Connecting dynamic representations of simple mathematical objects with the construction and exploration of conic sections

Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In this process, students have the opportunity of formulating questions, making conjectures, presenting arguments and communicating results. This article illustrates that simple geometric configurations can be used to generate all conic sections studied in a regular course of analytic geometry. Observing and interpreting loci, searching for mathematical arguments (including empirical reasoning) and presenting results are problem-solving activities that seem to be enhanced with the use of dynamic software. During the development of the activities, students can exhibit a line of thinking in which they constantly reflect on the meaning and connections among mathematical concepts.