Learning of level curves and level surfaces to generalize families of conic sections and quadric surfaces (Original)
Keywords:
level curves; level surfaces; conic sections; quadric surfaces; GeoGebraAbstract
We present a classroom experience in which a work guide and the GeoGebra program have been used, in order to support the teaching and learning of level curves and level surfaces of functions of two and three variables respectively, to generalize families of conic sections and quadric surfaces from algebraic and graphic explorations. The teaching and learning process of the conic sections and quadric surfaces has historically presented some difficulties in the Mathematics Degree. This subject is significant for the training of teachers, for the applications that it has intra and extra-mathematics. The research presents a workshop based on mathematical problems, which require the GeoGebra program for their resolution. The workshop is specified through a work guide, in order to support the teaching and learning of curves and surfaces of function level of two and three variables respectively. This process allows to generalize families of conic sections and quadric surfaces from algebraic and graphic explorations. This work has been developed with students of Mathematics Degree from the Universidad Pedagógica y Tecnológica de Colombia, in the subject Multivariable Calculus.
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