Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
Keywords:Álgebra Linear; Transformações Lineares; GeoGebra; Representações Semióticas; Design Experiment.
The purpose of this article is to present a teaching experiment on the content of linear transformations in the plane and the results of its application in a pair of students of Mechanical Engineering course. Difficulties of the students in Linear Algebra discipline concerning its formal aspect are pointed by Aydin, Hannah, et al. and Isik, furthermore, new pedagogical practices which considers this problematic are required. In this context, elaborating and applying a teaching approach to geometrical linear transformations is aimed at bringing innovative learning and teaching perspectives. This experiment essentially regards the concepts of composition, nucleus and image and also integrates the GeoGebra software to explore the relations among representations of different registers such as graphic, algebraic, figural and of natural language. The study is grounded on the registers of semiotic representations provided by Duval's theory and on a technology according to the views of Drijvers, Baki, Hoyles and Noss and Borba and Penteado, in order to allow different developments from those reached by paper and pencil environment. For the experiment preparation and conduction, it is used some aspects of the Design Experiment by Cobb et al., a specific method to build an innovative approach to the mathematics education. This research has a qualitative character and the results revealed that providing a favorable environment to the students to coordinate representations of different registers, there was progress in understanding the concepts related to linear transformations, mainly, nucleus and image. The autonomy in building concepts is privileged by the GeoGebra software utilization, regarding its dynamic character, the students could test their conjectures in its environment.
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