Análise de dificuldades de alunos com o algoritmo da subtração - Mello, Elisabete Marcon (2008)
This research analyzed the difficulties that students from Basic Education face up to the use of the algorithm of the borrowing (decomposition of the minuend) to solve subtractions operations. Therefore, it was made a comparison between the algorithm of the borrowing and algorithm of the compensation (addition of equal quantities in the minuend and the subtrahend) in order to check if using the algorithm of compensation it could diminish their mistakes. Once in the diagnosis study we found out that students make many mistakes when they have to use the algorithm of the borrowing, mainly when it is necessary to proceed some borrowings to solve the operation. This difficulty was found out in all grades from Basic Education 2 and sometimes it extends to High School level. It was analyzed sixty didactic books and five pedagogical publications from private schools systems of the second grade and we realized the use of the algorithm of the borrowing to solve the subtractions with reserve in all of them. Besides, we analyzed six books for teacher s formation and the same procedure was adopted. Most of teachers who were interviewed recognized that students have difficulties with the subtractions that involve some borrowings. We applied a didactic sequence for fifth grade students in order to introduce the use of the algorithm of the compensation. Based on results of our research, we believed that the use of the algorithm of the compensation could be more efficient for the subtraction problems faced to the students. Our research is based on the Theory of the conceptual fields of Gerard Vergnaud and on the Theory of the Situations of Brousseau