot of the DCM HCI style in ST<br />

Finally, the RDCM version allows users to manipulate transformation representations as in<br />

DCM, except that a number of features are ad<strong>de</strong>d. Children interact with the concepts in a<br />

progressively differentiated manner which is inten<strong>de</strong>d to cause epistemic conflict [Forman<br />

& Pufall, 1988]. The representations progressively fa<strong>de</strong> over three levels. In the specific<br />

case of rotation, Level 1 (like DCM) allows children to interact with the most generalized<br />

notion of rotation. The angle of rotation can be experientially adjusted till the ghost image<br />

assumes the <strong>de</strong>sired orientation; likewise, the center of rotation can be changed until the<br />

ghost image reaches the <strong>de</strong>sired target location. Level 2 <strong>do</strong>es not display the ghost image of<br />

the object being rotated, but the representation of the arc is still on screen. Without a visual<br />

feedback of the resulting operation, children must pay more attention to the numerical<br />

value of the angle of rotation, and its relation to the final state of the geometric operation.<br />

In Level 3, there is ultimately no visual representation of either the ghost image, or the arc<br />

of the rotation angle. The actual learning of all concepts un<strong>de</strong>rlying rotation can be tested<br />

as children successfully (or unsuccessfully) manipulate the red (angle of rotation) and<br />

green (center of rotation) circles on screen. Figure 3 shows a snapshot of ST at Level 3<br />

RDCM for a rotation operation.

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