Ментална аритметика – стратегије одузимања

Mаријана Ж. Зељић, Универзитет у Београду , Учитељски факултет, имејл: marijana.zeljic@uf.bg.ac.rs
Светлана М. Илић, Универзитет у Београду , Учитељски факултет
Мила С. Јелић, Универзитет у Београду , Учитељски факултет
Иновације у настави, XXX, 2017/4, стр. 49–61

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doi: 10.5937/inovacije1704049Z

 

Резиме: Ментална аритметика има важно место у настави и учењу математике. Конкретно, она развија вештине решавања проблема, пружа могућности за развијање способности процене у рачунању и доприноси дубљем разумевању појма броја и декадног система. Основне карактеристике менталне аритметике су следеће: 1) рачуна се бројевима, а не цифрама (без записивања парцијалних резултата); 2) стратешка флексибилност у смислу бирања стратегије у зависности од карактеристика бројева у задатку. Циљ ове студије је да се испита способност ученика да одузму два броја без папира и оловке (ментално), као и да се идентификују стратегије које ученици у том поступку користе. Посебно значајно питање које се поставља у раду јесте – да ли ученици флексибилно користе стратегије рачунања, то јест да ли избор стратегије зависи од структуре задатка. Узорак истраживања чини шездесет и шест ученика трећег разреда из две београдске основне школе. Коришћене су дескриптивна метода и техника интервјуисања. Наши резултати показују да ученици као доминантну стратегију приликом рачунања без папира и оловке користе алгоритам цифарског рачунања, што представља узрок грешака у рачунању. Даље, као важан резултат истраживања истичемо да ученици не поседују стратешку флексибилност приликом менталног одузимања, што може бити показатељ недовољног концептуалног разумевања структуре бројева и рачунских процедура. Резултати истраживања указују на потребу да се измене приступи аритметичким садржајима померањем фокуса са развијања вештина алгоритамског рачунања на развијање дубљег разумевања и коришћења различитих поступака рачунања.

Кључне речи: ментална аритметика, стратегије одузимања, стратешка флексибилност

Summary: Mental arithmetic plays an important role in teaching and learning mathematics. More precisely, it develops problem-solving skills, helps students to develop a skill of making estimations in calculations, and contributes to a better understanding of the concept of numbers and decade system. The basic characteristics of mental arithmetic are as follows: 1) mental   calculation uses numbers, not digits (without recording partial results); 2) strategic flexibility in terms of selecting a strategy relative to the characteristics of numbers in a mathematics task. The aim of this paper is to examine pupils’ ability to subtract two numbers without using paper and pencil (mentally) and to identify the strategies used by pupils while doing the calculations. The paper also focuses on the very important question of pupils’ flexibility in using calculation strategies, or more specifically, whether the choice of a strategy depends on the structure of a mathematical task. The research was conducted on a sample of 66 third-graders from two primary schools in Belgrade. A descriptive method and interview were used in the research. The obtained results indicate that pupils predominantly use the algorithm of digital calculation in trying to do a calculation without a paper and pencil, which is the cause of many errors. Equally important, the pupils lack flexibility in doing mental calculation, which may indicate the insufficient understanding of the structure of numbers and calculation procedures. In addition, the results point to the need to change the approaches to arithmetic content by shifting the focus from developing algorithm calculation skills to developing a more in-depth understanding and use of different calculation procedures.

Кeywords: mental arithmetic, subtraction strategies, strategic flexibility.

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