Алгоритамски и концептуални приступ мерењу површине фигура

Маријана Ж. Зељић, Универзитет у Београду, Учитељски факултет, имејл: marijana.zeljic@uf.bg.ac.rs
Милица Р. Иванчевић, ОШ ,,Кнез Сима Марковић”, Београд
Иновације у настави, XXXII, 2019/1, стр. 64–74

| PDF | | Extended summary PDF |
doi:10.5937/inovacije1901064Z

 

Резиме: Мерење површине представља важну тему школских програма и тесно је повезана са другим математичким темама и са реалним окружењем. Резултати бројних међународних студија показују да су постигнућа ученика у домену мерења површине ниска, што се повезује са алгоритамским приступом наведеној теми, а који карактерише доминантно наглашавање процедуралних вештина и примена формула. У раду су разматрани различити нивои и параметри концептуалног разумевања мерења површине. Циљ истраживања јесте испитивање нивоа и карактера знања о мерењу површине код ученика четвртог разреда основне школе. У истраживању су коришћене дескриптивна метода и техника тестирања. Тест чине стандардизовани задаци (Huang & Witz, 2013) и још два задатка која нису део стандардизованог теста и која су осмишљена на основу транскрипта интервјуа из наведеног истраживања. Узорак je пригодан и чине га два одељења четвртог разреда једне основне школе у Београду. Основни закључак јесте да су ученици развили инструментално разумевање поступка мерења површине и да стратегије одређивања површине фигура своде на примену формула, због чега често греше, бирајући погрешну формулу. Као импликацију истраживања видимо истицање потребе да се довољно времена посвети активностима концептуалног приступа подели фигура и поплочавању које ће премостити велики јаз од поплочавања површи и бројања јединица мере до разумевања формула за рачунање.

Кључне речи: мерење, површина фигуре, алгоритамски и концептуални приступ.

 

Summary: Surface measurement is an important topic of the school curricula which is closely related to other mathematical topics and to the real world. The results of numerous international studies show that students’ achievements in the area of surface measurement are low, which is explained by the algorithmic approach to the topic characterised by the emphasis on procedural skills and the application of formulas. The paper looks at different levels and parameters of the conceptual understanding of surface measurement.. The aim of the research is to examine the level and quality of knowledge about surface measurements among pupils of the fourth grade of primary school. The descriptive method and testing technique were used in the research. The test consists of standardised tasks (Huang & Witz, 2013) and two more tasks that are not part of the standardised test and that were designed based on the transcript of the interviews from the above study. The convenience sample consisted of two classes of the fourth-grade pupils of a primary school in Belgrade. The key conclusion is that students have developed an instrumental understanding of the surface measurement procedure and that the strategies for determining the surface of the figures reduce the application of the formula, which is why they choose, often mistakenly, the wrong formula. Based on the research findings, we conclude that more time should be devoted to activities involving the conceptual approach to the division of figures and tiling. These activities will bridge the great gap between surface tiling and counting the units of measure and the understanding of calculation formulas.

Keywords: measurement, surface area, algorithmic and conceptual approach.

 

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