Encouraging strategies of matehematical argumentation

Matematično utemeljevanje je eden izmed načinov poučevanja matematike, pri katerem učenci svojim sošolcem utemeljujejo svoje ideje, mišljenje in poglede. Učenje skozi utemeljevanje temelji na teoriji simboličnega interakcionizma, ki poudarja, da posameznik spreminja svoje mišljenje in ideje na podlagi dejanj drugih. V magistrskem delu smo predstavili principe in strategije, ki spodbujajo utemeljevanje pri pouku matematike. Na osnovi pregleda literature navajamo nekatere izmed preizkušenih principov in strategij. Principi za spodbujanje matematičnega utemeljevanja so ustvarjanje konfliktne in sodelovalne situacije ter zagotavljanje pripomočkov za oblikovanje in preverjanje hipotez. Strategije, ki pomagajo učitelju zastaviti naloge za utemeljevanje, so naslednje: učenec mora izbrati stran, razkrivanje napačnih predstav učencev in priklic preteklih napačnih predstav. Takšen način poučevanja omogoča pridobivanje trajnejšega in kakovostnejšega znanja. V magistrskem delu smo s pomočjo preizkusa znanja ugotavljali, ali učenci utemeljijo svoj odgovor in na kakšen način. Zanimalo nas je tudi, ali na podano utemeljitev vpliva izbira odgovora in način razmišljanja učencev o enačaju. V raziskavo smo vključili 107 učencev 3. razreda. Pridobljene podatke smo obdelali s kvalitativnimi in kvantitativnimi metodami pedagoškega raziskovanja. Rezultati kažejo, da je večina učencev utemeljila svoj odgovor, vendar pa so bili le-ti zelo kratki. Ugotovili smo, da učenci povečini niso uporabljali grafičnih reprezentacij kot pomoč za utemeljitev. Raziskava je pokazala, da učenci o enačaju razmišljajo relacijsko ali operacijsko. Glede na pogostost pravilnega rezultata sklepamo, da so učenci, ki so o enačaju razmišljali relacijsko, pogosteje odgovorili pravilno, medtem ko so učenci z operacijskim razmišljanjem večkrat odgovorili nepravilno. Glede na način razmišljanja o enačaju smo opazili razlike tudi v pogostosti pojavitve tem. Rezultati so pokazali tudi, da je več učencev, ki so odgovorili pravilno, utemeljilo svoj odgovor, kot pa učencev, ki so odgovorili nepravilno. Prav tako se kažejo razlike v pogostosti pojavitve tem glede na odgovor učencev.This master\u27s thesis talks about argumentation in mathematics which is one of the ways to teach mathematics. By using it, pupils can argument either their ideas or ways of thinking and can explain how they see things. To begin with, teaching via argumentation is based on a theory of symbolic interactionism which emphasises that an individual changes his/her way of thinking and ideas on the basis of what others do. Firstly, this master\u27s thesis presents principles and strategies which encourage argumentation in mathematics. Some of them are cited on the basis of the revision of literature. For example, principles to encourage argumentation in mathematics are: creating conflictive and cooperative situation and ensuring accessories to form and check hypotheses. Then, strategies, which help a teacher to give assignments for argumentation, are: choosing a page by pupils, revealing their wrong visualisations and recalling their wrong visualisations from the past. So, this way of teaching enables gaining more time-lasting and qualitative knowledge. Secondly, in this thesis there has been a school test used in order to find out if pupils give arguments for their answers and in which way. Moreover, the thesis has tried to answer the question if the choice of an answer and a way of thinking about equation play an important part when giving an argumentative answer. There have been one hundred and seven pupils from the third grade included in a survey. The gained data have been analysed with qualitative and quantitative methods of a pedagogical research. The results show that most of the pupils have explained their answers, however, in a short way. Next, it has been found out that pupils have mostly not used graphic presentations as help for argumentation. So, the survey has shown that pupils think about an equation either relationally or operationally. Moreover, pupils who have thought relationally, have had more correct answers in comparison to those who have thought operationally. Another thing that has been noticed, is the difference in appearance of topics. Those pupils who have answered correctly have given an argument for their answer rather than those who have answered wrongly. What is more, if we consider pupils’ answers, there can be differences in appearance of topics seen