Different Perspectives on Success in Solving Stand-Alone Problems by 14 to 15-Year-Old Students / Različite prespektive o uspješnosti 14 i 15-godišnjaka u rješavanju izoliranoga problema

The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7 th and 8 th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students’ skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics. Key words : isolated problem; mathematical task ; problem solving; problem evaluation. --- U radu se definira posebna vrsta problemskoga zadatka te se razmatra njegov didakticki potencijal kao i uspjesnost ucenika u rjesavanju odabranoga problema. Instrument istraživanja je geometrijski zadatak s državne mature koji se postavlja u tri inacice: kao tekstualni problem, kao tekstualni problem uz odgovarajucu sliku te kao zadatak u kontekstu. U istraživanju je sudjelovalo 182 ucenika 7. i 8. razreda hrvatskih gradskih osnovnih skola. Didakticki potencijal razmatra se s aspekta iskoristivosti matematickih koncepata i veza, a uspjesnost ucenika u rjesavanju problema razmatra se s aspekta provedbe procesa rjesavanja i otkrivanja tocnoga rjesenja ovisno o nacinu postavljanja zadatka. Rezultati pokazuju da promatrani problem kao posebna vrsta problemskoga zadatka ima veliki didakticki potencijal, ali da ucenici imaju nedovoljno razvijene vjestine otkrivanja i povezivanja matematickih koncepata i njihovih svojstava. Osim toga, nacin postavljanja zadatka znacajno utjece na proces rjesavanja, a posljedicno i na uspjesnost određivanja rjesenja. Na temelju rezultata daju se prijedlozi primjene opisane vrste problema u nastavi Matematike. Kljucne rijeci : izolirani problem; matematicki zadatak; rjesavanje problema; vrednovanje problema