The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition

Abstract

Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German–French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.

Units first or tens first: How bilingualism affects two-digit number transcoding?

“…This advantage in LM+ compared to mother tongue was also found for simple multiplication in adult population (Salillas & Wicha, 2012). In a study with a similar population of bilingual participants (Van Rinsveld, Brunner, Landerl, Schiltz, & Ugen, 2015), we recently observed that not only complex (solutions up to 99) but even simple addition problems with one-digit addends were solved slower in LM-(i.e. French) than in LM+ (i.e.…”

Language-dependent knowledge acquisition: investigating bilingual arithmetic learning

“…German uses a unit-ten order (e.g., “24” = four-and-twenty), whereas Italian, French, and English (for numbers higher than twenty) use a ten-unit order (e.g., “24” = twenty-four). This difference in word structure has been shown to influence arithmetic performance (e.g., Ellis & Hennelly, 1980; Göbel, Moeller, Pixner, Kaufmann & Nuerk, 2014; van Rinsveld et al, 2015). French, however, adds a second interference by making use of a base-20 structure for numbers between 70 and 99, while the other languages have a clear base-10 structure.…”

“…Similarly, German–French bilingual adolescents showed better performance when arithmetic tasks were presented in L1 (German) compared to L2 (French), even though later, in secondary education, mathematics had been taught in French. The effect was greater for complex addition problems (e.g., 56 + 32) compared to more simple addition problems (e.g., 4 + 2; van Rinsveld, Brunner, Landerl, Schiltz & Ugen, 2015). Taken together, research in the field of bilingual mathematics learning suggest that language is relevant for task performance.…”

Early Literacy and Numeracy Skills in Bilingual Minority Children: Toward a Relative Independence of Linguistic and Numerical Processing

“…In secondary school students enrolled in a bilingual program, Saalbach et al (2013) found a cognitive cost related to language switching from the instructional to the non-instructional language in arithmetic tasks. Similarly, Rinsveld et al (2015) found that adolescents and young adults were always better at solving complex mathematical tasks in their instructional language; on the other hand, their skills in solving complex calculations in the other language improved with their language proficiency. Another important aspect is the influence of language-specific number word structures in bilinguals’ arithmetic performances ( Prior et al, 2015 ; Rinsveld et al, 2015 ).…”

“…In contrast, an increasing number of studies also suggest that language abilities may play a pivotal role in the development of arithmetic skills (e.g., LeFevre et al, 2010 ; Purpura and Ganley, 2014 ). Third, the study of calculation skills in the bilingual population (e.g., Mondt et al, 2011 ; Prior et al, 2015 ; Rinsveld et al, 2015 ) has recently received increasing interest with the assumption that bilingualism, and specifically the case of language minority children, may offer a unique opportunity to disentangle the role of language skills in the development of calculation skills.…”