Modeling in Math Teching

Glavni cilj ovog rada je upoznati čitatelje, posebno nastavnike matematike, s uključivanjem primijenjene matematike u nastavu. Modeliranje problema iz svakod- nevnog života u čijem postavljanju aktivno sudjeluju i učenici čini njihova znanja dugotrajnijim i mijenja njihov pristup prema matematici. Na početku rada definirali smo model i matematičko modeliranje te naveli i različite pristupe matematičkog modeliranja. Objasnili smo proces modeliranja kao ciklički proces u kojem problem iz svakodnevnog života zapisujemo matematičkim jezikom te da modeliranju kao otvorenom procesu ne možemo predvidjeti kraj. Is- taknuli smo korake matematičkog modeliranja s aspekta primijenjene matematike u nastavi krenuvši od postavljanja cilja modeliranja koji olakšava filtriranje informa- cija i podataka do postavljanja i rješavanja modela. Valjanost rješenja provjeravamo i na kraju slijedi analiza. Zbog uglavnom negativnog stava učenika prema matematici drugo poglavlje ovog rada posvetili smo motivaciji za primijenjenu matematiku u nastavi koja bi kod učenika trebala promijeniti njihovu dosadašnju sliku o matematici. Naveli smo i nekoliko savjeta za nastavnike kako bi smo im olakšali uključivanje primijenjene matematike u nastavu i potaknuli ih na promjene u njihovoj nastavi. U posljednjem poglavlju rada naveli smo probleme iz svakodnevnog života i opisali moguće načine njihovog rješavanja. Kako bi smo pokazali da se svaki stvarni problem iz života može modelirati, detaljnije smo objasnili odabir odgovarajuće mobilne tarife. Za većinu opisanih problema u radu, ali i za ostale svakodnevne probleme svjesno ili nesvjesno primjenjuje se matematika kako bi se došlo do njihovog rješenja.The main aim of this paper is to introduce various ways of how applicable mathematics can be incorporated into teaching. It is meant for every reader, but especially for those who are math teachers. When setting a task, it is their job to model the assignment regarding everyday problems and also to actively involve students into the setting and solving of the task, thus making their knowledge more permanent and changing their approach to mathematics At the beginning of this study, model and mathematical modeling is defined and different approaches to mathematical modeling are introduced. The modeling process is described as a cyclical process in which an everyday life problem is written down in the language of mathematics. Due to the fact that modeling is an open process its end cannot be predicted. Each step of mathematical modeling from the aspect of applicable mathematics in teaching is illustrated and clarified. Starting with the setting of a modeling goal that facilitates the filtering of information and data we progress towards structuring and solving that model. The validity of the solution is checked and finally the analysis follows. Due to the mostly negative attitude of students towards math, the second chapter of this paper is devoted to the motivation for applicable mathematics in teaching which should change students’ previous image of math. Also, several teachers’ tips are mentioned to help incorporate applicable mathematics into teaching and encourage teachers to change their teaching methods. In the last chapter of the paper, problems of everyday life are listed and possible solutions for these problems are shown. To show that every real-life problem can be modeled, the choice of the appropriate phone provider is explained in more detail. For most of the problems described in the paper, but also for other everyday problems, mathematics is consciously or unconsciously applied in order to reach a solution