| Sažetak | Najčešća aktivnost učenika u nastavi matematike jest rješavanje matematičkog zadatka i on je ključni element interakcije između učitelja i učenika. Zato matematički zadatak zauzima ključno mjesto u učenju i poučavanju matematike kao i u vrednovanju znanja. Polazeći od tih činjenica, u radu se raspravlja o definicijama matematičkog zadatka, što je rješenje, a što proces rješavanja te što znači riješiti zadatak. Razmatraju se tri značajne klasifikacije zadataka: prema cilju, prema kognitivnim zahtjevima i prema namjeni u poučavanja, opisuju se njihove karakteristike i daju odgovarajući primjeri. Odabirom odgovarajućih zadataka različitih vrsta, ukoliko poznaje njihove karakteristike, učitelj ima priliku osigurati dobro okruženje za učenje, a učenici aktivnim sudjelovanjem u radu na zadacima imaju priliku postupno otkrivati matematičke ideje, usvajati matematičke koncepte s razumijevanjem, razvijati različite oblike matematičkog mišljenja i stjecati matematičku pismenost. Didaktički potencijal matematičkog zadatka otkriva se tek u cjelovitom radu na zadatku što se demonstrira kroz proces rješavanja nekoliko odabranih zadataka iz različitih područja matematike: od aritmetike, preko algebre do geometrije. Ipak, puni didaktički potencijal matematičkog zadatka dolazi do izražaja tek kad se predstavi učenicima, a zatim razmatraju njihovi načini rješavanja zadatka. Stoga ovaj rad može služiti kao teorijska osnova za empirijsko istraživanje didaktičkog potencijala matematičkog zadatka. |
| Sažetak (engleski) | The most common activity of students in mathematics classes is solving a mathematical task, and it is a key element of the interaction between teacher and student. That is why the mathematical task occupies a key place in the learning and teaching of mathematics as well as in the evaluation of knowledge. Based on those facts, here, we discuss the definitions of a mathematical task, what is a solution, what is the process of solving, and what does it mean to solve a problem. Three important classifications of tasks are considered: according to goal, according to cognitive requirements and according to purpose in teaching, their characteristics are described and appropriate examples are given. By choosing appropriate tasks of different types, if he knows their characteristics, the teacher has the opportunity to provide a good environment for learning, and students, by actively participating in the work on the tasks, have the opportunity to gradually discover mathematical ideas, adopt mathematical concepts with understanding, develop different forms of mathematical thinking and acquire mathematical literacy. The didactic potential of a mathematical task is revealed only in complete work on the task, which is demonstrated through the process of solving several selected tasks from different areas of mathematics: from arithmetic, through algebra to geometry. However, the full didactic potential of a mathematical task comes to the fore only when it is presented to students, and then their ways of solving the task are studied. Therefore, this work can serve as a theoretical basis for an empirical research of the didactic potential of a mathematical task. |
