Interactions between internal representations and external representations generated by 11. class secondary students' related with geometric problems

The purpose of this study is to investigate possible interactions between internal and external representations generated by 11. class secondary students? related with geometric problems. The participants of this research were three high school students choosen by a purposeful sampling. While we were choosing the participants, we also considered via results of gometry achievement exam prepared by researcher, average of written examinations which were belong to first semester, and geometry teacher?s opinions about students.The data were collected using by the methods which were think aloud method, three geometry problems focused on polygons, and unstructered interviews. Each student practiced the think aloud method before solving three geometry problems. After that, students worked on each problem seperately and they were interviewed at the end of each problem solving sessions. These data were analyzed using the within-case and cross-case techniques. Data gathered were categorized using a constant comperative method to conceptualize a model of interactions between representation. Codes and theme used in analyzing data were generated via Goldin?s (1998a) representational model.The findings of this study show that while participant were solving geometry problems, they generated some external representations such as ?geometric figures?, ?written expressions? and ?algebraic expressions?. However, these representations varied according to students and the nature of problems. On the other hand students? internal representations which were generated by them such as ?verbal?, ?formal? and ?imagistic? systems.The other consequence of the research is that there were two type interactions between internal and external representations. If students pass on the same kind of representations (internal-internal / external-external) in problem solving process, there will be a ?horizontal interaction? between these kind of representations. However, if they pass on the different kind of representations (internal-external), there will be a ?vertical interaction? between them. These interaction processes varied according to students? perceptions and representations generated by students while solving geometric problems.Keywords: internal representation, external representation, representation, systems of representation, geometry, problem solving