Vzorci kot učno okolje za učenje matematike

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Language:	Slovenian
Year of publishing:	2012
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[N. Markočič]
UDC:	51:37.02(043.2)
COBISS:	9545801
Views:	911
Downloads:	263
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Patterns as learning environment for learning mathematics
Secondary abstract:	The thesis is about patterns in mathematics and their role in learning mathematics in lower secondary school. The thesis consists of two parts, a theoretical and an empirical one. In the theoretical part we describe what patterns in everyday life are. Then we consider in greater detail the patterns as a means in school mathematics. We define patterns as a sequence of objects together with perceived regularity among them. We classify patterns according to two criteria: the type of objects and the type of regularity. The typical objects in patterns are numbers, geometric shapes, arithmetic expressions. These objects give rise to arithmetic, geometric, and operational patterns. Regarding the regularities we consider repetitive, linear, quadratic, and recursive patterns. We consider also patterns based on geometric transformations and tilling of the plane. The main topic of the theoretical part is the role of patterns in school mathematics. We describe several levels of understanding patterns, ranging from the perception of regularity, continuation, prediction, and expressing generality. Using these classifications we reviewed the Slovenian mathematics curriculum and textbooks for grade 8. Finally, we considered some interesting learning environment, in which patterns can be developed. In the empirical part we study whether and how mathematics teachers use patterns in teaching mathematics. To find out their point of view we devised a questionnaire in which they compared pattern based tasks with other introductory tasks into various topics.
Secondary keywords:	mathematics;primary school;matematika;osnovna šola;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in tehnika
Pages:	84 str., VII f. pril.
Type (ePrints):	thesis
Title (ePrints):	Patterns as learning environment for learning mathematics
Keywords (ePrints):	matematika v osnovni šoli
Keywords (ePrints, secondary language):	classification of patterns
Abstract (ePrints):	V diplomskem delu obravnavamo vzorce v matematiki. Namen diplomskega dela je predstaviti vzorce in preučiti njihovo obravnavo v osnovnih šolah. Diplomsko delo je razdeljeno na dva dela, teoretičnega in empiričnega. V teoretičnem delu je najprej kratek uvod v vzorce, kjer opišemo vzorce v vsakdanjem življenju. Nato podrobneje obravnavamo vzorce v osnovnošolski matematiki. Vzorec definiramo kot nabor objektov skupaj z zaznano pravilnostjo v naboru. Klasificiramo jih glede na vrsto objektov in načinom širjenja. Pri klasifikaciji glede na objekt podrobneje opišemo številske, geometrijske in operacijske vzorce. Glede na širjenje pa ločimo linearno, kvadratno in rekurzivno širjenje ter širjenje na osnovi geometrijskih transformacij. Opisani so še vzorci tlakovanj ter fraktali. Podrobno je obravnavan pomen vzorcev v osnovnošolski matematiki. Opišemo pomene pravilnosti, nadaljevanja, napovedovanja in posploševanja vzorcev. Ob koncu poglavja navedemo namen vzorcev v osnovnošolski matematiki. V osrednjem delu diplomskega dela preučimo vzorce v osnovni šoli. Pregledali smo učni načrt iz leta 2011 ter učbenike osmih razredov in naredili primerjavo učbenikov. Zbrali smo tudi primere nalog, ki jih lahko uporabimo pri pouku, in jih razvrstili po sklopih. V diplomskem delu predstavimo tudi nekatera zanimiva učna okolja, v katerih lahko razvijamo vzorce. V empiričnem delu opišemo izvedbo ankete med učitelji matematike. V anketi so učitelji uvajanje izbranih učnih vsebin z vzorci primerjali z drugačnimi načini uvajanja. S pomočjo zastavljenih kriterijev in vprašanj smo raziskali, ali učitelji uporabljajo vzorce pri pouku ter mnenje učiteljev o njih.
Abstract (ePrints, secondary language):	The thesis is about patterns in mathematics and their role in learning mathematics in lower secondary school. The thesis consists of two parts, a theoretical and an empirical one. In the theoretical part we describe what patterns in everyday life are. Then we consider in greater detail the patterns as a means in school mathematics. We define patterns as a sequence of objects together with perceived regularity among them. We classify patterns according to two criteria: the type of objects and the type of regularity. The typical objects in patterns are numbers, geometric shapes, arithmetic expressions. These objects give rise to arithmetic, geometric, and operational patterns. Regarding the regularities we consider repetitive, linear, quadratic, and recursive patterns. We consider also patterns based on geometric transformations and tilling of the plane. The main topic of the theoretical part is the role of patterns in school mathematics. We describe several levels of understanding patterns, ranging from the perception of regularity, continuation, prediction, and expressing generality. Using these classifications we reviewed the Slovenian mathematics curriculum and textbooks for grade 8. Finally, we considered some interesting learning environment, in which patterns can be developed. In the empirical part we study whether and how mathematics teachers use patterns in teaching mathematics. To find out their point of view we devised a questionnaire in which they compared pattern based tasks with other introductory tasks into various topics.
Keywords (ePrints, secondary language):	classification of patterns
ID:	8311196