Line Research Papers - Academia.edu (original) (raw)

The objective of this study is to investigate how students presented the two different environments - from one side paper and pencils and other information, include notions of straight lines and circumferences, and the formalization of their equations in Cartesian, polar and parametric representation. In this sense we analyze the expected institutional relations and existing for the study of these planar curves in Analytic Geometry in secondary and higher education. We seek to identify the retrospective knowledge of students and see how the timing of representations, through work with the views parametric, cartesian and polar, favors the identification of plane curves through the graphics ostentatious. In this diapason, we note the possibility of implementation this articulation of the three views of these planar curves in both school steps. For the development of this research, we began to preliminary studies related to the topic discussed, which guided us toward topics and problems related to the cartesian representation, parametric and polar flat curves present in articles, dissertations and national and international theses of the last 10 (ten) years, magazines and institutions, with access via libraries and Internet. Then we present some similar research dealing with the transition between secondary and higher education. Elected as a central theoretical framework to approach the Anthropological Theory of the Didactic - (TAD), particularly in praxeology notions - overt and not ostentatious - and as support, we consider the theoretical approaches to the notion of point of view, as Dias and Rogalski; the notion of Douady framework; the notion of knowledge levels expected of students, according to Robert and the computer transposition notion Balacheff. Being a qualitative study, we present the analysis as instruments of institutional documents and textbooks, the development of a teaching sequence, and the trial and preliminary analysis, a priori, a posteriori and its validation. In this teaching sequence, we propose didactic sessions that take the student to make a link between the points of view cartesian, polar and parametric and the formalization of lines and circles equations, in the plane, favoring the understanding of these mathematical objects. Such a possibility would be guided based on (i) the mathematical landscape of Analytical Geometry, especially lines and circles, in the plan; (Ii) the expected institutional relationships and existing on these curves in secondary and higher education and (iii) the use of free graphics plotters as Winplot and GeoGebra. For the analysis of textbooks and teaching sequence used by the elaborate Days analysis grid, which was instrumental in identifying both existing mathematical and educational organizations, as expectations in terms of retrospective knowledge expected of students in the transition from education secondary and higher education for the study of these objects. In the subsequent analysis it was found that the relationship between the cartesian representations, parametric and polar plane curves, with mediation and interaction of two rooms, a paper and pencil and other information, to promote student understanding of line and circumference of the notions study of analytic geometry flat. The survey results support the proposal to differentiate the understanding of lines and circles, for views that allow, in the field of analytic geometry, the work “do math” and know “mathematical thinking”. For future research study indicated the coordinates and vectors in space already in high school, which would favor the study of line and circle in space and their cartesian, parametric and polar representations in the transition from secondary and higher education.