Mensuração, algarismos significativos e notação científica: um estudo diagnóstico do processo ensino-aprendizagem, considerando o cálculo e a precisão de medidas - Santos, Ailton Martins dos (2002)
The objective of this study was to analyse the teaching and learning of the object we will term "measures, meaningful algorithms and scientific notation" for students in the final year of high school (18 year-olds). We turned to the work of the psychologist Raymond Duval concerning registers of semiotic representation and to the orientations related to transversality and interdisciplinarity proposed in the Parameters for the National Curriculum (PCN) for Mathematics. We also intend to show, through a diagnostic study, that this object appears not to be worked with. A preliminary study indicated that the teaching-learning problem is related to the lack of its emphasis in the teaching plans of schools and in didactic proposals. The next step was to attempt to respond to the following questions: "Which difficulties arise for students when the mathematics teacher tries to work in an interdisciplinary way? Particularly, what are the difficulties that students have to resolve when faced with problems related to measures, meaningful algorithms and scientific notations? What pedagogic alternatives can be proposed to reduce these difficulties?" We adopted as our basis the hypothesis that it is possible to find problem situations in which (a) historic knowledge about algorithms helps the comprehension and the distinction between dimensional and adimensional numbers; (b) the study of the first measurements helps the student to define standard measures and how to operate with these fundamental measures without interrupting the approximation sequence; and (c) when he expresses any number that represents a measure in scientific notation, considering meaningful algorithms, the student is capable of correctly applying the rounding norms to the result of any operation. To validate our hypothesis, we designed a teaching sequence related to the object of research, which was applied with final year students from the school Colégio Lázaro Silva in the city of Auriflama in the western region of the state of São Paulo. After the teaching sequence, a post-test was applied. Qualitative and quantitative analyses of this instrument confirmed that our hypotheses are relevant, since we could show that, in various problem situations, mathematical definitions related to the objects of research were presented which could be used as validations to the hypotheses. Therefore, through our analysis of the teaching sequence and the post-test, we could verify the importance of including the object in the mathematics curricula (PCNs) for both primary and secondary education and that this will necessitate its programming into teaching plans of schools and didactic proposals