Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Revisitando o problema de visibilidade para visualização tridimensional

We revisit the problem of visibility, which is to determine a set of primitives potentially visible in a set of geometry data represented by a data structure, such as a mesh of polygons or triangles, we propose a solution for speeding up the three-dimensional visualization processing in applications. We introduce a lean structure , in the sense of data abstraction and reduction, which can be used for online and interactive applications. The visibility problem is especially important in 3D visualization of scenes represented by large volumes of data, when it is not worthwhile keeping all polygons of the scene in memory. This implies a greater time spent in the rendering, or is even impossible to keep them all in huge volumes of data. In these cases, given a position and a direction of view, the main objective is to determine and load a minimum ammount of primitives (polygons) in the scene, to accelerate the rendering step. For this purpose, our algorithm performs cutting primitives (culling) using a hybrid paradigm based on three known techniques. The scene is divided into a cell grid, for each cell we associate the primitives that belong to them, and finally determined the set of primitives potentially visible. The novelty is the use of triangulation Ja 1 to create the subdivision grid. We chose this structure because of its relevant characteristics of adaptivity and algebrism (ease of calculations). The results show a substantial improvement over traditional methods when applied separately. The method introduced in this work can be used in devices with low or no dedicated processing power CPU, and also can be used to view data via the Internet, such as virtual museums applications