Making sense of the minus sign or becoming flexible in “negativity”

By Joëlle Vlassis. 2004

155 citations recorded by the source corpus.

Abstract This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to their strategies and to the meaning they gave to the minus sign. The analysis of the students’ oral and written discourse attests to the presence of two major kinds of conceptual change: the first one results from students’ attempts to reconcile their arithmetical presuppositions about natural numbers and the algebraic rules required to operate with negatives. The nature of the second kind of conceptual change relates to the minus sign and develops through an enlarged understanding and a flexible use of what we called ‘negativity’. We argue that these two kinds of conceptual change cannot fully occur without the students developing a meta-conceptual awareness of their symbolizing activities.

Subfields: Developmental and Educational Psychology, Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2991166b563454253413bfa38b40281d5f6a38aa

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In Developmental and Educational Psychology

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Citations in the corpus

A Proposed Instructional Theory for Integer Addition and Subtraction (2012, background): “Many researchers have interviewed, surveyed, and conducted teaching experiments (Steffe & Thompson, 2000) as a way to document students’ conceptions of integers from very early ages (Bofferding, 2010) to early adolescence (Gallardo, 2002; Vlassis, 2004, 2008).”
Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples (2013, background): “…than of balance between the two sides (Baroody & Ginsburg, 1983; Kieran, 1981), that negative signs represent subtraction but do not modify the terms they precede (Vlassis, 2004), and that variables represent a single value (Booth, 1984; Knuth, Stephens, McNeil, & Alibali, 2006; Küchemann, 1978).”
Diagnosing misconceptions: Revealing changing decimal fraction knowledge. (2015, background): “Repeatedly, conceptual change has been shown to be a gradual process, and students' strongly held misconceptions require extended instruction and time to be overcome (Vamvakoussi & Vosniadou, 2004; Vlassis, 2004).”
Design-Based Research Within the Constraints of Practice: AlgebraByExample (2015, background): “For many students, these misconceptions persist even after traditional classroom instruction on the relevant topic (J. L. Booth, Koedinger, & Siegler, 2007; Vlassis, 2004).”
Developmental changes in the comparison of decimal fractions (2010, methodology): “Previous studies have applied the conceptual change theory to other mathematical reorganizations, like extensions of number systems (Merenluoto & Lehtinen, 2002; Stafylidou & Vosniadou, 2004; Vamvakoussi & Vosniadou, 2004) or extension of a mathematical symbol and the related operation (Prediger, 20”
Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition (2012, background): “Vlassis, 2004 ). They offer descriptions and analyses of the erroneous use of integers due to the students’ experiences with natural numbers (Gallardo, 2002; Glaeser, 1981; Hefendehl-Hebeker, 1989; Thompson & Dreyfus, 1988; Vergnaud, 1989).”
What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra (2012, background): “” Some other researchers have also noted a similar phenomenon (Chiarugi, Fracassina, & Furinghetti, 1990; Crowley et al., 1994; Gallardo, 2002; Vlassis, 2004).”
A study on the teaching of the concept of negative numbers (2010, background): “The second concerns the difficulties experienced with regard to the meaning of arithmetic operations [6].”
Negative Integer Understanding: Characterizing First Graders' Mental Models (2014, background): “Numbers (n = 2) Fagnant, Vlassis, and Crahay (2005) Circle all of the numbers in the equation.”
Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics (2014, background): “, 2012), and comparing quantities (Vlassis, 2004) after negative integers have been introduced.”