*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.
terça-feira, 28 de agosto de 2012
Teaching Mathematics and English to English Language Learners Simultaneously - PART I
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."
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 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.