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1
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Dwudziesty jubileusz istnienia European Society for Research in Mathematics Education i dziesiąty międzynarodowy kongres CERME

100%
Sajka M.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2016
|
tom 8
189-196
2
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Refleksje na temat określania wiedzy przedmiotowej nauczycieli matematyki

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Sajka M.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2006
|
tom 1
297-319
PL
This article presents the author’s reflections, comments and problems that arise in relation to the issue of defining the subject matter knowledge a teacher should have in the context of Even’s theoretical framework. They incline to start working on a considerable modification of this conception in order to explore its adaptability in other contexts. This paper also includes initial results of this modification.
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100%
Sajka M.
Didactica Mathematicae
|
2005
|
tom 28
|
nr 01
EN
The article contains no abstract
4
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Mathematical problems designed with the use of functional equations as theoretical tools for examining subject matter knowledge of functions

100%
Sajka M.
Didactica Mathematicae
|
2008
|
tom 31
PL
Assessing the mathematics teachers' Subject Matter Knowledge (SMK) is currently important problem of research. Mathematics teachers should have profound and thorough SMK, understood as skills and knowledge of mathematics, its methods and history, which are indispensable for teaching. There is a need to find appropriate tools for continuous assessment of that competence of mathematics teachers. However, literature review reveals that functional equations have not been used yet as diagnostic tools. I claim that specially designed tasks related to functional equations can very effectively reveal teachers' SMK of function. As such, this dissertation is a new contribution to the research on possibilities of using the mathematical discipline of Functional Equations (39BXX AMS Subject Classification) in the field of Didactics of Mathematics.The paper is a modified version of the author's lecture presented 2nd July 2008 at the Pedagogical University of Krakow during the doctoral defense. Prof. Maciej Klakla (Pedagogical University of Krakow, Poland) was a supervisor of the PhD thesis; reviewed by: Prof. Anna Sierpinska (Concordia University, Montreal, Canada); Prof. Stanisaaw Midura (University of Rzeszow, Poland) and Prof. Bogdan Jan Nowecki (Pedagogical University of Krakow, Poland).
5
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O liczbach ujemnych z perspektywy historycznej i dydaktycznej

64%
Błaszczyk P., Sajka M.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2017
|
tom 9
5-36
EN
We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second one considers the idea of the algebraic group (G,+, 0) alone. Through the analysis of source texts, we show that the first model originates in John Wallis’ 1685 Treatise of Algebra, while the second one comes to form the theory of polynomials, as developed by Descartes in his 1637 La Géométrie. In mathematical education, the first model is applied in the overwhelming majority. Still, we identify a theory that applies to the second model. We show how to develop it further and simplify the representation of the operation a + (−a) = 0 by turning the second model into a tablet game.
PL
We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second one considers the idea of the algebraic group (G,+, 0) alone. Through the analysis of source texts, we show that the first model originates in John Wallis’ 1685 Treatise of Algebra, while the second one comes form the theory of polynomials, as developed by Descartesin his 1637 La Géométrie. In mathematical education, the first model is applied in the overwhelming majority. Still, we identify a theory that applies to the second model. We show how to develop it further and simplify the representation of the operation a + (−a) = 0 by turning the second modelin to a tablet game.
6
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Enrichment of elementary school symmetry-learning process by using melody transformations

64%
Sajka M., Fraś P.
Didactica Mathematicae
|
2019
|
tom 41
EN
Mathematics and Music - two dierent aspects of human creativity, seemingly belonging to separate areas: science and humanities. Despite this, there are multiple well-known common elements and analogies between the two. Especially well explored is the use of mathematics in music. The opposite, which is the use of music in mathematics, seems unusual and is rarely discussed, including the educational aspect. This paper proposes an exemplary approach of using music to enrich and facilitate mathematics teaching and provides its initial empirical verification. The research presented in this paper describes an additional model which presents the possibility and efectiveness of using music to teach geometric transformations of the plane (reflection symmetry and point reflection) at 6th-7th elementary music school grade levels (12 - 13 years old students). The research initially confrmed the hypothesis that the analysis of musical themes and their transformations can be used in music schools as a new model of facilitating the mathematical understanding of reflection symmetry and point reflection. After an experimental music theory lesson concerning melody transformations and a presentation of the parallels between geometric transformations and their melodic transformation equivalents, the results of the POST-TEST in mathematics were significantly better than the PRE-TEST results for the entire experimental class. Moreover, the spontaneous transfer of knowledge from music to mathematics, concerning the understanding of point and reflection symmetry, was observed. The new musical model turned out to be a useful artifact to some students. The additional research results concern the awareness of the possibility of knowledge transfer between mathematics and music. The teachers of mathematics and music theory involved with the experimental class have not made use of the possibility of transferring musical knowledge to mathematics before, while elementary-level music school students are aware of some analogies between mathematics and music.
7
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The Ninth and the Tenth Congress of the European Research in Mathematics Education (CERME 9 and CERME 10)

64%
Maj-Tatsis B., Sajka M.
Didactica Mathematicae
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2017
|
tom 39
PL
CERME is one of the largest world congresses bringing together scientists fromall continents and entirely devoted to Mathematics Education.The scientific activities of CERME conferences are always focused mainlyon common work within the so-called Thematic Working Groups(TWGs). The particular way of organising the conference gives the opportunityfor in-depth analyses of the presentations and papers and for working outcommon conclusions after many discussions.
8
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CIEAEM 58 - Sprawozdanie z konferencji Srni, 9-15 lipca 2006 roku

51%
Pawlik B., Sajka M., Zaręba L.
Didactica Mathematicae
|
2007
|
tom 30
PL
Przypadająca na rok 2006 konferencja Międzynarodowej Komisji do Spraw Studiowania i Ulepszania Nauczania Matematyki - CIEAEM 58, odbyła się w dniach 9-15 lipca w Srni - małej miejscowości położonej na terenie uroczego czeskiego Parku Narodowego - Sumava.
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CIEAEM 59 - Sprawozdanie z konferencji Dobogóko, 23-29 lipca 2007 roku

51%
Pawlik B., Sajka M., Zaręba L., Swoboda E.
Didactica Mathematicae
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2007
|
tom 30
PL
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.
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