Razvijanje algebraičnega mišljenja pri učencih 1. razreda

Oblak, Ana (author), Manfreda Kolar, Vida (mentor)

Učenci se v prvih letih šolanja pri matematiki najprej učijo aritmetičnih vsebin, šele kasneje sledi prehod k algebri. To pa ne pomeni, da učitelji v izobraževanje učencev, v prvih letih šolanja, ne morejo vključiti nalog, s katerimi bi spodbujali razvijanje algebraičnega mišljenja. Vključevanje nalog, s katerimi spodbujamo algebraično mišljenje, ima pozitivne vplive pri učenju, hkrati pa izboljšuje razumevanje matematičnih vsebin pri učencih. V magistrskem delu smo opredelili mišljenje in vrste mišljenja. Predstavili smo aritmetično in algebraično mišljenje ter primere razvijanja algebraičnega mišljenja pri pouku matematike. Preučili smo teme in cilje v učnem načrtu od 1. do 5. razreda, ki omogočajo razvijanje algebraičnega mišljenja. Predstavili smo zglede pretvarjanja nalog iz aritmetičnih v algebraične. Ker reševanje problemov spodbuja razvijanje algebraičnega mišljenja, smo se dotaknili tudi področja problemskega pouka. Pri algebraičnem mišljenju je pomembna zmožnost oblikovanja pravil in posplošitev, zato smo predstavili tudi vrste posplošitev v matematiki, induktivno in deduktivno sklepanje. Namen raziskave je bil ugotoviti, ali imajo prvošolci že razvito algebraično mišljenje in če da, v kolikšni meri ga pokažejo. Zanimalo nas je, v kolikšni meri lahko s programom poučevanja s poudarkom na nalogah za razvijanje algebraičnega mišljenja izboljšamo algebraično mišljenje pri prvošolcih. Zanimalo nas je tudi, če prihaja do razlik med spoloma pri preverjanju začetnega in končnega stanja v razvitosti algebraičnega mišljenja. Raziskava je pokazala, da prvošolci, pred začetkom izvajanja programa poučevanja s poudarkom na nalogah za razvijanje algebraičnega mišljenja, le-tega v večini niso pokazali, se pravi njihovi postopki reševanja nalog niso vsebovali elementov algebraičnega mišljenja. Ugotovili smo, da so prvošolci po koncu programa poučevanja delno pokazali algebraično mišljenje. Povzamemo lahko, da je s programom poučevanja mogoče izboljšati algebraično mišljenje prvošolcev. Iz rezultatov raziskave je tudi razvidno, da ni razlike med spoloma pri preverjanju začetnega in končnega stanja v razvitosti algebraičnega mišljenja.

• Language: Slovenian
• Keywords: algebraično mišljenje
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2020
• PID: 20.500.12556/RUL-117140
• COBISS.SI-ID: 20649219
• Publication date in RUL: 30.06.2020

Secondary language

• Language: English
• Title: Developing algebraic reasoning of first graders

Abstract

In the first years of schooling in mathematics, pupils at first learn arithmetic, followed by a transition to algebra. This does not mean, however, that teachers in the first years of schooling cannot include in the education tasks encouraging development of algebraic reasoning. The inclusion of tasks promoting algebraic reasoning has positive effects on learning and pupils’ better understanding of mathematical content. In the master's thesis we defined reasoning and types of reasoning. We presented arithmetic and algebraic reasoning and examples of algebraic reasoning development in mathematics lessons. We examined the topics and objectives in the curriculum from 1st to 5th grade that enable algebraic reasoning development. We presented examples of converting problems from arithmetic to algebraic. Since problem solving encourages algebraic reasoning development, we also touched on the area of problem-based learning. In algebraic reasoning, the ability to formulate rules and generalizations is important, so we also presented the types of generalizations in mathematics, inductive and deductive reasoning. The purpose of the research was to determine whether first-graders have already developed algebraic reasoning and, if so, to what extent they show it. We were interested in the extent to which we can improve algebraic reasoning in first-graders, with a teaching program with an emphasis on tasks for algebraic reasoning development. We were also interested in whether there are gender differences in checking the initial and final state in algebraic reasoning development. The research showed that the first-graders, before starting the teaching program, with an emphasis on tasks for algebraic reasoning development, did not show it in the majority, i.e. their problem-solving procedures did not contain elements of algebraic reasoning. We found out that the first-graders showed algebraic reasoning at the end of the teaching program. We can summarize, that algebraic reasoning of the first graders can be improved with a teaching program. The results of the research also showed, that there is no difference between the gender in checking the initial and final state in algebraic reasoning development.

• Keywords: algebraic reasoning