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1
Content available On teaching of geometric transformations in school
Stępień L., Stępień M. R., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
153--164
EN
The current core curriculum in mathematics for lower secondary school (3-rd educational level in Poland) omits formal definitions of concepts related to geometric transformations in the plane and is based on their intuitive sense. Practice shows that the current approach makes teaching very difficult and the students solve the typical tasks, not understanding the meaning of geometrical concepts. The article contains basic concepts connected with geometric transformations and examples of geometric tasks that are solved in the third and also in the fourth educational level in an intuitive way, sometimes deviating or even incompatible with the mathematical definition. We show how they could be solved in easier way with introducing definitions of geometric transformations in a simple and understandable for students way sometimes using vector calculus. We take into account isometries: reflection and point symmetry, rotation and translation and similarities with particular consideration on homothetic transformation.
2
Content available Non-standard tasks in mathematical education
Major J., Major M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
115--119
EN
Mathematical knowledge and skills have been playing a more and more important role in our daily lives. At the same time, solving tasks is the essence of mathematics understood as a field of human activity. The subject of this paper are selected issues concerning some atypical tasks which play important role in mathematical education. Presented task is related to the elementary knowledge of probability theory.
3
Content available Divisibility and its application in teaching mathematics in the third educational level
Jędrzejewski J., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
71--82
EN
Elements of theory of divisibility are present in many various interesting mathematical tasks, especially in tasks that are addressed to talented pupils taking part in mathematical competitions. Good understanding of it lets solve very interesting and difficult (at first glance) issues. On the other hand, there are a lot of problems with understanding such terms as: multiple, divisor, divisibility, prime number, LCM, GCD etc. The purpose of the article is presenting the base terms of theory in the language understood for pupil of the gymnasium (3-rd educational level, 13-16 years old). In addition, we present some algorithms that are used to solve problems from the theory of divisibility and we discuss the influence the choice of the algorithm on its effectiveness (so we analyse its complexity). Presented algorithms let us create computer programs that solve the problems mechanically. We also enlarge a bit some topics for those ones which can be taught in the class of pupils which are interested in Mathematics.
4
Content available Can information technology change attitude of the student in the teaching of mathematics?
Kowalski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
101--110
EN
The article shows a specific example of extracurricular activities conducted in secondary school, how the graphing calculator helped the first class student in learning mathematics to solve a very difficult task (math problem): How many elements has the equation: a x = log a x. The article describes the reasoning and attitude of the student who voluntarily of his own accord, inspired by other students to experiment, putting, generalizing and verifying hypotheses coped with the solution of this task. It describes the impact of this teaching mean that triggered activity and aroused student’s interest with the task on the degree of knowledge and skills in mathematics, the student’s skills in the use of mathematical language, self-reliance in solving a mathematical problem.
5
Content available Mathematics competences of pedagogy students at the beginning of their university studies
Šupíková K., Novák B.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
355-360
EN
In the contribution the results of the same set of mathematics tasks given to two different pedagogy students groups are compared. It deals with comparison of these two examinations' results. The first group of students was represented by applicants for mathematics pedagogy studies, and the test was applied as an entrance exam in 1985 and 2001. The second group was represented by students of the same field of study at the beginning of their studies in 2010. These students did not sit for an entrance exam because of low number of applicants at that time. The comparison shows a significant decline of current students' competences which are necessary for solving mathematical tasks.
6
Content available remote Chińskie korzenie matematyki rekreacyjnej. Cz. III
Biernacki W.
Wiadomości Naftowe i Gazownicze
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2007
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R. 10, Nr 3 (107)
21-25
7
Content available remote Chińskie korzenie matematyki rekreacyjnej. Cz. II
Biernacki W.
Wiadomości Naftowe i Gazownicze
|
2007
|
R. 10, Nr 2 (106)
21-25
8
Content available remote The realisation of selected attributes of „function” using the project method
Orłowska J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
311-318
EN
The notion of function plays a crucial role in teaching mathematics. Why is this important issue so problematic for students? It is worth noticing that precise specification of this notion took place relatively late, in 19th century. This is why it is so important to attempt students” active participation in defining and understanding the notion of „function”.
9
Content available remote Mathematical task statement
Hodaňová J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
227-232
EN
The text describes a task which must be solved on the analyze of propounded problem. Pupils and students solving these types of tasks are taught to think about the mathematical problem and to develop mathematical consideration. The following task also shows what way the mathematical problem statement can affect the difficulty of task solving.
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