*By Dr. Deni Basaraba, RME Assessment Coordinator*

The number of English Learners (ELs) in the United States is growing at an unprecedented rate that shows no signs of slowing. As of 2013, for example, over 60.6 million people (21%) spoke a language other than English in the home and, of those, 37.6 million (62%) spoke Spanish in the home (Ryan, 2013). Moreover, the National Center for Educational Statistics (2011) reported that the number of ELs attending public schools has increased in the last three decades, from 4.7 million to 11.2 million. In Texas specifically, the percentage of students classified as ELs increased from 15.3% to 17.5% from 2003 to 2013 and the percentage of students receiving bilingual or English as a second language services grew from 14% to 17.1% (Texas Education Agency [TEA], 2014). This steady increase in the number of ELs attending our schools, combined with a persistent achievement gap in mathematics on both state and national assessments on which ELs exhibit consistently lower levels of proficiency than their non-EL peers, (NCES, 2013), underscore the need to ensure that our mathematics instruction incorporates evidence-based principles of instructional design and delivery to support the development of ELs mathematics understanding and proficiency.

Listed below are three research-based recommendations for supporting ELs mathematics understanding and proficiency.

**Situate mathematics problems in contexts that are familiar to students.**One of the primary goals of education is to provide students with instruction and practice in skills that they can generalize outside of the classroom to real-world contexts. Consequently, situating mathematics problems for students to solve in contexts that are familiar to them is important not only because it increases their likelihood of engaging in meaning-making actions that rely on conceptual understanding (as opposed to carrying out rote procedures) (Domínguez, 2011) but also because it increases students’ engagement in the problem-solving process (Brenner, 2002; Domínguez, LópezLeiva, & Khisty, 2014). Examples might include: grocery shopping, preparing meals, playing video games, reading books aloud to siblings and/or adults, or eating meals in the school cafeteria.

**Focus explicitly on mathematical vocabulary.**Although proficiency in mathematics requires students to think in terms of abstract ideas, concepts, and symbols that may be similar across languages, this does not support the common misconception that mathematics is “culture free” (Garrison & Mora, 1999). Rather, it could be argued that explicit instruction of mathematics vocabulary may be critical for some ELs because some mathematical words such as odd, times, table, or line may have specific mathematical definitions that are different than their meaning in everyday conversation (Fang, 2012; Garrison & Mora, 1999; Schleppegrell, 2007)

**Strategically incorporate visual representations and manipulatives.**One means of fulfilling the recommendation for developmental mathematics instruction put forth by the National Council of Teachers of Mathematics (NCTM, 2000) is to scaffold students’ understanding of abstract mathematical concepts with concrete and visual representations. Concrete representations, or manipulatives such as tangrams, for example, can be used to provide students with tangible experience with mathematical concepts such as greater than and less than, larger and smaller, or concepts of size (e.g., small, smaller, smallest) (Garrison & Mora, 1999). Visual representations, such as graphs or tables, may be useful methods for helping ELs to communicate their preliminary understanding of complex mathematical concepts such as multiplication or division that can be represented graphically more easily than they can verbally or with written words. Not only do these representations provide ELs with opportunity to see and touch while simultaneously being exposed to new mathematical vocabulary, but they also provide ELs with access to the key mathematical concepts in formats that don’t require dependence on language (Cirillo, Bruna, & Herbel-Eisenmann, 2010).

References

Brenner, M. (2002). Everyday problem solving and curriculum implementation: An invitation to try pizza. In M. E. Brenner & J. N. Moschkovich (Eds.) Journal for research in mathematics education. Monograph (Vol. 11): Everyday and academic mathematics in the classroom (pp. 63-92). Reston, VA: National Council of Teachers of Mathematics.

Cirillo, M., Bruna, K. R., & Herbel-Eisenmann, B. (2010). Acquisition of mathematical language: Suggestions and activities for English language learners. Multicultural Perspectives, 12, 34-41.

Domínguez, H., LópezLeiva, C. A., & Khisty, L. L. (2014). Relational engagement: Proportional reasoning with bilingual Latino/a students. Educational Studies in Mathematics, 85, 143-160.

Domínguez, H. (2011). Using what matters to students in bilingual mathematics problems. Educational Studies in Mathematics, 76, 305-328.

Fang, Z. (2012). Language correlates of disciplinary literacy. Topics in Language Disorders, 32, 19-34.

Garrison, L., & Mora, J. K. (1999). Adapting mathematics instruction for English-language learners: The language-concept connection. Changing the Faces of Mathematics: Perspectives on Latinos, 35-48.

National Center for Educational Statistics. (2013). NAEP data explorer [Data file].Washington, DC: U.S. Department of Education. Retreived from http://nces.ed.gov/nationsreportcard/naepdata/report.aspx.

Ryan, C. (2013). Language use in the United States: 2011. American Community Survey report (ACS-22). U.S. Census Bureau; U.S. Department of Commerce. Retrieved 02/26/14 from http://www.census.gov/prod/2013pubs/acs-22.pdf

Schleppegrell, M. J. (2007). Linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23, 139-159.

Texas Education Agency (2014). Enrollment in Texas public schools: 2013-2014. (Document No. GE15 601 03). Austin, TX: Author.