Nonstandard mathematical problems

Na početku ovog rada definiraju se nestandardni matematički zadatci, iznose tipovi zadataka te opisuju etape procesa rješavanja zadataka s korisnim heurističkim i usmjerujućim pitanjima i uputama za uspješno svladavanje svake od etapa. Nadalje, dan je niz riješenih nestandardnih zadataka (vezanih uz problem rješavanja jednadžbi i nejednadžbi) te standardnih zadataka korištenjem nestandardnih metoda i korištenjem svojstava funkcija (monotonost, parnost i periodičnost). Na kraju rada napravljeno je istraživanje o uspješnosti studenata u rješavanju nestandardnih zadataka, sklonost korištenju nestandardnih metoda u standardnim zadatcima te sklonost rješavanju nestandardnih zadataka.In the beginning of these paper, nonstandard mathematical problems are defined and types of tasks are listed. Moreover, stages of problem solving process are described, along with favorable heuristic and orienting questions or guidelines on how to successfully master each of the stages. Further, the series of solved nonstandard problems are given (connected to the problem of solving equations and inequalities), standard problems, resolved by using nonstandard methods and by using function properties (monotonic function properties, even and odd function properties, periodic function properties). In the end, paper contains research conducted on efficacy of students on nonstandard problem solving, tendency to use nonstandard methods on standard problems and inclination for nonstandard problem solving