Feedback of teachers and pupils on mathematical tasks in additional mathematics classes from 3rd to 5th grade

Vodilna ustvarjalna aktivnost v matematiki, ki jo moramo ponuditi nadarjenim učencem, je reševanje matematičnih problemov. Nadarjeni učenci naj bi pri dodatnem pouku pridobili nova izkustva, različna znanja in spretnosti, pri tem pa je potrebno upoštevati njihove želje in interese ter se z njimi posvetovati o izboru nalog oz. problemov. Pestrost nalog in poznavanje želja učencev pomembno vplivata na motivacijo pri reševanju matematičnih nalog. V magistrskem delu smo natančneje opredelili matematično nadarjene učence. Opisali smo, kako poteka odkrivanje in prepoznavanje matematično nadarjenih učencev v osnovni šoli, njihove značilnosti, naravo matematičnih sposobnosti, delo z matematično nadarjenimi pri rednem pouku matematike in pri dodatnem pouku matematike. Našteli in opisali smo vrste znanja po Gagnjevi klasifikaciji znanja, s poudarkom na reševanju matematičnih problemov. Reševanje nalog smo povezali tudi z učno motivacijo učencev. Namen raziskave je bil ugotoviti priljubljenost različnih vrst nalog pri dodatnem pouku matematike z vidika učencev in učiteljev, posledično pa tudi povezavo med želeno in dejansko uporabo nalog pri dodatnem pouku matematike od tretjega do petega razreda. Empirični del je sestavljen iz treh delov. V prvem delu raziskave so predstavljeni rezultati anketnih vprašalnikov za učitelje, v drugem delu so predstavljeni rezultati anketnih vprašalnikov za učence, tretji del raziskave pa vsebuje predstavitev izvedbe dodatnega pouka matematike in analizo intervjujev z učenci v 3. razredu osnovne šole. Rezultati so pokazali, da si učenci pri dodatnem pouku matematike želijo zahtevnejše in motivacijsko bolj spodbudne naloge. Ne moremo pa posploševati, da si vsi nadarjeni učenci želijo dodatnih učnih ur, pri katerih bodo reševali težje naloge. Glede na to, da moramo nadarjenim nuditi predvsem problemske naloge, so rezultati pokazali, da jih učitelji ne uporabljajo dovolj pogosto. Pri učencih so najbolj priljubljene naloge tiste, ki jih rešujejo v skupinah, pri učiteljih pa naloge, ki predstavljajo izziv. Najmanj zaželjene naloge so tako pri učencih kot pri učiteljih naloge, ki zahtevajo računanje dolgih računov. Raziskovanje na področju učiteljevih in učenčevih stališč do matematičnih nalog lahko pripomore k bolj kakovostnemu dodatnemu pouku in boljšemu delu z matematično nadarjenimi učenci. S skupnim sodelovanjem učiteljev in učencev bi delo lahko poenostavili in prilagodili željam, ki jih imajo učenci. Tako bi učenci razvijali svoje potenciale in pri pouku uspešno napredovali.The leading creative mathematical activity, we need to offer to the gifted pupils, is solving mathematical problems. In supplementary lessons talented pupils should gain new experiences, different knowledge and skills, according to their preferences and interests, and considering the selection of tasks or problems. The diversity of tasks and the awareness what pupils desire have an important impact on motivation in solving mathematical tasks. In this master’s thesis, we have thoroughly defined mathematically talented pupils. We have outlined how identifying mathematically gifted students in primary school proceeds, their characteristics, the nature of mathematical ability, work with the mathematically talented during the regular mathematic lessons and in supplementary mathematic lessons. We have outlined the types of knowledge according to Gagne’s Taxonomy, with the emphasis on solving mathematical problems. We have connected problem solving tasks with the students’ learning motivation. The purpose of the research was to determine the popularity of different types of tasks in the supplementary lessons from the point of view of teachers and pupils, and consequently the connection between the desired and the actual use of the tasks in supplementary maths lessons from the third to the fifth grade. The empirical part consists of three parts. The first part of the research presents the survey of the questionnaires for the teachers, the results of the pupil’s questionnaire are presented in the second part, and the third part of the survey presents the implementation of a supplementary mathematical lesson and the analysis of the interviews with 3rd grade primary school pupils. The results have showed that pupils in supplementary maths lessons want more advanced and motivationally more inspiring tasks. However, we cannot generalize that all gifted pupils want extra lessons to deal with more difficult tasks. Considering that gifted pupils have to be offered mainly problem tasks, the results have showed that teachers do not use them often enough. The most popular tasks with students are those solved in groups, but the ones that pose a challenge are preferred among teachers. The least desirable tasks with students as well as teachers are thus which require prolonged calculation. The research of teacher and student’s attitudes towards mathematical tasks can contribute to higher quality supplementary lessons and better work with mathematically talented pupils. With the participation of teachers and pupils, work could be simplified and adapted to the students’ preferences. In this way, students would develop their potential and progress successfully