(CZ) Experimentální výzkum efektivity odstupňované pomoci při řešení problémových úloh a možnosti uplatnění ve výuce
(EN) Expreimental Research on the Effectiveness of Graded Assistance in Solving Problem Assignments and the Possibilities of Practical Application in the Teaching Process

This work has attempted to give a concrete shape to the demands on an individual’s education in the period of the Scientific and Technological Revolution (the subject’s activity, development of capabilities, independent and creative approach to the solving of assigments) by uniting the advantages and eliminating the shortcomings of problem and programmed instruction in the form of the project of a problem programme. The project proceeds from some conclusions of the psychology of thinking and problem solving (S. L. Rubinštejn, V. Kulič, R. M. Gagné, J. Linhart and others) and is supported by pedagogical moments and findings formulated by J. Skalková, A. M. Maťuškin, E. Stračár, L. Klingberg and others. The principal targets of the research were to form the conception of a considered problem programme to verify its effectiveness and to consider the possibilities of its application in the educational process.
The aim of a problem programme is to guide the pupil’s steps in solving the problem, but at the same time not to restrict his creative initiative, on the contraiy, to encourage, as far as possible, the pupil’s own independent search for a solution. As the starting and the regulation of the learning process is based on graded assistance which the programme gradually provides. The model of the problem programme with graded assistance which we defined by means of characteristic signs, is based on the theoretical conclusions by S. L. Rubinštejn on generalization and transfer in solving two assignments (one more difficult, the other easier) with the same principle of solution, and it is also keeping with the conception of problem solution as a process of creating and verifying hypotheses. The aim of learning here is not only concrete knowledge and skills, but the capability of transfer and analytical and synthetical thinking.
The objective of the experimental research was to test the concord of theoretical conclusions of the qualitative analysis with empirical results. The objective of the main experiment was to compare the effectiveness of problem programme with graded assistance and that of the nonproblem programme of the traditional type. The experiment was carried out in mathematics at the Faculty of Engineering in Prague.
A statistical analysis has shown that a problem programme with graded assistance provides average students (in mathematics) with significantly more permanent knowledge and skills and is more adaptive than a non-problem one. Better students went through the programme in a significantly shorter time than better students who went through a non-problem programme, and for them, too, programme with graded assistance is more adaptive. In a class of bellow-average students no statistically significant difference appeared in any of the four parameters involved.
The main experiment was supplemented by three partial ones. Two of them are mentioned briefly in the article.
The problem programme with graded assistance can be effectively used in pupils' own independent work, in homework (including part-time studies) and in problem instruction. It may be presented in the form of text a or as a programme for a teaching machine or a computer with suitable terminals.