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*This We Believe Characteristics
· An
inviting, supportive, and safe environment
· Curriculum
that is relevant, challenging, integrative, and exploratory
· Multiple
learning and teaching approaches that respond to their diversity
*Denotes
the corresponding characteristics from NMSA's position paper,This We
Believe, for this article.
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David
Slavit & Gisela Ernst-Slavit
Oksana,
born in the Ukraine, has been in the United States for more than a year. Her
family lives in a new development in town, and her parents speak very little
English. Like her three younger siblings, she has made friends, but tends to
interact only when approached. While her English skills are improving and her
hard work is evident, she experiences a great deal of frustration in the
mathematics classroom. In the past, Oksana was asked to solve problems and give
the answer, often told exactly how to arrive at the solution. Now, to succeed,
Oksana not only has to provide the right answer, but she has to explain her
reasoning and the process by which she arrived at her solution. Oksana is
sometimes confused, sometimes frustrated, but always challenged by this new
classroom norm that requires sophistication on both mathematical and linguistic
levels.
Oksana's
situation is not unique. While English language learners (ELLs) have varying
levels of mathematical proficiency, those in reform-oriented classrooms rich in
problem solving, reasoning, and communication (National Council of Teachers of
Mathematics, 2000) are faced with added challenges. Here, students are required
to "talk math" (paraphrasing Lemke, 1990); that is, to use the
specific academic language needed to learn and express mathematical knowledge.
Talking math not only makes use of specialized vocabulary (e.g.,
"logarithmic," "asymptotic," and "collinear"),
but it also uses a variety of words and phrases that mean one thing in
mathematics and another in everyday contexts (e.g., "rational" and
"circular"). Just as the use of formal algebraic symbols can be a
barrier to some students who are first learning about algebraic concepts,
conversation in mathematics classrooms can be a barrier to understanding for
ELLs.
This
article discusses ways in which middle school mathematics teachers can assist
their students, and particularly ELLs, in a two-for-one learning
experience—learning both mathematics and the discourse skills needed to
successfully participate in reform-oriented mathematics classrooms. Much of the
discussion can easily generalize to other content areas. We begin with a brief
overview of the changing U.S. demographic picture and its impact on schools. We
then focus on the unique characteristics of common mathematical discourse, the
challenges it can pose to ELLs, and strategies that can help students learn to
"talk math."
Who are our English language
learners?
Current census data indicate that school
districts throughout the United States are increasingly serving a student
population whose home languages and cultures are diverse. For the 1993–1994
school year, the National Clearinghouse for English Language Acquisition
(NCELA) (2004) reported an ELL student enrollment of 3 million in the U.S. This
increased to 5 million just 10 years later, representing approximately 10% of
the student body. States with historically large percentages of ELLs (e.g.,
Arizona, California, Florida, Illinois, New York, and Texas) continue to show
increases in this student population. However, current data also show large and
unexpected growth of school-aged ELLs in states that have historically reported
low numbers (e.g., Tennessee, Indiana, Georgia, Nebraska, North Carolina, &
South Carolina).
English
language learners are very different from each other as well as from native
speakers; the above description of Oksana is but one example. Some ELLs come to
the United States having attended school regularly and bring with them literacy
skills and content knowledge, although in another language. For these students,
the transition into an academic setting in a second language will likely be far
easier than for students who may come with a history of survival within a
war-torn country or from an area where schooling was not always available or
accessible. Many will belong to very low-income families, although their
parents may be highly educated and once held professional positions. Some will speak
a degree of English, and some will speak no English at all. For all learners,
it is imperative that we find out "who our students are" so that we
can appreciate and build on the resources they bring and better understand
their needs.
Fortunately,
in spite of these differences, there are needs all ELLs share. In addition to
having to build their oral English skills, they also need to acquire reading
and writing skills in English, while at the same time keeping up their learning
in all content areas, including mathematics. Some ELLs will have other
compounding needs. For example, many students (e.g., Chinese and Arabic
speakers) might not be familiar with the Latin alphabet, and some students will
have no familiarity with using letters of any kind. Difficulty in changing to
the Latin alphabet can be compounded by the common use of these same symbols in
algebraic and other mathematical representations. Regardless of these
differences, and as stated by the National Council of Teachers of Mathematics
(1994) position on language minority students:
Cultural
background and language must not be a barrier to full participation in
mathematics programs preparing students for a full range of careers. All
students, regardless of their language or cultural background, must study a
core curriculum in mathematics based on the NCTM standards. (p. 20)
Thus,
the NCTM standards have special implications for mathematics teachers working
with ELLs. As the number of ELLs continues to increase, mathematics teachers
increasingly need to consider two-for-one teaching strategies that address both
the language and mathematical learning needs of these students. The recently
publishedTESOL PreK–12 English Language Proficiency Standards (Teachers
of English to Speakers of Other Languages, 2006) also provide specific
recommendations for developing English language learners' oral language and
literacy through academic content. Below we discuss some of the unique
characteristics of the specialized language needed to talk math and then provide
an assortment of teaching strategies for learning and talking mathematics.
The specialized language of
mathematics
The
development of the math register, that is, the language used to
talk about mathematics, is a critical component of developing mathematical
understanding in all students, including ELLs. But research on language
acquisition suggests that mathematical discourse and representations have
features that make it difficult for ELLs to draw meaning (Moschkowitz, 2000;
Secada, Fennema & Adajian, 1995). The use of specialized symbols, technical
language, and the various ways mathematical operations can be represented are a
few of these features. A discussion of language, vocabulary types, and the
unique grammar used in the teaching and learning of mathematics is presented in
this section.
Differences
between social and academic language
Social language is used in everyday, face-to-face interactions. While this is
the speech most used during recess, in the hallway, and outside the school, it
is also much needed in the classroom. ELLs generally acquire social language in
two years (Cummins, 2005). Academic language, on the other hand, is used to
acquire new knowledge or skills, develop deeper understanding of a topic, and
communicate that understanding to others; it is the language students must use
to effectively participate in content-rich discourse. There is evidence
(Cummins, 2005; Scarcella, 2003) that the acquisition of academic language and
literacy skills needed to fully participate in the mathematics classroom can
take five to seven years. Obviously, distinctions between social and academic
language are not precise, as classroom discourse (and even mathematical
discourse) often makes use of both. Because of this, Moschkowitz (2000) points
out that ELLs not only translate between English and their home language, but
between both sets of social and academic languages. Thus, mathematics teachers
who value communication in the classroom must consider an ELL's ability to
participate in both "everyday" and "mathematical" kinds of
interactions.
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