STUDENTS’ INTERPRETATION OF VARIABLES AND THE PHENOMENAL SIGN OF ALGEBRAIC EXPRESSIONS

Publication Type:

Journal Article

Source:

MENON ©online Journal Of Educational Research, 4th Issue, April 2017, University of Western Macedonia - Faculty of Education, Issue 4, Florina, Greece, p.14 (2017)

Keywords:

literal symbols, natural number bias, number concept, phenomenal sign, variables

Abstract:

Students face a series of difficulties understanding the concept of variable when introduced to algebra. This study focuses on one of these difficulties namely students’ tendency to think of literal symbols, which stand for variables in algebraic expressions, to represent only natural numbers. The study tested the students’ understanding of the numerical values of variables in algebra, and its relation with the way they interpret the sign of the algebraic expressions. 110 10th graders were asked to assign numbers to the variables of two given functions, in order to make their graph, and also to determine the sign of algebraic expressions that appeared in inequalities and functions. The results supported the hypothesis of the study, that students have a strong tendency to interpret variables as standing for natural numbers only, and this tendency appeared to be related with their tendency to misinterpret the phenomenal sign of the algebraic expressions as always being identical with their actual one. The phenomenal sign is the sign an algebraic expression appears to have as a superficial characteristic of its form, i.e. students tended to think of -2x-1 as a negative quantity, and 4+3x as a positive one

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