Strategies for solving fraction problems in 4th and 6th grade

Veliko osnovnošolcev ima težave z razumevanjem ulomkov in z njimi povezanimi aktivnostmi. Zato je pomembno, da se učitelji tega zavedajo in poskušajo odkriti učenčevo razmišljanje o ulomkih, za namen oblikovanja nadaljnjega učnega procesa. V magistrskem delu smo želeli ugotoviti, katere strategije za reševanje problemskih nalog z ulomki uporabljajo slovenski osnovnošolci in kakšno je njihovo razmišljanje o ulomkih. Magistrsko delo je sestavljeno iz teoretičnega in empiričnega dela. V teoretičnem delu so najprej predstavljeni ulomki na splošno ter glavne smernice za njihovo poučevanje. Nato so predstavljeni cilji iz učnega načrta, ki pokrivajo to področje. Poudarjena je tudi učiteljeva in učenčeva predstava o ulomkih ter razvoj koncepta ulomkov in mentalne reprezentacije. Na koncu je predstavljena še problemska naloga kot oblika formativnega spremljanja ter strategije za reševanje problemskih nalog z ulomki. V empiričnem delu so predstavljeni rezultati preizkusa znanja, ki so ga rešili učenci 4. in 6. razredov treh slovenskih osnovnih šol. Preizkus znanja je vseboval nalogo deljenja osmih sendvičev med šest ljudi. Rezultati so pokazali, da je več kot polovica učencev za rešitev problemske naloge uporabila strategijo poimenovano »deljenje enega predmeta naenkrat«, pri čemer so se pokazale razlike glede na razred in matematične sposobnosti. Skoraj polovica učencev je za izražanje količine uporabila ulomek, prav tako pa je več kot polovica učencev podala rešitev naloge v obliki simbolnega zapisa.Many primary school pupils have difficulty understanding fractions and related activities. Therefore, it is important that teachers are aware of this and try to identify the pupil’s thinking about fractions in order to prepare the future learning process. In the Master’s thesis we wanted to find out, which strategies for solving of problematic tasks with fractions are used by Slovenian primary school pupils and how they think about fractions. The thesis consists of the theoretical and empirical part. In the theoretical part we first presented fractions in general and the main guidelines for teaching them. We then presented the goals from the teaching plan, covering this field. We stressed out the teacher’s and pupil’s idea about fractionsthe development of concept of fractions and mental representations. Finally, we presented a problematic tasks as a form of formative assessment and strategies for solving problematic tasks, involving fractions. In the empirical part we presented results of the knowledge test, done by pupils of the 4th and 6th grades from three Slovenian primary schools. The knowledge test contained a task of dividing eight sandwiches between six people. The results showed that more than half of the pupils solved the problematic tasks by using the strategy, called “dividing one object at a time”, whereby we noticed differences related to the grade and mathematical skills. Almost half of the pupils used a fraction to express quantities and more than a half of them also provided a solution of the task in a symbolic format