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Wyświetlanie 1-15 z 20
Tytuł:
Between intuition and definition: an attempt of identifying 11-12 years old students’ competences in defining similar figures
Autorzy:
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/749100.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
The article contains no abstract
Źródło:
Didactica Mathematicae; 1997, 19, 01
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
.
Autorzy:
Swoboda, Ewa
Urbańska, Elżbieta
Turnau, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/749138.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
The article contains no abstract
Źródło:
Didactica Mathematicae; 1997, 19, 01
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Epistemological triangle in research on creation of mathematical knowledge
Autorzy:
Jagoda, Edyta
Pytlak, Marta
Swoboda, Ewa
Turnau, Stefan
Urbańska, Aleksandra
Powiązania:
https://bibliotekanauki.pl/articles/749512.pdf
Data publikacji:
2004
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
The article contains no abstract
Źródło:
Didactica Mathematicae; 2004, 27, 01
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The symbol of fraction and its connection with the understanding of ratio and proportion by 2nd year gimnasium students
Autorzy:
Drewniak, Halina
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/749522.pdf
Data publikacji:
2004
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
The article contains no abstract
Źródło:
Didactica Mathematicae; 2004, 27, 01
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
CIEAEM 59 - Sprawozdanie z konferencji Dobogóko, 23-29 lipca 2007 roku
Autorzy:
Pawlik, Bożena
Sajka, Mirosława
Zaręba, Lidia
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/749398.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
W zacisznie położonej węgierskiej miejscowości Dobogóko w dniach 23-29 lipca 2007 roku odbyła się 59. konferencja Międzynarodowej Komisji do Spraw Studiowania i Ulepszania Nauczania Matematyki - CIEAEM.
Źródło:
Didactica Mathematicae; 2007, 30
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ewolucja znaczenia słowa w matematyce jako problem dydaktyczny
Autorzy:
Slezakova, Jana
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/749136.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
The research problem of this investigation is what are the sources of misunderstandings between the teacher and a student that spontaneously occur during a mathematical discourse. Several episodes of mathematics classes are here analyzed, in which the meaning of a word or expression was different for the teacher and a student. They are analyzed with respect to four kinds of cognitive obstacles identified previously: Different understanding of the context of a situation or a problem. The teacher while designing a problem or a context situation, which aims at bringing a concept closer to the student, is able to extract the concept out of the context, knows what is important and what is not. A projection concept ą context situation is functioning in her thinking. A student solving the problem designed by the teacher will try to exploit all his school and out-of-school knowledge. Associating experience may be linked with different mathematical concepts or be detached from mathematics. The students' mathematical knowledge may prove to be different from that expected by the teacher, and the out-of-mathematics knowledge may cause some aspects of the situation, for the teacher unimportant, to dominate. Focusing on own goals. The teacher knows what she intends to achieve when proposing to solve a certain problem. It can be getting a skill or discovering some property or connections, important for the science of mathematics. Those objectives often determine the desired way of handling the problem, deviations of it being considered faulty. The student is focused on finding the solution and doing it with least effort. So she/he will apply approaches that she/he knows and thinks to be most efficient. Focusing on different pieces of information. Understanding of an utterance is possible because of all words being kept in memory, so that the meaning of each can be located in a context. The sense of the whole utterance depends on which part of it has been highlighted. Different meanings assigned to the same key word. Building once own mathematics is a long-lasting process, in the course of which some words may change their meanings. Different meanings assigned to the same words stimulate enacting different procedures and operations attached to the given concept. As a result, the same word evokes different properties, connections, and relations. Example A mathematics class, 2nd year of junior secondary school (17-year-old students). The topic: Transforming algebraic expressions with the use of formulas. Teacher: Represent the given expression in the form of an algebraic sum: $$ (x + 3)^2 + (2x + 5)(2x - 5) $$ Teacher 01: Who would come to do this example? Student 01: (sitting) But there is a sum here already, though. T02: Who? Come, come. S02: But there is nothing to do here. T03: Why? Nothing can be transformed? S03: Well, one could, but a sum is there already. T04: So, if one could then calculate. S04: But... T05: Please come to the blackboard. S05: (reluctantly): $(x + 3)^2 + (2x + 5)(2x - 5) = (x^2 + 6x + 9) + (4x^2 - 25)$. T06: Speed up, remove those brackets. S06: $x^2 + 6x + 9 + 4x^2 - 25$. T07: What next? S07: underlines similar terms. T08: How is it called? Redu... S08: Reducing similar terms. $5x^2 + 6x - 16$. T09: Thank you, sit down please. S09: (returning to his chair) Ha, and it is a difference coming out, not a sum... Different meanings assigned to the same key word For the teacher, an algebraic sum should be composed of monomials with the plus signs between them. The student associated with the word sum its original meaning: the adding operation, usually coded with +. On the blackboard he saw numbers and letters: symbols used in algebra. To him, an "algebraic sum" referred to a situation where the plus sign occurred in-between algebraic symbols. Different understanding of the context of a situation or a problem In previous lessons students practiced translation of a verbal formula to the symbolic one and inversely. The student may have associated the present task with the former one where calling a sum the expression $(x+3)^2+(2x+5)(2x-5)$ would be approved. Hence his reaction But there is a sum here already, though. Focusing on different pieces of information To the teacher, importance of the task was in Represent the given expression. Representing (transforming) an expression is meant as a process, in which the student should show her/his ability to use the $(a + b)^2$ formula, to reduce similar terms, and to get the "simplest form". To the student, the most important was the word sum. In the given situation no action was needed as the expression was a sum already. Focusing on own objectives The event shows that the student's action was forced by the teacher. The former for long could not catch the teacher's intention. She/he worked under the pressure of the teacher's expectations, yet her/his own understanding of the objective did not fit her/his action. The teacher on her part expected executing an algorithm, showing skill, as well as theoretical knowledge. In further analysis the authors show that the dominant reason of a misunderstanding is the difference of meanings assigned to words by the teacher and the student. There are two causes of this phenomenon: the teacher uses words, common to her, to which the student is not accustomed, in the course of learning meanings of mathematical words evolve. The research has made the authors aware of a cultural gap, which exists in the mathematics classroom. The teacher's mathematical culture in incomparable with that of a student.
Źródło:
Didactica Mathematicae; 2008, 31
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Space, geometrical regularities and shapes in childrens learning and teaching
Autorzy:
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/748800.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
Geometrical activities for young children cannot be oriented towards the `ready-made' products like geometrical concepts or skills. An early childhood education could be dedicated to the gathering of experiences, which will be the 128 Ewa Swoboda base for a conscious mental process of creating such concepts at later stages of mathematical education. In other words { it is a very important, indispensable preparatory period for `true' mathematics, and at the same time, it is a period which can be devoted to stimulating the child's intellectual development. Vopenka wrote: In order to penetrate the geometrical world, we must turn attention to it. Hejny underlines the fact that the geometrical world emerges from the real one, from the observations and actions in this world. Analyses showed that the process of creating geometrical regularities goes beyond entertainment. It is a means of focusing attention on the geometrical world. During fun activities a child can perceive various geometrical phenomena and subordinate all further actions to them. In this way, relations on a plane acquire a status of a geometrical individuality.
Źródło:
Didactica Mathematicae; 2008, 31
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Five-year-old children construct patterns, deconstruct them and talk about them
Autorzy:
Swoboda, Ewa
Tatsis, Konstantinos
Powiązania:
https://bibliotekanauki.pl/articles/748978.pdf
Data publikacji:
2009
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
Pięciolatki układają szlaczki, burzą je i rozmawiają o regularnościach
Źródło:
Didactica Mathematicae; 2009, 32
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamic reasoning in elementary geometry – how to achieve it?
Autorzy:
Swoboda, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/748920.pdf
Data publikacji:
2012
Wydawca:
Polskie Towarzystwo Matematyczne
Opis:
Theories of creating mathematical concepts and mathematicalreasoning do not say much about the way in which dynamic reasoningis associated with the development of geometrical thinking. Historicalreview shows that using movement in geometry was differently seen byits creators. Also, approach by psychology does not indicate a simpleway how to connect visual thinking (present at preparatory stage of reasoning)with operational thinking and movement in geometric reasoning.Therefore identification of the way a pupil, working in a geometrical environment,uses physical or imaginary movement has a significant meaningfor didactical designing. In this article results of research led among 4-6years old children is presented. The aim of the research was to investigatethe role of gestures and manipulation in solving geometrical problems.Children were subject to a series of observations during an experiment,aimed at finding a special placement for the figures in the symmetricalpattern. Results show, that rotation was taken as the first, most intuitivemovement for them. Manipulation with rotation was taken independentlyon visual recognition of the relation of axis symmetry. It suggests thatsuch approach can have a great impact on “tacit knowledge” used in furtherlearning about geometrical transformations, and as consequence thedynamic imagination of rotation could be closer to acquaintance thanother rigid movements on the plane.
Źródło:
Didactica Mathematicae; 2012, 34
2353-0960
Pojawia się w:
Didactica Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matematyka dla uczniów szkół zawodowych – co to znaczy? (podejście teoretyczne)
Mathematics for Vocational Schools – What Does it Mean (A Theoretical Approach)
Autorzy:
SWOBODA, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/457799.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Rzeszowski
Tematy:
matematyka w szkołach zawodowych, kompetencje kluczowe, umiejętności hybrydowe, dyskurs wertykalny, dyskurs horyzontalny.
Vocational mathematics education, hybrid competence, key competence, vertical and horizontal discourse.
Opis:
Badania wskazują potrzebę rozwijania u uczniów szkół zawodowych kompetencji hybrydowych dotyczących z jednej strony wiedzy teoretycznej (wymiar wertykalny), a z drugiej – matematyki praktycznej (wymiar horyzontalny). Propozycje dydaktyczne powinny wychodzić od problemów praktycznych. W artykule podane zostały pewne założenia teoretyczne dotyczące matematyki dla szkół zawodowych oraz został omówiony przykład propozycji zadaniowej.
Research related to mathematic for vocational schools indicate the need to develop a hybrid competence, related, on the one hand to theoretical knowledge (vertical dimension), on the other – to practical mathematics (horizontal dimension), Educational proposals should be related to practical problems. In the article, some theoretical assumptions are given, supported by the example of educational proposal.
Źródło:
Edukacja-Technika-Informatyka; 2015, 6, 1; 210-2015
2080-9069
Pojawia się w:
Edukacja-Technika-Informatyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 20

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