The goal of this proposal is to determine the neurodevelopmental trajectory for multiplication fact retrieval in bilingual children, who make up 21% of the US school population. Our research with bilingual adults shows that the language in which arithmetic was learned (LA+) has better access to arithmetic facts than the other language (LA-), and that experience using arithmetic facts in LA- can reduce this LA+ advantage in adulthood. However, what impact LA+, or experience using LA-, has on the foundational period in childhood for learning arithmetic is still unclear. Children transition from solving simple arithmetic problems procedurally (e.g., counting) to retrieving arithmetic facts from verbal memory (e.g., multiplication tables). The absence of this transition between strategies has been associated with poor higher math fluency. Bilingual children may be at a disadvantage compared to monolinguals when accessing facts from their weaker language. This proposal will test the overarching hypothesis that LA+ establishes the predominant memory network for arithmetic fact learning in bilingual children. We will use event-related brain potentials (ERPs), specifically the N400 component, to quantify this transition. Novice multipliers (3rd graders) and practiced multipliers (5th graders) will judge the correctness of single-digit multiplication problems, which will be presented as Arabic numerals (digits) or, in a novel cross-modal paradigm with the first and second operand spoken followed by a visual digit solution. Operands will be small (2x3) and large (9x8), to make the solutions easier or harder to retrieve from verbal memory, respectively. We will measure the changes in brain and behavior as verbal fluency increases in children from 3rd and 5th grades, and between languages in bilinguals to measure preferential access to math facts.
Aim 1 will quantify the transition as children become experienced multipliers, comparing English-monolinguals and early Spanish-L1 bilinguals in both digit and spoken word formats.
Aim 2 tests if bilingual children make this transition in one or both languages. We will compare 1) early Spanish-L1 bilinguals in an English immersion classroom, 2) native English-speaking bilinguals in a Dual Language (DL) classroom and 3) native Spanish-speaking DL bilinguals. Each group will perform the cross- modal multiplication task with English and Spanish operands, separately. First, performance and ERP indices of the transition to verbal memory should be observed for small, but not large multiplications. Second, the LA+ should establish the predominant arithmetic-learning trajectory, such that early bilinguals and monolinguals both tested in their LA+ (English) will have similar trajectories, and DL students who learn arithmetic in both languages will have strong learning trajectories in both. In contrast, early bilinguals will have limited access to multiplications in their LA-. Our researc will lay the foundation for identifying malleable factors in bilingual children transitioning to an efficient memory strategy for multiplication facts. Our finding will have important implications about bilingual learning environments for both typically and atypically developing bilingual children.
This proposal aims to understand the neurodevelopmental trajectory for learning simple arithmetic in bilingual children, a building block that can have consequences on higher math fluency and, ultimately, long term impact on quality of life. Bilingual novice and practiced multipliers (3rd through 5th graders) will judge the solutions of simple multiplication problems for correctness in each of their languages, while performance accuracy and electrical brain waves are measured. The outcome of these studies will determine how bilingual children learn and use simple multiplications in each of their languages, helping to identify malleable factors to increase math fluency in bilingual children and potentially impacting 11.4 million school children, or 21% of the US school population.
| Dickson, Danielle S; Cerda, Vanessa R; Beavers, Rosemary N et al. (2018) When 2?×?4 is meaningful: the N400 and P300 reveal operand format effects in multiplication verification. Psychophysiology 55:e13212 |
