Милана М. Дабић Боричић, Универзитет у Београду, Учитељски факултет, Република Србија, имејл: marijana.zeljic@uf.bg.ac.rs
Маријана Ж. Зељић, Универзитет у Београду, Учитељски факултет, Република Србија
Иновације у настави, XXXIV, 2021/1, стр. 30–43

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doi: 10.5937/inovacije2101030D

Резиме: Један од појмова који је у литератури препознат као кључан за разумевање алгебарских идеја је појам еквивалентности израза. За разумевање наведеног појма важан је контекст који се користи као основа за развијање значења, као и језик којим се исказују генерализације. Циљ рада је двојак: а) испитати да ли контекст текстуалног задатка и активности моделовања утичу на разумевање трансформације израза у еквивалентне форме; б) утврдити да ли на разумевање еквивалентности израза утиче ниво апстрактности израза (алгебарски или аритметички) који се користe. Истраживање је квазиексперименталног дизајна са две експерименталне и контролном групом. Узорак чини 148 ученика четвртог разреда. Постојање статистички значајних разлика између ученика експерименталних и контролне групе упућује да процес моделовања утиче на развијање појма еквивалентности израза. У овом истраживању нису се показале разлике у резултатима ученика који су били подучавани помоћу алгебарских, односно аритметичких израза. Ово имплицира да разумевање еквивалентности које је развијано кроз процес моделовања није у вези са нивоом апстрактности математичког језика који се користи, већ да на основу разумевања значења појма ученици са подједнаком успешношћу могу трансформисати и аритметичке и алгебарске изразе.

Кључне речи: еквиваленција математичких израза, моделовање, математички симболизам, алгебра.

Summary: The notion of expression equivalence is one of the terms that has been recognized in the literature as key to understanding algebraic ideas. To understand this term, the context used as a basis for developing meaning is important, as well as the language in which generalizations are expressed. The aim of this paper is twofold: a) to examine whether the context of a textual task and modeling activities influence the understanding of the transformation of expressions into equivalent forms; b) determine whether the understanding of the equivalence of the expression is affected by the level of abstractness of the expression (algebraic or arithmetic). The research is of a quasi-experimental design with two experimental groups and one control group. The sample consists of 148 fourth-graders. The existence of statistically significant differences between the students of the experimental groups and the control group suggests that the modeling process influences the development of the notion of expression equivalence. This research did not show any differences in the results of the students who were taught using algebraic or arithmetic expressions. This implies that the understanding of equivalence developed through the modeling process is not related to the level of abstractness of the mathematical language used, but that, based on understanding the meaning of the term, students can transform arithmetic and algebraic expressions with equal success.

Keywords: equivalence of mathematical expressions, modeling, mathematical symbolism, algebra.

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