Vloga stotičnega kvadrata pri raziskovanju zaporedij števil v 3. razredu osnovne šole

Jaklič Žagar, Uršula (author), Manfreda Kolar, Vida (mentor)

V teoretičnem delu magistrskega dela smo predstavili razvoj pojma število, vlogo štetja pri razvijanju številskih predstav, razvoj številskih predstav po Piagetu ter proces abstrakcije. Predstavili smo uporabo stotičnega kvadrata pri poučevanju števil do 100. Predstavili smo problemski pristop pri poučevanju zaporedij števil, strategije reševanja problemov z zaporedji števil ter ugotavljali uporabnost stotičnega kvadrata pri reševanju nalog iz zaporedij števil. Opisali smo cilje iz učnega načrta za področje razvijanja številskih predstav in zaporedij števil. Empirični del vsebuje kvantitativno in kvalitativno raziskavo. Z anketo smo raziskali, kako učitelji poučujejo zaporedja števil v 3. razredu in ali pri tem učencem pomagajo z uporabo stotičnega kvadrata. Analizirali smo, za katere cilje iz učnega načrta učitelji uporabljajo stotični kvadrat. Z učenci smo izvedli preizkus znanja, ki so ga reševali individualno. Ugotavljali smo povezavo med številsko predstavljivostjo in uspešnostjo reševanja nalog iz zaporedja števil ter vpliv stotičnega kvadrata na uspešnost reševanja nalog iz zaporedij števil. Kvalitativno smo analizirali tudi startegije njihovega reševanja nalog. Ugotovili smo, da učitelji pogosto uporabljajo stotični kvadrat pri poučevanju števil do 100, manj pa ga uporabljajo pri poučevanju zaporedij števil. Stotični kvdrat se učiteljem zdi dober pripomoček ter pri njem vidijo več prednosti kot slabosti. Večina učiteljev se strinja, da je stotični kvadrat dober pripomoček za računanje do 100, premalo pa se zavedajo pomanjkljivosti stotičnega kvadrata, saj učenci pri računanju do 100 s stotičnim kvadratom ne razvijajo miselnih procesov, ki bi podpirale razumevanje računanja do 100. Povezave med dolžino delovne dobe ter uporabo stotičnega kvadrata pri pouku nismo dokazali. Ugotovili smo, da učenci, ki imajo boljše številske predstave, tudi boljše rešujejo naloge o zaporedjih števil. Učenci so reševali linearna ter tudi kvadratna zaporedja, pri čemer so kvadratna zaporedja reševali slabše. Oba tipa zaporedij pa so reševali bolje, ko so bila le ta predstavljena na stotičnem kvadratu. Glede na rezultate ankete učiteljev o uporabi stotičnega kvadrata in glede na ugotovitev, da učenci bolje rešujejo zaporedja predstavljena na stotičnem kvadratu lahko zaključimo, da se učitelji premalo zavedajo možnosti uporabe stotičnega kvadrata tudi za poučevanje zaporedij števil.

• Language: Slovenian
• Keywords: stotični kvadrat
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2019
• PID: 20.500.12556/RUL-108535
• COBISS.SI-ID: 12504905
• Publication date in RUL: 17.07.2019

Secondary language

• Language: English
• Title: Hundred square in the number sequences research in the third grade of elementary school

Abstract

In the theoretical part of this Master’s Thesis, we present the development of the concept of numbers, the role of counting in developing number awareness, the development of number sense according to Piaget and the process of abstraction. We present the use of the hundred square as a teaching resource for teaching numbers up to 100, recurring issues in teaching numeric sequences, strategies in solving problems with learning numeric sequences and the benefits of the hundred square in solving exercises involving numeric sequences. We described objectives regarding development of number sense and numeric sequences in the Elementary School curriculum. The empirical part consists of a qualitative and a quantitative research. By means of a survey, we researched how teachers taught numeric sequences in the 3rd grade and whether they used the hundred square. We analysed for which curriculum objectives the hundred square was used. We conducted a qualitative research among the students, who wrote a test paper. We investigated the connection between the numerical perception and the solving of exercises in numeric sequences and whether the use of the hundred square had any influence on the success in solving exercises in numeric sequences. We have established that teachers often used the hundred square in teaching numbers up to 100, though not so often for teaching numeric sequences. Teachers, who see in it more advantages than disadvantages, predominantly perceive the hundred square as a good teaching resource. Only half of the teachers agree that the hundred square supports calculating up to 100 according to the pre-learnt algorithm. We were not able to prove the connection between the teacher’s length of service and the use of the hundred square. We determined that students with better numbers sense are also better in solving exercises concerning numeric sequences. Students solved linear and square sequences, and were better in solving linear sequences. They solved both types of sequences better when they were presented on the hundred square. According to the results of the survey on the use of the hundred square and the findings that students are better in solving sequences presented on the hundred square, we can conclude that teachers are insufficiently aware of the possibility of using the hundred square also for teaching numeric sequences.

• Keywords: hundred square