Learning more than one language alters behavior and the structural and functional organization of the brain, with changes extending beyond the realm of language. Thus the bilingual cannot be viewed as simply two monolinguals in one brain, and in a country where 1 in 5 people speak a language other than English at home, it is essential to understand how being bilingual can impact other cognitive systems. This proposal aims to understand how arithmetic facts, such as multiplication tables, are represented and accessed for the multiple bilingual formats, digits and number words in each language. Language and arithmetic are thought to be tightly linked because arithmetic concepts are learned through verbalization. Thus, knowing more than one language may affect the way in which these concepts are organized and processed. We propose a series of studies that use event related potentials (ERPs) - a technique sensitive to the rapid temporal dynamics of cortical brain activity - along with behavioral assays of performance, to uncover qualitative and quantitative differences in processing arithmetic concepts in each format. We measure response times (RT) and ERPs to the solutions of simple multiplication problems (3x2=6) in which the congruence between operands and solutions is manipulated. Processing differences between congruent and incongruent trials across formats can shed light on the connections and basic structure of arithmetic fact representation. Preliminary data indicate that the language of learning for arithmetic (LolA), rather than the dominant language (L1), has stronger and more precise representations than the other language (LL2).
Aim 1 tests the intercode connections between representations by manipulating the solution to create language switches between codes. This will allow us to determine any asymmetrical switching costs based on the direction of a switch and in turn test inhibitory mechanisms.
Aim 2 will determine if the level of proficiency in Ll2 can improve the representation of arithmetic facts in this format. In a similar vein, Aim 3 asks whether experience specifically using arithmetic facts in Ll2 can improve the representations in this network. That is, can relearning through practice, such as for individuals teaching math in their second language, reverse the strong asymmetries between LolA and Ll2. We will first measure the speeded correctness judgments and accuracy for each aim, to uncover any overt behavioral differences across the codes. We will then measure 2 ERP components that are sensitive to arithmetic congruency and relatedness between arithmetic concepts, the N400, a negative wave peaking 400 ms post-stimulus onset sensitive to the spread of activation between entries in the mental lexicon, and the Late Positive Component, reflecting more controlled processing of unexpected solutions. Changes in amplitude, latency or distribution of these components can elucidate the connections within and between codes. Our studies will test the only current model for bilingual arithmetic, and lead to a better understanding of the brain organization for arithmetic, with consequences for learning and use under normal and abnormal conditions.

Public Health Relevance

Studies have focused on the connection between language and arithmetic concepts (e.g., Dehaene et al., 2003;Campbell, et al., 1999;Campbell and Epp, 2004), but have not been able to show the relationship between these definitively in a single language system, nor have they elucidated the unique circumstances surrounding arithmetic processing in a brain with more than one language. The current project uses a direct measure of electrical brain activity - event related potentials - along with behavioral assays to uncover the connections between the conceptual representations for simple arithmetic in a bilingual's three codes (first and second languages and Arabic digits), as well as to understand the nature of the underlying cognitive and neural processes within each code. These studies will begin to elucidate the basis of performance differences observed across a bilingual's languages, and at the same time inform models of language and arithmetic more generally, which can ultimately inform our understanding of impaired processing in childhood learning disabilities, such as dyscalculia, as well as to improve teaching and testing methodologies taking into account differential processing strategies for bilinguals and monolinguals alike.

National Institute of Health (NIH)
Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD)
Small Research Grants (R03)
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Pediatrics Subcommittee (CHHD)
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Mann Koepke, Kathy M
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University of Texas Health Science Center San Antonio
Schools of Arts and Sciences
San Antonio
United States
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Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y Y (2015) Arithmetic memory networks established in childhood are changed by experience in adulthood. Neurosci Lett 584:325-30
Salillas, Elena; Wicha, Nicole Y Y (2012) Early learning shapes the memory networks for arithmetic: evidence from brain potentials in bilinguals. Psychol Sci 23:745-55