The role of language on the reversal error. A study with bilingual Basque-Spanish students

González‐Calero, José Antonio; Alcaraz, Ainhoa Berciano; Arnau, David

doi:10.1080/10986065.2020.1681100

Cited by 7 publications

(9 citation statements)

References 36 publications

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“…Furthermore, even restricting our attention to the reversal error, its sources are different depending on the country. In the Spanish case the word order matching and the syntactic comparison would both have some explanatory power for the reversal error, which is in line with other results about Spain (González-Calero et al, 2015;González-Calero et al, 2020;Soneira et al, 2018) and the United States (Clement, 1982;Clement et al, 1981;Cohen & Kanim, 2005;Fisher et al, 2011;Martin & Bassok, 2005;Wollman, 1983). In the South African context, just the word order matching and not the static comparison would have some explanative power.…”

Section: Discussion and Concluding Remarkssupporting

confidence: 87%

“…This tendency has been identified in studies with students who speak English (e.g. Cohen & Kanin, 2005;Fisher et al, 2011;Sung et al, 2014) and those who speak Spanish (González-Calero et al, 2015;González-Calero et al, 2020;Soneira et al, 2018). Our study now extends this result to students who speak isiZulu.…”

Section: Discussion and Concluding Remarkssupporting

confidence: 83%

“…On the one hand, when first introducing the algebraic language in Spanish schools, the study suggests that teachers need to highlight the meaning of the equal sign as an algebraic equivalence instead of correspondence, and the fact that letters represent quantities instead of being labels for objects. This would be so because these aspects have been proposed as the reasoning underlying the use of the static comparison strategy (Clement, 1982;Cohen & Kanim, 2005;Fisher, 1988;González-Calero et al 2020;Soneira et al, 2018;Sung-Hee et al, 2014). Teachers in Spain need to pay attention to the tendency to keep the structure or the visual display of the sentences in natural language when expressing them as equations, as this would underlie the use of the word order matching strategy (Clement, 1982;Fisher et al, 2011;Landy et al, 2014).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…For teaching interventions to be effective, these need to be based on the knowledge of the specific cognitive process and contextual circumstances that trigger the misconception. In addition, the phenomenon is complex because it involves the difficulties linked to the transition from arithmetic to algebra (MacGregor & Stacey, 1993;Malisani & Spagnolo, 2009), as well as the general difficulties related to the change of representation from the natural to a formal language (González-Calero, Berciano, & Arnau, 2020). This study, using a quantitative approach, examined Spanish and South African pre-service teachers' responses to translating word problems based on direct proportionality into equations.…”

Section: Introductionmentioning

confidence: 99%

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

2021

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This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’ proficiency in expressing direct proportionality word problems as equations, with a particular focus on the extent of the reversal error among the students’ responses. Furthermore, the study sought to test the explanatory power of word order matching and the static comparison as causes of the reversal error in the two contexts. The study found that South African students had a higher proportion of correct responses across all the items. While nearly all the errors made by Spanish students were reversals, the South African group barely committed reversal errors. However, a subgroup of the South African students made errors consisting of equations that do not make sense in the situation, suggesting that they had poor foundational knowledge of the multiplicative comparison relation and did not understand the functioning of the algebraic language. The study also found that the word order matching strategy has some explanatory power for the reversal error in both contexts. However, the static comparison strategy offers explanatory power only in the Spanish context, suggesting that there may be a difference in curriculum and instructional approaches in the middle and secondary years of schooling, which is when equations are taught.

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Section: Discussion and Concluding Remarkssupporting

confidence: 87%

Section: Discussion and Concluding Remarkssupporting

confidence: 83%

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2021

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“…Use S for the number of students and P for the number of professors" (Clement, 1982, p.17). In these statements, it was observed that most of the wrong answers were in the form of P = 6 • S, which they called RE because students reversed the order of the letters, compared to the correct answer S = 6 • P. The initial research by was preceded by numerous behavioral studies on RE González-Calero et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Neuroscience in algebraic problem solving: Studying the reversal error

Ferrando¹

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An important line of research related to the resolution of verbal problems is the study of the cognitive processes involved when subjects translate problems into the language of algebra. Therefore, it is essential to know which brain areas are associated with this process. One of the most common errors in problem solving is the reversal error (RE). A case where students recognize the information in the statement, but are not able to build a correct equation. The aim of this neuroeducational study is to investigate the brain anatomy differences between two groups, one group that commits RE and a second group that does not. Magnetic resonance images of 37 normal and healthy participants between the ages of 18-25 years were acquired. Changes in gray matter were assessed using voxel-based morphometry analysis. Our results show that the RE group has larger volume in the putamen, suggesting that these subjects have to make a greater effort to solve problems, which results in the putamen not maturing properly. To our knowledge, this is the first brain anatomy report showing the structure that supports the learning of problem solving and algebraic competence.

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The underlying neural bases of the reversal error while solving algebraic word problems

Ventura‐Campos

Ferrando

Epifanio

2022

Sci Rep

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Problem solving is a core element in mathematical learning. The reversal error in problem solving occurs when students are able to recognize the information in the statement of comparison word problems, but they reverse the relationship between two variables when building the equations. Functional magnetic resonance images were acquired to identify for the first time the neural bases associated with the reversal error. The neuronal bases linked to this error have been used as inputs in 13 classifiers to discriminate between reversal error and non-reversal error groups. We found brain activation in bilateral fronto-parietal areas in the participants who committed reversal errors, and only left fronto-parietal activation in those who did not, suggesting that the reversal error group needed a greater cognitive demand. Instead, the non-reversal error group seems to show that they have developed solid algebraic knowledge. Additionally, the results showed brain activation in the right middle temporal gyrus when comparing the reversal error vs non-reversal error groups. This activation would be associated with the semantic processing which is required to understand the statement and build the equation. Finally, the classifier results show that the brain areas activated could be considered good biomarkers to help us identify competent solvers.

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The role of language on the reversal error. A study with bilingual Basque-Spanish students

Cited by 7 publications

References 36 publications

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

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

Neuroscience in algebraic problem solving: Studying the reversal error

The underlying neural bases of the reversal error while solving algebraic word problems

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