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Title:Risanje skic pri reševanju matematičnih problemov
Authors:Nidorfer, Rahela (Author)
Antolin Drešar, Darja (Mentor) More about this mentor... New window
Files:.pdf MAG_Nidorfer_Rahela_2017.pdf (1,83 MB)
 
Language:Slovenian
Work type:Master's thesis/paper (mb22)
Typology:2.09 - Master's Thesis
Organization:PEF - Faculty of Education
Abstract:Reševanje matematičnih problemov je eden izmed pomembnejših ciljev v učnem načrtu. Le te lahko rešujemo s pomočjo različnih strategij. Ena izmed teh je tudi uporaba skice, ki jo v številnih literaturah omenjajo kot eno izmed pomembnejših strategij. V teoretičnem delu smo tako izpostavili nekaj avtorjev, tujih in domačih, ki skico predstavljajo kot pomembno strategijo ali kot ključen element pri reševanju matematičnih problemov. Pomemben poudarek smo dali tudi konkretni uporabi vpeljave skice ter kako naučiti učence uporabe vizualnih reprezentacij in kakšne vrste le-teh poznamo. V empiričnem delu magistrske naloge smo s pomočjo preizkusa znanja želeli ugotoviti, kako spretni so učenci v 6. razredu osnovne šole pri reševanju problemov s pomočjo ene izmed strategij, tj. risanja skice. Zanimalo nas je tudi, kako uporabne so njihove skice, ali označijo ob skici ustrezne pomembne informacije, kakšno vrsto reprezentacije so uporabili in ali jih njihova skica pripelje do pravilnega rezultata. Vključenih je bilo 132 učencev iz treh slovenskih osnovnih šol. Podatke smo obdelali s pomočjo kvalitativnih in kvantitavnih metod pedagoškega raziskovanja. Rezultati raziskave so pokazali pomembno povezavo pri skicah, ki so vsebovale pomembne informacije in so bile uporabne, ter končnim rezultatom. Le-ta je bil v višji meri napačen pri nalogah, kjer ni bilo skice, ali kjer le-te niso bile uporabne in niso vsebovale pomembnih informacij. Pokazalo se je, da so imeli učenci pri prvi nalogi, ki je bila veliko lažja, manj težav z uporabo skice, kakor pri drugi in tretji nalogi. Tako so pri prvi nalogi v veliki večini skice uporabne in vsebujejo pomembne informacije, pri drugi in tretji nalogi pa je delež takšnih precej nižji. Glede vrste reprezentacij pri risanju skice pa so naši rezultati pokazali, da so prevladovale konkretne reprezentacije, sledila je uporaba delno konkretnih reprezentacij, v najmanjši meri pa so učenci uporabljali simbolne reprezentacije.
Keywords:matematika, matematični problemi, strategije reševanja, skica, reprezentacije, osnovnošolci
Year of publishing:2017
Publisher:[R. Nidorfer]
Source:Maribor
UDC:37.091.3:51(043.2)
COBISS_ID:23181064 Link is opened in a new window
NUK URN:URN:SI:UM:DK:EXAC7GRQ
Views:553
Downloads:86
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:PEF
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Secondary language

Language:English
Title:Drawing diagrams when solving math problems
Abstract:Solving mathematical problems is one of the most important goals included in the curriculum. Mathematical problems can be solved with the help of different strategies, one being the use of a diagram, which is considered one of the key strategies by several authors. The theoretical part therefore introduces several authors, both domestic and foreign, who present the diagram as an important strategy or as a key element in solving mathematical problems. In addition, the present work emphasizes the importance of establishing the use of the diagram, as well as a way to teach children how to use visual representations, and the different kinds of representations. With the help of tests, the empirical part of this Master’s Thesis strived to evaluate the skills of 7th grade primary school students in solving problems with the help of one of the strategies, i. e. the drawing of the diagram. It also considered the usefulness of their diagrams; whether they wrote down the important information next to the diagram, what kind of representation was used, and whether their diagram led them to the correct result. The survey included 132 students from three Slovenian primary schools. The data was processed with the help of the qualitative and quantitative methods of pedagogical research. The results of the survey show a significant relation between the diagrams which were useful, and included the important information with the end result. A lack of diagram or a diagram which was not useful or did not include important information meant a higher chance for a false result. The survey also found that students struggled less with drawing the diagram for the first exercise, which was significantly easier than the second and third exercise. As a result, the majority of the diagrams in the first exercise is useful, and includes important information, whereas this is not the case with the second and third exercise. In regard to the different kinds of representations in drawing diagrams, the results show that concrete representations were the most common. Partly concrete representations were in second place, and symbolic representations were the ones that students used the least.
Keywords:math, mathematical problems, strategies of problem-solving, the diagram, representations, primary school students


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