To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Products of Geometric Transformations: Developing Expertise by Using the TI-84・s Cabri Jr.

Jack Carter
Mathematics & Computer Science
California State University

Beverly Ferrucci
Keene State College
United States


Motivated by the pioneering work of Dr. J.-J. Dahan (ATCM 2005), the present study explored how pre-service teachers constructed their understanding of isometries and dilations with figures that were drawn and transformed using Cabri Jr. In Part 1 of the study, the students constructed images using a single transformation, either a reflection, rotation, translation, or dilation. In Part 2, students used the technology to make images that were the result of one or more of the isometries followed by a size transformation.

Video analysis of students・ constructions of the images under transformations revealed that most difficulties related to misconceptions about basic geometric measures and to inexperience in adjusting or revising the geometric features that determined the images under the transformations. Assessment of students・ performances showed the future teachers developed high levels of confidence in their abilities to construct products of the geometric transformations. Follow-up test items required students to find pre-images and images of the isometries and dilations as well as geometric details that described the transformations. Scores on the test items indicated that the prospective teachers developed levels of expertise with the products of transformations that corresponded to their levels of confidence.

This presentation includes a review of the preliminary instructional materials and video clips of the instructional episodes that preceded each part of the study. The video clips also include segments that illustrate the pre-service teachers・ successful constructions and common obstacles that they encountered. Conclusions indicate that Cabri Jr. on the calculator is an example of the application of appropriate technology for developing future teachers・ expertise with products of geometric transformations.

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