Neformalno znanje o pisnem deljenju pri učencih tretjega in četrtega razreda osnovne šole

Skvarča, Tjaša (author), Manfreda Kolar, Vida (mentor)

Učenci se v šoli učijo formalnih metod, ki pa niso razumljive vsem, zato v vsakdanjem življenju sčasoma prenehamo z uporabo formalnih metod in uvedemo neformalne. Njihova prednost je, da temeljijo na razumevanju. V magistrskem delu smo predstavili računsko operacijo deljenja in prikazali dve strukturi, ki sta značilni za deljenje. Natančneje smo predstavili postopek pisnega deljenja ter podali primer, kako postopek pisnega deljenja vpeljati v šoli. Opisali smo, kaj je neformalno znanje in kaj je formalno, ter predstavili njune značilnosti. Dotaknili smo se tudi pojma motivacije in načinov s katerimi lahko učitelji spodbujajo motivacijo pri pouku matematike. Eden izmed načinov povečanja motivacije za matematiko je tudi uporaba učnih pripomočkov, zato smo nekaj osnovnih tudi predstavili. Namen raziskave je bil ugotoviti, katere njim od prej še nepoznane formalne strategije za reševanje računov pisnega deljenja uporabljajo učenci 3. in 4. razreda. Posledično nas je zanimalo tudi, ali se med učenci 3. in 4. razreda pojavljajo razlike glede uporabljanih strategij, in, ali stopnja predznanja vpliva na uspešnost izvedbe računov pisnega deljenja z neformalnimi postopki. Zanimalo nas je tudi, ali učenci uporabijo učni pripomoček, v kolikor ga imajo na razpolago, in, kako so sploh motivirani za reševanje neznanih računskih problemov. Rezultati so pokazali, da predznanje nima tolikšnega vpliva na uspešnost izvedbe računov pisnega deljenja, kot smo pričakovali in, da učenci pogosto posegajo po učnih pripomočkih, če jih imajo na voljo. V rezultatih smo predstavili različne, ustrezne in neustrezne, strategije, ki so jih za reševanje računov pisnega deljenja uporabili učenci 3. in 4. razreda. Učenci so visoko motivirani za reševanje računov pisnega deljenja, s katerimi še niso seznanjeni. Raziskovanje na področju odkrivanja učenčevih lastnih iznajdb računskih algoritmov lahko pripomore k večjemu zavedanju o pomembnosti uporabe neformalnih metod. Želimo si, da bi učitelji, bolj kot negativne vplive neformalnih metod, v ospredje postavljali pozitivne vplive uporabe le-teh. Z uporabo neformalnih metod se lahko razvija kritično mišljenje učencev in lažje odkriva izvor nerazumevanja posredovane snovi, kar bi lahko izboljšalo splošno znanje vseh učencev.

• Language: Slovenian
• Keywords: pisno deljenje
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2019
• PID: 20.500.12556/RUL-107911
• COBISS.SI-ID: 12451145
• Publication date in RUL: 17.06.2019

Secondary language

• Language: English
• Title: Informal knowledge of long division among pupils in the third and fourth grade of elementary school

Abstract

In schools, pupils are taught formal methods that are not understandable to all of them. Consequently, they gradually stop being used in everyday lives and are substituted by informal ones, which are based on understanding, instead. This Master's Thesis contains a representation of the mathematical operation of division and its two typical structures. The process of long division along with manners of incorporating it into schools is introduced in greater detail. The concepts of informal and formal knowledge and its characteristics are also presented. We touch upon the notion of motivation and means of encouraging it in Mathematics Class. Since one of them is also the use of teaching accessories, we presented some of the basic ones in this Thesis. The purpose of the Thesis is to establish which of the formal strategies for long division calculation solving, previously unknown to pupils in the third and fourth grade of Elementary School, are used. Consequently, we are interested in differences between the used strategies of pupils in the third and fourth grade and whether the level of prior knowledge affects the successfulness of performance if long division is carried out via informal procedures. We are also interested in whether pupils tend to use teaching accessories if available, and what drives them to solve unknown mathematical problems. Results show that prior knowledge has less influence on the successfulness of long division problem solving than expected and that pupils tend to use teaching accessories often if given the chance. Results show different, suitable and unsuitable, long division problem-solving strategies that were used by pupils of third and fourth grade. Pupils are highly motivated for formerly unknown long division problem-solving. Research in the field of observing the pupil’s own inventions of algorithms for calculating can help raise awareness of the importance of the use of informal methods. We wish for teachers to shed light on positive aspects of using such methods rather than focusing on the negative ones. The use of informal methods could improve the overall knowledge of pupils as it can help develop pupils ‘critical ways of thinking and benefit the teachers’ in detecting the source of a topic’s incomprehension more easily.

• Keywords: long division