Raziskujemo polovico

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Keywords

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[L. Gačnik]
UDC:	51:373.32(043.2)
COBISS:	9556553
Views:	826
Downloads:	223
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Investigating a half
Secondary abstract:	The diploma paper Investigating a Half consists of three key chapters: mathematical problems, a geoboard and parts of a whole. Mathematical problems encourage thinking in students and prepare them for solving everyday problem situations, that is why teachers should use them more frequently and as a replacement for routine exercises. Different didactic tools can be used to solve problems, one of them being a geoboard. It can be used to make classes more interesting and enable pupils to form their perceptions and remember the subject easier. It is possible to create mathematical problems on a geoboard in connection with different topics from the curriculum (e.g. symmetry, length, lines), also with parts of a whole. As with other topics, pupils in the first triad learn about parts of a whole and new terms through activities. This helps them to revise already known terms and clear up those perceptions that might not have been completely understood. This is followed by a gradual transition to concrete models, diagrams and putting down symbols. In the empirical part we joined all three key chapters of the theoretical part so that the pupils were given a problem situation on a geoboard. The problem was from arithmetic – parts of a whole: how to divide the geoboard in half in as many ways as possible. The survey included 54 pupils from the third, fourth and the fifth grade. We conclude that gender has no influence on solving the problem successfully; that solutions provided by the pupils from the third grade are simpler and those from the fifth grade more complex – while the former pupils relate the concept of a half with the congruence of both parts, the latter, older pupils are already aware that the areas of the halves need to be of the same size, while they need not be necessarily congruent; that pupils are more successful in recognising than forming solutions and that students form the third grade found the least solutions and the ones from the fifth grade the most.
Secondary keywords:	mathematics;primary school;matematika;osnovna šola;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Razredni pouk
Pages:	102 str.
Type (ePrints):	thesis
Title (ePrints):	Investigating a half
Keywords (ePrints):	matematični problem
Keywords (ePrints, secondary language):	mathematical problem
Abstract (ePrints):	Diplomsko delo z naslovom Raziskujemo polovico sestavljajo tri ključna poglavja: matematični problemi, geoplošča in deli celote. Matematični problemi pri učencih spodbujajo mišljenje in jih pripravljajo na reševanje vsakodnevnih problemskih situacij, zato bi jih morali učitelji bolj pogosto uporabljati in z njimi nadomestiti reševanje rutinskih nalog. Za reševanje problemov lahko uporabimo različne didaktične pripomočke, eden izmed njih je tudi geoplošča. Z njeno uporabo lahko pouk popestrimo in učencem omogočimo, da si lažje oblikujejo predstave in si snov hitreje zapomnijo. Matematične probleme na geoplošči lahko oblikujemo pri različnih vsebinah iz učnega načrta (npr. pri simetriji, dolžini, črtah), med drugim tudi pri vsebini o delih celote. Tako kot drugod tudi pri vsebini o delih celote učenci v 1. triletju spoznavajo in usvajajo pojme preko dejavnosti s konkretnim materialom. Ob njih ponovijo in obnovijo že znane pojme in razčistijo tiste predstave, ki niso najbolj jasne. Kasneje sledi postopen prehod na konkretne modele, diagrame in simbolični zapis. V empiričnem delu smo združili vsa tri ključna poglavja teoretičnega dela tako, da smo učencem zastavili problemsko situacijo na geoplošči, ki izhaja iz matematičnega sklopa aritmetike – deli celote: kako geoploščo na čim več različnih načinov razdeliti na polovico. V raziskavi je sodelovalo 54 učencev iz 3., 4. in 5. razreda. Ugotavljamo, da spol ne vpliva na uspešnost reševanja problema; da so rešitve učencev 3. razreda najenostavnejše, učencev 5. razreda pa bolj kompleksne – medtem ko učenci 3. razreda pojem polovice povezujejo predvsem s skladnostjo obeh delov, pa se učenci 5. razreda že zavedajo, da je pomembno, da sta polovici ploskovno enako veliki, pa čeprav nista nujno skladni; da so učenci uspešnejši pri prepoznavanju kot pri oblikovanju rešitev in da so učenci 3. razreda našli najmanj rešitev, učenci 5. razreda pa največ.
Abstract (ePrints, secondary language):	The diploma paper Investigating a Half consists of three key chapters: mathematical problems, a geoboard and parts of a whole. Mathematical problems encourage thinking in students and prepare them for solving everyday problem situations, that is why teachers should use them more frequently and as a replacement for routine exercises. Different didactic tools can be used to solve problems, one of them being a geoboard. It can be used to make classes more interesting and enable pupils to form their perceptions and remember the subject easier. It is possible to create mathematical problems on a geoboard in connection with different topics from the curriculum (e.g. symmetry, length, lines), also with parts of a whole. As with other topics, pupils in the first triad learn about parts of a whole and new terms through activities. This helps them to revise already known terms and clear up those perceptions that might not have been completely understood. This is followed by a gradual transition to concrete models, diagrams and putting down symbols. In the empirical part we joined all three key chapters of the theoretical part so that the pupils were given a problem situation on a geoboard. The problem was from arithmetic – parts of a whole: how to divide the geoboard in half in as many ways as possible. The survey included 54 pupils from the third, fourth and the fifth grade. We conclude that gender has no influence on solving the problem successfully; that solutions provided by the pupils from the third grade are simpler and those from the fifth grade more complex – while the former pupils relate the concept of a half with the congruence of both parts, the latter, older pupils are already aware that the areas of the halves need to be of the same size, while they need not be necessarily congruent; that pupils are more successful in recognising than forming solutions and that students form the third grade found the least solutions and the ones from the fifth grade the most.
Keywords (ePrints, secondary language):	mathematical problem
ID:	8311215