Equações algébricas no ensino médio: uma jornada por diferentes mundos da matemática - Lima, Rosana Nogueira de (2007)
This thesis presents a study on the conceptions of equations held by students from first and second years of High School. Five mathematics teachers collaborated in the design of the instruments for data collection: a concept map, a questionnaire, a equation solving task and interviews. Two of these teachers were also responsible for the application of the instruments with their classes: one of first year students and one of second year students from a public school, and one of second year students from a private school, both from the Greater São Paulo area. The data collected was analysed in the light of the theoretical framework of the Three Worlds of Mathematics (Tall, 2004a, 2004b). This analysis is mainly focused on the embodied and symbolic worlds, and the met-befores and met-afters that interfere in the students work with equations. Results indicate that the most evident conception of equation among these students is equation as a calculation. The unknown and the equals sign do not seem to be important characteristics of an equation, and the main met-befores used by the students are from Arithmetic with integer numbers and from Algebra. The quadratic formula is the only solving method for quadratic equations that is used successfully, and it acts as a met-after in the work of some students with linear equations. The analysis shows that the students use techniques to solve equations which are disconnected from the mathematical principle of performing the same operation in both sides. The students create their own ways of working and end up using procedural embodiments, treating the symbols as physical entities that can be moved from one side to the other of the equation