Izvleček
V prispevku sta predstavljena primera problemskih matematičnih nalog, ki ju lahko rešimo po različnih po teh. Pri prvem primeru dijaki računajo višino trikotnika v pravokotnem koordinatnem sistemu v ravnini, v
drugem primeru pa z različnimi praktičnimi metodami določijo višino drevesa ob šolskem igrišču. Zaradi
kompleksnosti sta nalogi primerni za gimnazijske programe. Izvedemo ju lahko tudi v programih srednjega strokovnega izobraževanja, če metode reševanja nalog prilagodimo znanju dijakov.
Ob reševanju nalog dijaki povežejo znanja različnih matematičnih vsebin, pri tem pa spretno uporabljajo informacijsko-komunikacijsko (IKT) tehnologijo, informacije pa iščejo s pomočjo literature in različnih virov. Z iskanjem različnih poti do rešitve razvijajo divergentno mišljenje, metodo analize in sinteze ter kritični odnos do interpretacije rezultatov. Na koncu vsake aktivnosti smo z dijaki analizirali delo. Dijaki so ocenili aktivnosti kot dobrodošli, saj so svoje znanje uporabili na drugačen način, in si želijo še več podobnih nalog.
Abstract
Power functions and metallic ratios
The article gives two examples of mathematical problem-solving tasks that can be solved in diff erent ways. In the fi rst example, secondary school students calculate the height of a triangle in a plane-rectangular coordinate system; in the second example, they determine the height of a tree next to the school recreation ground using various practical methods. Due to their complexity, the tasks are suitable for general secondary schools. They can also be implemented in secondary technical schools by adapting the task-solving methods to the students’ knowledge. When solving the tasks, the students integrate the knowledge of various mathematical contents, while skilfully using information and communication technology (ICT), and searching for information with the help of literature and various sources. By searching for diff erent paths to the solution, they develop divergent thinking, the method of analysis and synthesis, and a critical attitude towards the interpretation of results. At the end of each activity, the teacher and the students analysed their work together. Th e students assessed the activities as a welcome addition, since they were able to apply their knowledge in a diff erent way. They would like more tasks of this kind.