Modelovanje ekvivalencije matematičkih izraza u početnoj nastavi

Abstract

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.

The equals sign: The problem of early algebra learning and how to solve it

“…This means that students should not only be able to see the expression as a process of performing an operation, but to understand that it can exist on its own (Freudenthal, 1962;Kieran, 1981Kieran, , 1992Sfard, 1991;Sfard & Linchevski, 1994;Zeljić, 2014). Thus, from the mentioned research, Dabić Boričić and Zeljić (Dabić Boričić and Zeljić, 2021) notice that if expressions are understood "as processes (calculating the value of expressions), and not as objects with a meaning of their own, students will understand algebraic expressions as evaluation proce-dures, instead of mental entities that can be manipulated" (Dabić Boričić and Zeljić, 2021: 31). For example, when encountering the expression 8 + 5 for the first time, a student's first instinct will be to perform the operation, i.e.…”

“…The solution to this problem can be found in the use of visual representations, as noted by Dabić Boričić and Zeljić (Dabić Boričić and Zeljić, 2021), because they encourage structural conception, making abstract ideas more tangible (Fagnant & Vlassis, 2013). As a form of visual representation, schemes are representations comparable to the drawings students make when solving textual (word) problems, and have a positive effect on solving mathematical problems (Fagnant & Vlassis, 2013).…”