Effects of application of mathematical modeling on the teaching of the derivative of function in the higher education of applied sciences

Abstract

<p>U&nbsp; doktorskoj&nbsp; disertaciji&nbsp; je&nbsp; prezentovano&nbsp; pedago&scaron;ko&nbsp; istraživanje&nbsp; koje&nbsp; se&nbsp; odnosi&nbsp; na&nbsp; teorijsko&nbsp; i eksperimentalno&nbsp; ispitivanje&nbsp; efekata&nbsp; primene&nbsp; metodskih&nbsp; pristupa&nbsp; zasnovanih&nbsp; na&nbsp; matematičkom modelovanju u obradi izvoda funkcije i njegove primene u visokom strukovnom obrazovanju. Na osnovu teorijskih principa na kojima je zasnovan proces matematičkog modelovanja, osmi&scaron;ljen je način za implementaciju modelovanja u nastavni proces i kreirani su modeli za realizaciju obrade sadržaja iz oblasti izvoda funkcije i njegove primene. Predložen je i originalni pristup matematičkom modelovanju koji se realizuje u računarskom okruženju i istaknute su sve prednosti novog pristupa<br />koje&nbsp; se&nbsp; tiču&nbsp; realizacije&nbsp; nastavnog&nbsp; procesa&nbsp; i&nbsp; rezultata&nbsp; učenja&nbsp; i&nbsp; poučavanja.&nbsp; Disertacija&nbsp; se&nbsp; bavi&nbsp; i savremenim trendovima u obrazovanju nastavnika i njegovom unapređenju. Poseban akcenat je stavljen&nbsp; na&nbsp; osmi&scaron;ljavanje&nbsp; elemenata&nbsp; obuke&nbsp; nastavnika&nbsp; za&nbsp; primenu&nbsp; matematičkog&nbsp; modelovanja&nbsp; u &scaron;kolskoj praksi.<br />Istraživanje o efektima primene matematičkog modelovanja je sprovedeno u dva ciklusa. Prvi ciklus istraživanja je realizovan u periodu od 2009-2014. godine sa četiri generacije studenata strukovnih studija. U eksperimentu je učestvovalo ukupno 555 studenata organizovanih u paralelne grupe. U prvom&nbsp; ciklusu&nbsp; istraživanja&nbsp; je&nbsp; praćen&nbsp; uticaj&nbsp; primene&nbsp; matematičkog&nbsp; modelovanja&nbsp; na&nbsp; postignuća studenata iz oblasti izvoda funkcije i njegove primene. Od instrumenata primenjenih za ispitivanje postignuća&nbsp; studenata&nbsp; su&nbsp; kori&scaron;ćeni&nbsp; testovi&nbsp; znanja&nbsp; (kolokvijum&nbsp; i&nbsp; ispit)&nbsp; i&nbsp; anketa&nbsp; koja&nbsp; je&nbsp; ispitivala stavove studenata o realizaciji nastave matematike i njenoj korisnosti.<br />Drugi&nbsp; ciklus&nbsp; istraživanja&nbsp; je&nbsp; sproveden&nbsp; &scaron;kolske&nbsp; 2016/2017.&nbsp; godine.&nbsp; Eksperiment&nbsp; je&nbsp; realizovan&nbsp; sa paralelnim grupama u kojima su učestvovala 204 studenta Visoke&nbsp; tehničke &scaron;kole&nbsp; strukovnih&nbsp; studija.U&nbsp; drugom&nbsp; ciklusu&nbsp; istraživanja&nbsp; su&nbsp; ispitani&nbsp; efekti&nbsp; primene&nbsp; novog&nbsp; pristupa&nbsp; matematičkom modelovanju&nbsp; u&nbsp; računarskom&nbsp; okruženju&nbsp; na&nbsp; znanja&nbsp; studenata&nbsp; iz&nbsp; oblasti&nbsp; izvoda&nbsp; funkcije&nbsp; i&nbsp; njegovih primena (eksperimentalna grupa) i dobijeni rezultati su&nbsp; upoređeni sa rezultatima koje su studenti ostvarili&nbsp; kada&nbsp; je&nbsp; nastava&nbsp; realizovana&nbsp; primenom&nbsp; tradicionalnog&nbsp; ciklusa&nbsp; modelovanja&nbsp; (kontrolna<br />grupa).Na&nbsp; osnovu&nbsp; rezultata&nbsp; oba&nbsp; pedago&scaron;ka&nbsp; istraživanja,&nbsp; utvrđeno&nbsp; je&nbsp; da&nbsp; realizacija&nbsp; nastave&nbsp; matematike primenom matematičkog modelovanja, kao i matematičkog modelovanja u računarskom okruženju, na obradu pojma izvoda funkcije i njegovih primena&nbsp; ima značajan uticaj na kvalitet znanja studenata i ostvarenost optimalnih rezultata u učenju, razumevanju nastavnih sadržaja i nji hovoj primeni na re&scaron;avanje problema iz ove oblasti.</p>

<p>In the doctoral dissertation, pedagogical research is presented, which refers to the theoretical and experimental examination of the effects of the application of methodological approaches based on mathematical modeling in the field of the&nbsp; derivative of the function and its application in college education.<br />Based on the theoretical principles on which the process of mathematical modeling is based, a way has been devised for the implementation of modeling in the teaching process and models have been created for the teaching process in the field of function &nbsp; derivative and its applications. An original approach to mathematical modeling that is realized in a computer environment is also proposed, and all the advantages of the new &nbsp; approach concerning the realization of the teaching process and the results of learning and teaching are highlighted. The dissertation also deals with modern trends in teacher education and its improvement. Special emphasis is placed on designing elements&nbsp; of&nbsp; teacher&nbsp; training&nbsp; for&nbsp; the&nbsp; application&nbsp; of&nbsp; mathematical&nbsp; modeling&nbsp; in&nbsp; school&nbsp; practice.<br />The research on the effects of the application of mathematical modeling was conducted &nbsp; in two cycles. The first cycle of research was realized in the period from 2009-2014 with&nbsp; four generations of students. A total of 555 students organized in parallel groups participated in the experiment. In the&nbsp; first&nbsp; cycle&nbsp; of&nbsp; research,&nbsp; the&nbsp; influence&nbsp; of&nbsp; the&nbsp; application&nbsp; of&nbsp; mathematical&nbsp; modeling&nbsp; on&nbsp; the achievements of students in the field of function derivative and its applications was examined. Among the instruments used to examine students achievements, knowledge tests (colloquium and final&nbsp; exam)&nbsp; and&nbsp; a&nbsp; survey&nbsp; that&nbsp; examined&nbsp; students&#39;&nbsp; attitudes&nbsp; toward&nbsp; the&nbsp; teaching&nbsp; process&nbsp; and usefulness of mathematics were created and used.<br />The second cycle of research was conducted in the 2016/2017 school year. The experiment was realized&nbsp; with&nbsp; parallel&nbsp; groups&nbsp; in&nbsp; which&nbsp; participated&nbsp; 204&nbsp; students&nbsp; of&nbsp; the&nbsp; Technical&nbsp; College&nbsp; of Applied Sciences. In the second cycle of the research, the effects of applying a new approach to mathematical&nbsp; modeling&nbsp; in&nbsp; the&nbsp; computer&nbsp; environment&nbsp; on&nbsp; students&#39;&nbsp; knowledge&nbsp; of&nbsp; function derivative and its applications (experimental group) were examined and the obtained results were compared&nbsp; with&nbsp; the&nbsp; results&nbsp; achieved&nbsp; by&nbsp; students&nbsp; using&nbsp; traditional&nbsp; modeling&nbsp; cycle&nbsp; (the&nbsp; control group).<br />Based&nbsp; on&nbsp; the&nbsp; results&nbsp; obtained&nbsp; from&nbsp; both&nbsp; pedagogical&nbsp; researches,&nbsp; it&nbsp; was&nbsp; determined&nbsp; that&nbsp; the realization of teaching mathematics by applying mathematical modeling, as well as mathematical modeling&nbsp; in&nbsp; the&nbsp; computer&nbsp; environment,&nbsp; has&nbsp; a&nbsp; significant&nbsp; impact&nbsp; on&nbsp; the&nbsp; quality&nbsp; of&nbsp; students&#39; knowledge and the realization of optimal learning outcomes, and their application on solving the problems from this area.</p>