Growth in Math Computation among Monolingual and English Language Learners:Does the Executive System have a Role?

ABSTRACT

This cohort-sequential study explored the components of working memory that underlie math calculation in elementary school children who are monolingual (English) or English language learners (ELLs) whose first language is Spanish. To this end, children (N = 789) in grades 1, 2, and 3 at wave 1 were administered a battery of math, vocabulary, reading and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again one year and two years later to the same participants. Three important findings emerged. First, along with naming speed, the results suggest that growth in the executive component of WM was significantly related to growth in calculation performance. Second, performance on measures of reading, fluid intelligence, naming speed and executive processes in wave 1 were significantly related to wave 3 math calculation performance. Finally, the full latent growth model showed that monolingual and ELL children were statistically comparable in computation at wave 3. Thus, strong support was found for the notion that the executive component of WM was related to math computation but weak support for the notion ELL children experienced a math achievement gap.

Notes

1. The literature is unclear as to what terms appropriately capture our sample (e.g., English language learners, English learners, limited English-proficient, balance vs. unbalanced bilingual, emerging bilinguals). We used the term English language learner to align with the literature, but realize the sample is best described as bilingual or emerging bilingual. This is because the children varied in proficiency in their primary language and/or were weak in both language systems.

2. The CELDT assesses English learners in the following areas: listening, speaking, reading and writing. The test is given to students whose Home Language Survey indicates a language other than English is spoken in the home, and for whom there is no prior record of English language testing. The test is administered annually to track English proficiency. The test score yields a proficiency level represented numerically as 1–5. The five levels of the CELDT are: Beginning, Early Intermediate, Intermediate, Early Advanced, and Advanced. This measure has been validated as a measure of English Proficiency (e.g., Llosa, 2007) and because this was a public school classification of ELL students in our study, we assumed the measure had face validity.

3. Colom, Flores-Mendoza, Quiroga, and Privado (2005), Rosen and Engle (1997), Swanson, Mink, and Bocian (1999) find that the numbers reversed task is a short-term processing capacity measure. For example, Rosen and Engle (1997) stated that “We found no evidence that backward recall required more complex recall than did forward recall. Also, we found that participants used a phonological code for both forward and backward serial recall” (p. 46). Other studies have found forward and backward recall of digits load on the same factor (e.g., Colom et al., Swanson et al., 1999). We did however, run the analysis without backward digit span and found that the pattern of results was comparable. Thus, in the present study, the backward span task as a measure of phonological STM was maintained and provided an excellent fit to the data.

Additional information

Funding

This research is based on two four-year longitudinal studies funded by the U.S. Department of Education, Cognition and Student Learning [R305H020055; R324A090092], Institute of Education Sciences (IES). This earlier foundational work is being extended under a National Science Foundation (NSF) grant, Division of Research on Learning [award number 1660828] Sciences awarded to the first author. This study does not necessarily reflect the views of the U.S. Department of Education, IES, NSF, or the participating school districts. Special appreciation is given to Margaret Beebe-Frankenberger, Cathy Lussier, Bev Hedin, Lelani Saez, Olga Jerman, Xinhua Zheng, Melina, Melgarejo, Joseph Rios, Elizabeth Arellano, Nicole Garcia, Alfredo Aviles, Steve Gómez, Paula Aisemberg, Valerie Perry, Loren Albeg, Dennis Sisco-Taylor, Wenson Fung, Georgia Doukas, Rebecca Greg, Kelly Rosston, Crystal Howard, Mike Gerber, Michael Orosco, and School District Laison and Consultant: Erin Bostick Mason for data collection and/or analysis.