An assessment of the sources of the reversal error through classic and new variables

• Published in: Educational studies in mathematics Vol. 99; no. 1; pp. 43 - 56
• Main Authors: Soneira, Carlos, González-Calero, José Antonio, Arnau, David
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.09.2018; Springer Netherlands; Springer Nature B.V
• Subjects: Algebra; Comparative Analysis; Education; Educational research; Empirical analysis; Equations (Mathematics); Error Patterns; Expressions (Mathematics); Matching; Mathematical models; Mathematics; Mathematics Education; Preservice Teachers; Word Order; Reversal error; Algebra; Word problem solving; Magnitude
• ISSN: 0013-1954; 1573-0816
• DOI: 10.1007/s10649-018-9828-1

We present two empirical studies with 241 and 211 pre-service teachers that evaluate the explanatory power of word order matching and static comparison as models for the reversal error. We used tasks consisting of generating an algebraic equation representing a comparison given in a verbal statement. We introduce the types of magnitude involved in the statement as variables of analysis, something that was not previously tackled in previous works. Our results show that there are no statistical differences in the production of reversal errors depending on the information included in the name used to designate the variable, and that there are statistical differences depending on the syntactic configuration as well as the type of magnitude involved in the statement. The interpretation of these results indicates that both word order matching and static comparison have some potential as explanatory models for the reversal error, and that neither one of them, alone, is enough to completely explain the phenomenon.