ISSN: 2375-3781
International Journal of Modern Education Research  
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Strategy and Methods for Solving Combinatorial Problems in Initial Instruction of Mathematics
International Journal of Modern Education Research
Vol.2 , No. 6, Publication Date: Dec. 1, 2015, Page: 77-87
1255 Views Since December 1, 2015, 1292 Downloads Since Dec. 1, 2015
 
 
Authors
 
[1]    

Valerija Krekić-Pinter, University of Novi Sad, Hungarian Language Teacher Training Faculty, Subotica, Serbia.

[2]    

Josip Ivanović, University of Novi Sad, Hungarian Language Teacher Training Faculty, Subotica, Serbia.

[3]    

Žolt Namestovski, University of Novi Sad, Hungarian Language Teacher Training Faculty, Subotica, Serbia.

[4]    

Lenke Major, University of Novi Sad, Hungarian Language Teacher Training Faculty, Subotica, Serbia.

 
Abstract
 

The development of logical and combinatorial thinking begins in the earliest activities of children. Ideas of combinatorics may appear in many forms, above all in solving certain situations that occur during play, in everyday life, in certain school subjects, and in other areas. Initial instruction of mathematics introduces students to different relations, but it is not particularly concerned with the grouping and distribution of elements, namely with combinatorial problems. This paper is an attempt to highlight some relevant aspects as the basis for teaching combinatorics in the initial instruction of mathematics, as well as to examine the needs and the possibilities of its development. The aim of the paper is to contribute to the realization of the contents of the combinatorial nature, by defining strategy and adequate approach to methodological elements of teaching combinatorics and logical-combinatorial tasks in initial instruction of mathematics. Another aim of the paper is to examine the educational effects of defined methodological transformation. The result of the research is an original creative teaching strategy and methodological transformation of combinatorial elements in initial instruction of mathematics. This strategy has proved, during the experimental test, that its effects are remarkable and that in comparison to the existing low level of solving combinatorial problems, it highly on tributes to the quality of initial instruction of mathematics. This research has systematized methods and teaching and learning models of combinatorics in initial instruction of mathematics and showed that significant results in this area can be achieved by systematic methodological transformation.


Keywords
 

Combinatorial Thinking, Creativity Strategy, Methodical Transformations, Problem Solving


Reference
 
[01]    

Author (2009). Computer simulation as representation of knowledge in education.

[02]    

Author (2013). Creativity Strategy for Mathematics Instruction.

[03]    

Author (2009). Didaktičko-metodičke osnove istraživanja savremene metodičke transformacije elemenata kombinatorike u početnoj nastavi matematike.

[04]    

Author (2011). How to create games from mathematical problems.

[05]    

Author (2008). The development of children`s combinatorial capabilities in the early stage of mathematics teaching.

[06]    

Author (2010). Matematikadidaktika.

[07]    

Author (2006). Savremene metodičke transformacije kombinatorike u početnoj nastavi matematike.

[08]    

Barratt, B. B. (1975). Training and transfer in combinatorial problem solving. The development of formal reasoning during early adolescence. Developmental Psychology, 11, 700-704.

[09]    

Bruner, J. S., Oliver, R. & Greenfield, P. M. (1971). Studien zur kognitiven Entwicklung [Studies in cognitive growth]. Stuttgart, Germany: Klett.

[10]    

Bruner, J. S. (1974). Entwurf einer Unterrichtstheorie [Toward a theory instruction]. Berlin, Germany: Berlin-Verlag.

[11]    

Cotič, M., Hodnik, T. (1993). Prvo srečanje z verjetnostnim računom in statistiko v osnovni šoli [The introduction of a probability calculus and statistics in primary school]. Matematika v šoli2/1, 5-14.

[12]    

Cotič, M., Felda, D. (2007). Otrok in preproste kombinatorične situacije [How to teach and learn mathematics]. Osijek, Croatia: Josip Juraj Strossmayer University of Osijek.

[13]    

Csapó B. (2001). A kombinatív képesség fejlődésének elemzése országos reprezentatív felmérés alapján, Magyar Pedagógia, 4, 511-530.

[14]    

Fischbein, E., Pampu, I., Minzat, I. (1970). Efects of age and instruction on combinatory ability in children. British Journal of Educational Psychology, 40, 261-270.

[15]    

Freudenthal, H. (1974). Lernzielfindung im Mathematikunterricht [Objective Determination in mathematics education]. Zeitschrift für Pädagogik, 1974/5.

[16]    

Inhelder, B., Piaget, J. (1967). A gyermek logikájától az ifjú logikájáig [The Growth of Logical Thinking from Childhood to Adolescence]. Budapest, Hungary: Akadémiai Kiadó.

[17]    

Kishta, M. A. (1979). Proportional and combinatorial reasoning in two cultures. Journal of Research in Science Teaching, 5, 439-443.

[18]    

Lockwood E. (2013). A model of students’ combinatorial thinking, The Journal of Mathematical Behavior, 32, 251-265.

[19]    

Miljković, S. D., Marinković, B., (2005). Kombinatorni zadaci u slici i reči [Combinatorics tasks in pictures and words]. Beograd, Serbia: Klub mladih matematičara „Arhimedes”.

[20]    

Ministarstvo prosvete Republike Srbije (1995). Osnovno i obavezno obrazovanje u svetu [Primary and compulsory education in the world]. Beograd, Serbia: Sektor za istraživanje i razvoj.

[21]    

Novotná, J., Kysilková, M. (2014).Logické a kombinatorické problémy v matematice na ZŠ. In Moderní trendy ve vyučování matematiky a přírodovědných předmětů IV. Vyd, 1, 54-59.

[22]    

Piaget, J., Inhelder, B. (1951). La genese de l’idée de hasard chez l’enfant [The Principles of Genetic Epistemology]. Paris: Presses Universitaires de France.

[23]    

Piaget, J., Inhelder, B. (1966). The Psychology of the Child: 2nd English Edition 2000. Basic Books. New York, United States of America: Basic Books.

[24]    

Roberge, J. J. (1976). Developmental analyses of two formal operational structures: Combinatorial thinking and conditional reasoning. Developmental Psychology, 6, 563-564.

[25]    

Scardamalia, M. (1977). Information processing capacity and the problem of horizontal décalage: A demonstration using combinatorial reasoning tasks. Child Development, 48, 28-37.

[26]    

Skemp, R. R. (1971). The Psychology of Learning Mathematics, Penguin Books Ltd. United Kingdom: Harmondsworth.

[27]    

Varga, T. (1967). Combinatorials and probability for young children. Budapest, Hungary: Scherbrooke, The International Study Group for Mathematics Learning.

[28]    

Yu-Ling Tsai, Ching-Kuch Chang (2009). Using Combinatorial Approach To Improve Students’ Learning Of The Distributive Law And Multiplicative Identities.International Journal of Science and Mathematics Education, 7, 501-531.





 
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