PL

In the article I submit partial results of three years lasting researches, which relate to the use of mathematical software in the process of mathematics teaching and learning, particularly in independent, after-school student activities. The aim of my researches is to solve the following problem: What is the role of computer in the independent work of the student? The following issues are the most interesting for me: Do students, during their independent after-school work, notice the necessity of using a computer software? In what situations students use computer programs in their after-school activities? Does applying a computer software in uence learning results, development of activeness, and mastering mathematical skills? Does applying a computer software change the students' attitude toward solving mathematical problems? My researches were carried out in grade 2 of senior secondary schools among volunteering students. They received computer software (\Compass" and \Ruler and Winplot") with instructions. During the first two years of the study (I present partial results of these stages in the article) the observed students did not use computer during classes; they did not have any experience in working with mathematical computer programs. My observations made during these studies let me conclude that the application of computer in independent after-school work of the students favorably in uenced the process of mathematics learning, development of mathematical activeness and creative attitude to problems. It was also noticed that majority of the students were not interested in using the computer in their independent work, despite the fact, that all of them would like it to be applied as didactic means in the lessons. In my opinion the reasons of this outcome are as follows: No experience in work with the programs, Insufficient reason for learning and using computer programs (this work was voluntary and not assessed), Attachment to the traditional learning methods, No possibilities to utilize experiences from work with computer on the exams. Those students who were learning with the support of mathematical computer programs most often applied it to the following: Searching for an idea to solve the problem, Visualization of the situation described in the problem, Quickly making correct function graphs, Reading properties of a function, Comparing their own graphs to the computer ones, Discovering properties, Visualization of theorems. In the article I submit four examples of mathematical computer programs utilization in after-school student work relating to: quadratic function, transformation of function graphs, areas of plane figures. By analyzing results of the researches carried out I deduct, that utilization of the computer in independent after-school work of students can contribute to: Formation of active and creative attitude of the students to problems, Formation of the research attitude, Stimulating own initiative, Building students' confidence of their mathematical possibilities, Critical estimation of data and results (thanks to the possibility of observing many examples and counterexamples), Development of visualization, modeling, reasoning and interpretation skills.