Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas - Ferreira, Maridete Brito Cunha (2016)
This study investigated a didactic proposal whose tasks coordinate proofs and demonstrations as a teaching methodological strategy for easing some of the difficulties related to the topic ‘quadrilaterals’ on a teaching certification course in mathematics. The tasks involve geometric constructions within a paper-and-pencil setting in which students are asked to build figures and mathematically justify the techniques used. Upon carrying out the tasks, students perform conversions of registers and mobilize different understandings of a geometric figure (sequential, perceptive, operative, and discursive). In order to meet the objective, didactic engineering was elected as the investigative method and analyses were based on the theory of registers of semiotic representation, the theory of didactic situations, and the anthropological theory of the didactic. In a preliminary study, the conceptions of students regarding the proofs and demonstrations were investigated and three geometry books used on the teaching certification courses in mathematics were analyzed. The preliminary analyses showed that the conceptions of proofs and demonstrations of the students investigated were influenced by the didactic books. Analysis of the experience revealed that the students appeared to have become aware of the limitations of perceptive understanding, subsequently performing discursive interpretation of the figure, which led to evolution from pragmatic proofs to conceptual proofs, according to Balacheff. With regard to the functions of demonstration, the students performed these not only with the function of validation, but also with the functions of explanation, systematization, and communication, according to De Villiers. In summary, it was concluded that tasks which coordinate proofs and demonstrations are conducive for students to experience the phases of Brousseau’s theory of didactic situations; carry out conversion of registers, semiotic representation and treatments; and coordinate the understandings of the figure, thereby contributing to the (re)construction of implicit and formalized knowledge on quadrilaterals, proof, and demonstration