Influence of additive and multiplicative structure and direction of comparison on the reversal error

Abstract

An empirical study has been carried out to evaluate the potential of word order matching and static comparison as explanatory models of reversal error. Data was collected from 214 undergraduate students who translated a set of additive and multiplicative comparisons expressed in Spanish into algebraic language. In these multiplicative comparisons we used a format that can be translated from Spanish word-for-word as Bn times more than( increasing comparison) and Bn times less than^(decreasing comparison) instead of Bn times as many^, which is usual in other studies. Data analysis shows a significantly lower incidence of reversal error in the decreasing comparisons compared to the increasing ones. Additionally, no significant differences were found between additive and multiplicative comparisons. These results cannot be explained by the static comparison model.

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

“…Currently, fewer literature has been found related to reversible reasoning investigations in conceptual relationships for inverse function problems. The focus of previous researchers are more on the operational aspects, for example by identifying error reversals that students make for the problem of "students and professors" (González-Calero, Arnau, & Laserna-Belenguer, 2015;Soneira, González-Calero, & Arnau, 2018;Tunç-Pekkan, 2015), reversible multiplication relationships (Hackenberg, 2010), cognitive conflict and insufficient mental processes to reverse problem situations (Ramful, 2014), the type of task that causes reversible reasoning (B. Dougherty, Bryant, Bryant, & Shin, 2017;B. J. Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015;Sangwin & Jones, 2017;Simon, Kara, et al, 2016;Vilkomir & O'Donoghue, 2009).…”

Testing a Model for the Monitoring of Worked-out Algebra-Problem Examples: From Behaviours to Outcomes on a Math Task

“…Statements and the full solving procedure were segmented in information units, i.e., complete sentences or equations, as shown in Table 1 (text units were translated from Spanish into English). A 'reversal mistake' (Cooper 1986;González-Calero et al, 2015) was embedded in equation R1, causing this equation to be wrong, i.e., inconsistent with unit S1 (see footnote in Table 1). Data collection was done using the Read & Answer software (Vidal-Abarca & Cerdán, 2013).…”

Insights into the reversal error from a study with South African and Spanish prospective primary teachers

“…There have also been many studies that have looked at students' understanding of the variable. Some studies have reported the common misconception of taking a variable as a label standing for an object instead of standing for an unknown quantity (Fisher et al, 2011;González-Calero et al, 2015;Soneira, González-Calero, & Arnau, 2013;Stacey & MacGregor, 1999). Other misconceptions that have been identified include students thinking that the same letter appearing at different points in a number sentence could not represent the same number (Filloy, Rojano, & Puig, 2008), that letters can only stand for whole numbers, among many others.…”

“…Another explanative model of the reversal error is that students understand the mathematical relationship, but hold misconceptions about the equal sign (e.g. Clement, 1982;Cohen & Kanim, 2005;Fisher et al, 2011;González-Calero et al, 2015). Whatever the explanation, it is clear that the reversal error seems to be rooted in common algebra learners' misconceptions.…”