(Page 1 of 3) - English Language Learners: Developing Mathematical Understanding authored by Olson, Jo., Braun, Karmin., Colasanti, Meghan., Groth, Karla. and Wilcox, Bruce.

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ENGLISH LANGUAGE LEARNERS:

DEVELOPING MATHEMATICAL UNDERSTANDING

Jo Clay Olson

Washington State U

## email not listed ##

Karmin Braun

Aurora Public School

## email not listed ##

Meghan Colasanti

Aurora Public School

meghan.## email not listed ##

Karla Groth

Aurora Public School

## email not listed ##

Bruce Wilcox

Aurora Public School

## email not listed ##

Today mathematics reform efforts face the challenge of raising the performance levels of

students and are forced to examine how to accomplish this within growing culturally and
linguistically diverse populations (Grant & Lei, 2002; Gebhard, 2002). Analysis of the National
Assessment of Educational Progress (NAEP) indicated that English language learners (ELLs) do
not achieve at the same level as their English speaking counterparts . In 2005, 71% of the non-ELL
eighth-grade students were at the basic level or above compared to only 29% of the ELL eighth-
grade students who were at the basic level or above. The report documents that both ELL and non-
ELL student mathematics achievement has slowly increased since 1996 and the achievement gap
between ELLs and non-ELLs was slightly reduced. But, with only 6% of the ELL eighth-grade
students reaching proficiency, inequities are significant.

Cocking and Mestre (1988) suggested that the language used to describe mathematical ideas in

English has specific interpretations and is problematic for students with limited understanding of
English. Thus, achievement gap may not be due solely to difficulties with math concepts or to
second language acquisition but to a complex interaction of the two. Students interpret math
related words and symbols based on previously constructed understanding. When students are also
learning English, the process of acquiring new mathematical understanding is mediated through
two sets of meanings developed in their native tongue and English. Translation alone, without
attention to prior knowledge of math concepts is not effective. Helping students who are ELLs
develop a rich understanding of mathematics is challenging because everyday and abstract ideas
may have been internalized in one or the other language, based on individual experiences.
Therefore it is extremely difficult for teachers to identify the prior knowledge upon which they
should build.

This research report is part of a longitudinal study that examines the how ELLs assimilate

mathematical understanding while acquiring English language skills. The purpose of this report is
to describe the mathematical ideas that fourth- and fifth-grade ELLs understood after using
Investigations in Number, Data, and Space .

Theoretical Framework

Theorists (e.g., Cobb, Wood, & Yackel, 1970; Kumpulainen & Mutanen, 2000) suggests that

social activities influence the learning of mathematics as individuals negotiate meaning through
interactions. From the perspective of symbolic interactionism (Blumer, 1969), an individual
interprets another person’s words and gestures to create meaning. Shared meanings are constructed
through a dynamic process of creating and re-creating meanings as individuals interact with each
other. People attach particular meanings to words, symbols, and gestures through these social

Lamberg, T., & Wiest, L. R. (Eds.). (2007). Proceedings of the 29

annual meeting of the North

American Chapter of the International Group for the Psychology of Mathematics Education,
Stateline (Lake Tahoe), NV: University of Nevada, Reno