Strategije reševanja geometrijskih problemov o zaporedjih in oblikovanje posplošitev pri učencih 5. razreda

Vaupotič, Anja (author), Manfreda Kolar, Vida (mentor)

V magistrskem delu z naslovom Strategije reševanja geometrijskih problemov o zaporedjih in oblikovanje posplošitev pri učencih 5. razreda se v teoretičnem delu ukvarjamo s tem, kaj je matematični problem, predstavimo dve klasifikaciji (Fobisherjevo in Mialaretovo) in druge delitve problemov, ki jih predstavi Cotič. Opišemo umestitev reševanja problemov v učnem načrtu za matematiko in obravnavamo problemski pouk tako, da ga primerjamo s klasičnim razlagajočim poukom. Naštejemo strategije, načine in postopke reševanja problemov, vključimo tehniko reševanja problemov po Polyi in 6 faz reševanja problemov po Žakelj. Potem predstavimo še posploševanje, ga definiramo in razdelimo na različne vrste posploševanj, ki jih ponudi Ciosek. Posvetimo se tudi naraščajočim zaporedjem, ki so osrednji del naše raziskave, prikažemo vlogo učitelja pri reševanju problemov in opišemo nekaj drugih raziskav, v katerih se pojavljajo naraščajoča zaporedja ali se kaže vloga učiteljevega vodenja pri reševanju problemov. Empirični del je namenjen analizi strategij reševanja geometrijskih problemov iz naraščajočih zaporedij. Vzorec so predstavljali naključni učenci 5. razreda osnovne šole z različnim učnim uspehom pri matematiki. Pri raziskavi smo uporabili kvalitativni raziskovalni pristop ter deskriptivno in kavzalno neeksperimentalno metodo pedagoškega raziskovanja. Z učenci smo opravili individualne polstrukturirane intervjuje, v katerih so z našim vodenjem reševali 3 matematične probleme iz naraščajočih zaporedij. Medtem smo si beležili njihovo uspešnost, hitrost, stopnjo pomoči in vrsto uporabljene strategije pri reševanju danih problemov. Rezultati so pokazali, da učenci 5. razreda uporabljajo različne strategije reševanja problemov in nekateri celo znajo izbrati ustrezno, najučinkovitejšo pot, ki jih bo kar najhitreje pripeljala do cilja in rešitve. Rezultati raziskave kažejo tudi, da za naš vzorec učencev obstaja pozitivna povezanost med učno uspešnostjo učenca pri matematiki in uspešnostjo pri reševanju danih matematičnih problemov. Ugotovili smo, da učno šibkejši učenci potrebujejo za reševanje problemov več časa in učiteljeve pomoči. Čeprav so skoraj vsi prišli do pravila vsaj enega naraščajočega zaporedja, so povsem samostojnega posploševanja in oblikovanja pravila zmožni le nekateri učenci.

• Language: Slovenian
• Keywords: matematični problem
• Work type: Master's thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Year: 2022
• PID: 20.500.12556/RUL-142129
• COBISS.SI-ID: 126393091
• Publication date in RUL: 27.10.2022

Secondary language

• Language: English
• Title: Geometric problem-solving strategies on sequences and generalizations in primary school students in grade 5

Abstract

The theoretical part of the master's thesis, titled Geometric Problem-Solving Strategies on Sequences and Generalizations in Primary School Students in Grade 5, treats what a mathematical problem is, how mathematical problems are classified (Fobisher and Mialaret) and divided (Cotič). We describe where mathematical problems are located in the curriculum of mathematics and what problem-based learning is compared to traditional learning. Problem solving strategies and procedures are presented (Polya’s problem solving technique and Žakelj’s 6 phases of problem solving) with the definition of generalization and its different sorts. In addition, a description of growing patterns is offered, how important teacher’s role is in problem solving and leading to some researches similar to ours and their conclusions. The empirical part presents the analysis of problem solving strategies on growing patterns. We interviewed random grade 5 students with different average grades in Mathematics and used qualitative research approach and descriptive and casual non-experimental method of pedagogical research. Students were solving 3 mathematical problems based on growing patterns by our lead. Meanwhile, we recorded their performance, speed, level of assistance and the type of strategy they used in solving given problems. The data were than categorized and processed using the IBM SPSS Statistic 22 program. We noticed that grade five students use different problem solving strategies and some of them are even capable of choosing the most effective way, which will lead them to the solution the fastest. The results have shown there is a positive correlation between the learning achievement in mathematics and accomplishment in solving the given mathematical problems for our group of 25 students. Research also shows that students with lower learning capabilities need more time and teacher’s assistance to solve a problem. Even though almost everyone formed a rule of at least one growing pattern, only a few are skilled enough to generalize and form a rule independently.

• Keywords: mathematical problem