Komputer jako narzędzie badania sytuacji zadaniowej w długoterminowej pracy domowej ucznia

In the article I submit a fragment of my research carried out in 2004-2007, which was connected with the role of mathematical computer programs in the independent extracurricular work of the pupil. These examinations were conducted in a group of 119 pupils from the second grade of secondary schools. The article concerns the specific form of homework in mathematics – a long-term homework. The purpose of this homework was to answer the questions: a) In what mathematical situations do pupils use mathematical computer programs by themselves, without recommendation of the teacher? b) What are their motives to use a computer program as the means which enables them to discover and structure the task solution? c) What reasoning can computer program provoke and what intuitions can it improve? d) What functions in the learning process can be met by computer program and what can not be met not only within the range of acquired knowledge, but also from the point of view of thinking forms, creation types and sorts of pupils’ activity as well? In the article I present the concept and proposal of the long-term homework in mathematics. I analyse solutions of the task by the pupils. Task: Check the graph of the square function y = ax2 + bx + c depending on the coefficients a, b, c, where a 6= 0. Observation carried out, and the analysis of its results lead to the following conclusions: 1. The presented concept of the long-term homework in mathematics with the use of a suitable mathematical program allows pupils to organize their learning with the time rate adequate for themselves, to increase their self-reliance, and to stimulate their participation in the process of learning mathematics. 2. The Winplot program appeared to be a useful tool in the phase of preliminary examination of the problem, conducting experiments, perception of relation, formulating and demonstrative verification of hypotheses. 3. The Winplot program enabled to conduct reasoning on a different level of abstraction than it usually takes place during lessons of mathematics in the secondary school.