Abstract
The purpose of this study was to develop a lesson which connects the three representational modes of the geometric definition, the figure, and the equation of an ellipse through mathematical activities. In order to encourage learner autonomy, we implemented an experimental class based on the constructive approach with internal and external translations of the three representational modes, i.e. linguistic, illustrative, and symbolic representation. We used the graphing software GRAPES to support students' unskillful mathematical activities. The following results were obtained: (1) Although students felt that the experimental class was difficult, they tackled mathematical activities positively and enthusiastically throughout the learning process of the constructive approach. Approximately 70 percent of students were able to understand the equations of an ellipse. (2) As a result of internal and external translations of the three representational modes dependent on students' abilities, students were able to construct and acquire the connection between the geometric definition, the figure, and the equation of an ellipse with their teacher and other students. (3) We concluded that using the GRAPES method in this type of experimental class is a useful approach to confirm the figure and the graph of the equation of an ellipse visually and intuitively.
