A Lesson Study to Develop Teachers' Geometric Habits of Mind / Studija predavanja u svrhu razvoja geometrijskih mentalnih navika nastavnika

Abstract

The general purpose of this study is to investigate the development of geometricthinking of elementary school mathematics teachers. To achieve this, the model ofresearch is defined as a lesson study. The implementation process of the study wascarried out with five mathematics teachers from different schools. Firstly, a fiveweekseminar process was carried out with teachers. As part of this process, thelesson study was explained with the theoretical framework of Geometric Habits ofMind and its practices were implemented. Then a lesson study was performed whichtook about three months. Data was collected by using multiple data collection toolsand data analysis was carried out by using a video analysis model developed byPowell, Francisco, and Maher (2003). As a result of this study, geometric thinking ofteachers has improved through the lesson study. During the process from the first lessonstudy to the seventh lesson study, we observed the improvement in the mathematicallanguage used by teachers, their explanations, student questions in class, together withactivities and problems produced by teachers based on the geometric habits of mindfor the relevant concepts. In the instructional processes, we also observed the teachersconsidering and assessing these components and planning for and implementing themin the geometry lessons. After the lesson studies, teachers also considered the geometrichabits in their own school settings and reflected on the instructional process throughprepared activities and problems which were then identified.Keywords: geometric habits of mind; geometric thinking; lesson study; teacherprofessional development ---SažetakGlavni cilj ove studije je proučavanje razvoja geometrijskoga razmišljanja učiteljamatematike u osnovnim školama. Kako bi se to postiglo, model istraživanja definiranje kao studija predavanja. Proces provedbe studije proveden je uz sudjelovanjepet nastavnika matematike iz različitih škola. Prvo je s nastavnicima održanopet tjedana seminara. Kao dio ovoga procesa, studija predavanja objašnjena jeteorijskim okvirom geometrijskih mentalnih navika te je isti primijenjen u praksi.Zatim je izvedena studija predavanja koja je trajala oko tri mjeseca. Prikupljanjepodataka provedeno je pomoću nekoliko alata za prikupljanje podataka, a analizapodataka izvedena je pomoću modela videoanalize koju su razvili Powell, Franciscoi Maher (2003). Kao rezultat ovoga istraživanja, geometrijsko razmišljanjenastavnika poboljšalo se tijekom studije predavanja. U procesu od prve do sedmestudije predavanja, primijetili smo poboljšanje matematičkoga jezika kojim sekoriste nastavnici, njihova objašnjenja, pitanja učenika u učionici, kao i aktivnostii zadatke koje su nastavnici stvorili na temelju geometrijskih mentalnih navikaza relevantne pojmove. U procesima učenja, promatrali smo i nastavnike kakorazmatraju i vrednuju ove komponente te ih uključuju u planiranje i provedbusvojih satova geometrije. Nakon studija predavanja, nastavnici su takođerrazmatrali geometrijske navike u vlastitim školskim okruženjima i razmišljali oprocesu učenja putem pripremljenih aktivnosti i problema koji su se tad definirali.Ključne riječi: geometrijske mentalne navike; geometrijsko razmišljanje;profesionalno usavršavanje nastavnika; studija predavanja