Polynomials in mathematics teaching

Budući da se polinomi više ne obrađuju kao zasebna cjelina u nastavi matematike, cilj rada je analizirati gdje se kroz osnovnoškolsko i srednjoškolsko obrazovanje polinomi pojavljuju i poučavaju indirektnim putem. U tu svrhu se započelo s analizom udžbenika i razgovorom s nastavnicima iz različitih gimnazija. Nakon toga smo se posvetili definiciji polinoma i njegovim osnovnim svojstvima. Zatim detaljno obradili polinom drugog i trećeg stupnja, kao i kvalitativno crtanje grafova polinoma, što pridonosi analitičkom razmišljanju u rješavanju problema koji su prikazani kroz rad. Za kraj diplomskog rada odabrani su zadaci s natjecanja te prezentirani zajedno s metodičkim napomenama, kako bi se mogli implementirati u nastavu kroz diskusije i aktivnosti.Since polynomials are no longer treated as a separate unit in mathematics teaching, the aim of this thesis is to analyze where polynomials appear and are indirectly taught through primary and secondary education. Therefore, the analysis of textbooks and conversations with teachers from different high schools began. After that, we devoted ourselves to the definition of a polynomial and its basic properties. Then we processed in detail the polynomials of the second and third degree, as well as the qualitative drawing of polynomial graphs, which contributes to analytical thinking in solving the problems presented through the thesis. At the end of the thesis, the tasks from the competition were selected and presented together with methodological notes, so that they could be implemented in teaching through discussions and activities