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PL
W pracy podana jest pewna koncepcja całki oznaczonej Riemanna z funkcji o wartościach w dowolnej przestrzeni metrycznej. Znajduje się w niej również pewien warunek wystarczający całkowalności oraz kilka przykładów funkcji całkowalnych.
EN
In the paper, some conception of Riemann's definite integral of functions with values in any metric space is given. Also, one can find in it some sufficient condition for integrability and several examples of integrable functions.
2
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EN
The unaided acquiring of knowledge is the basic of higher studies, and the effectiveness of self-teaching depends on many factors, among other things, on motivation. The paper presents the results of investigations carried out at the Institute of Mathematics of Łódź University, concerning the student's attitude towards unaided work. Their attitude towards 6 partial aspects of self-education has been taken stock of. I. The unaided studying is an indispensable element of higher studies; II. Self-teaching should transcend the tasks deputed by the academic teachers; III. The weight of studies should be shifted from didactic activities at the educational institution to the students self-teaching. IV. The aim of studying is not only the acquirement of a definite portion of knowledge, but also of the ability to acquire it single-handed, to process and apply it. V. The academic teachers should acquaint the students with the techniques of intellectual work. VI. Although self-teaching is sometimes burdensome, the students must not be spared trouble in the unaided acquiring of knowledge, guiding them at every step. It has turned out that, although aware of the indispensability and importance of the unaided acquiring of knowledge, the students reject the proposal of the shifting of the weight of studies from didactic activities at the educational institutions to their self-teaching. They also feel that they do not know the techniques of intellectual work and think that the academic teachers ought to acquaint them with such techniques.
PL
Wykonano w ramach RPBP III.30.V.0
EN
The present paper is the outcome of investigations and theoretical analysts carried out for several years, aiming at an answer to the following questions: - what should the fund of the mathematics teacher's knowledge look like, within what scope and in what way should we convey this knowledge to him? In the commencing part of the paper, we analyze critically the existing system of educating teachers of mathematics; later, we present a proposal of a structure of five-year master's studies preparing the graduates for work in the profession of a mathematics teacher. Basing ourselves on the evolved criteria of choice of mathematical contents which should be considered indispensable in educating the teachers, we present a project of the minimum of knowledge of the fundamental subjects: mathematical analysis, algebra, geometry, probability and elements of statistics, theoretical arithmetic, logic and set theory, complex analysis, topology, differential equations, functional analysis, numerical methods, elements of computer science, the didactics of mathematics. Since the lecture at higher studies constitutes the basic form of conveying knowledge, the article closes with a discussion on modern ways of lecturing, activating the students. The scope of mathematical knowledge, proposed in the paper, which should be conveyed to the students - future teachers and the project of organizing the university teacher s studies can constitute the basic for the elaborating of the detailed curricula of such studies.
EN
The sixties of the XXth century have brought a reform in teaching, mainly mathematics, which in Poland was the deepest one after the Second World War and comprised both curriculum and system changes in our schools. In the article we analyse in brief the period preceding the reform and make a survey of the curriculum contents in mathematics on the elementary level of this and the next reforms. We also treat of the changes the curriculum underwent up to 1990.
PL
Artykuł ten nawiązuje do problematyki budowania dojrzałości matematycznej studentów. W szczególności omówiona została rola języka matematycznego i wartości estetycznych matematyki oraz znaczenie historii matematyki. Rozważono także związki informatyki z szeroko rozumianą kulturą matematyczną.
EN
This article refers to the problems of building the mathematical maturity of students. In particular, the role of the language of mathematics and the aesthetic values of mathematics as well as the weight of the history of mathematics are discussed. Also, the connections of computer science with mathematical culture understood broadly are considered.
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