This article describes the 3rd cycle of an intervention in a mathematics content course that was designed to foster awareness among middle school mathematics preservice teachers (PSTs) of the challenges that English language learner (ELL) students face and the resources they draw on as they learn mathematics and communicate their thinking in English-only classrooms. Pairs of PSTs engaged 2 different ELL students in a videotaped task-based interview using 4 measurement tasks. Following each interview, the PSTs wrote a structured report guided by Mason's (2002) framework of noticing. The results of the intervention indicated that the PSTs went beyond awareness of ELLs' needs and challenges and also adopted strategies outlined in the literature that were aligned with best practices for teaching ELLs. The article also discusses the potential of the intervention and how it can be used by other mathematics educators.
Clara Lee Brown, Jo Ann Cady and P. Mark Taylor
Various techniques can enhance mathematics instruction for English language learners.
Kathryn B. Chval and Óscar Chávez
A four-component process to teach mathematics to English language learners is explored. Research-based strategies within each example illustrate how research can be turned into practice.
Conrado L. Gómez and Terri L. Kurz
English language learners (ELLs) at the preproduction phase, or initial phase, of language proficiency have limited oral English language skills; however, they do not lack cognitive abilities (de Jong and Harper 2005). On the contrary, most ELLs possess previous language and academic experiences. They can understand and articulate through nonverbal means (such as by drawing pictures) much more than they can demonstrate through speaking. Because many teachers may not fully understand the relationship between cognitive ability and language proficiency, they fail to challenge ELLs with higher-level activities (de Jong and Derrick-Mescua 2003).
Lynda R. Wiest
According to the National Clearinghouse for English Language Acquisition and Language Instruction Educational Programs, the growing number of students with limited English proficiency includes slightly more than 10 percent of K–12 students in today's U.S. classrooms (NCELA 2006). English language learners (ELLs) may need special support to meet the educational standards we set for students. In its Equity Principle, the National Council of Teachers of Mathematics states, “Some students may need further assistance to meet high mathematics expectations. Students who are not native speakers of English, for instance, may need special attention to allow them to participate fully in classroom discussions” (NCTM 2000, p. 12). This need has become particularly important because mathematics tasks are increasingly contextualized and thus verbal in nature, in addition to the fact that greater emphasis has been placed on communication in mathematics classrooms.
Paichi Pat Shein
This revelatory case study examines a 5th-grade teacher's orchestration of discourse and interaction to create opportunities for English language learners to participate in the repair of mathematical errors during a unit on finding the area of geometric shapes. The analysis of discourse takes on a binocular perspective of considering gesture and speech as a unity (McNeill, 1992). The teacher's pointing, representational, and writing gestures were studied in relation to her questioning and revoicing. This research was guided by a social learning theory that characterizes learning as active and interactive participation in communities of practice (Lave & Wenger, 1991; Wenger, 1998). The findings detail how the teacher used gestures in grounding her questioning, revoicing students' strategies, and narrating the meaning of geometric features.
Deandrea L. Murrey
A commonly held notion is that students learning English will do well in a mathematics classroom because mathematics is not a subject dependent on language proficiency. However, a student who is an English language learner (ELL) may struggle to succeed in the mathematics classroom where only English is taught. In 2004, there were approximately 5 million children in grades K–12 who were considered ELLs (NCELA 2004). Students from various language backgrounds may be learning English at the same time that they are learning new concepts in mathematics taught through English. Further, students are also learning the academic language of mathematics. The NCTM states: “All students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding” (NCTM 2000, p. 5). There are strategies for teaching mathematics to students who are ELLs. However, in addition to using these strategies, mathematics teachers also need to provide explicit language instruction for those students learning English (Rothenberg and Fisher 2007). By differentiating instruction in mathematics for English language learners, teachers can plan and provide access to mathematics curriculum for all students, with the added goal of language instruction for students learning English.
Gina M. Borgioli
Although English Language Learners (ELLs) quickly acquire basic interpersonal communication skills, most struggle for several years with reading and writing academic content in English (Cummins 1981). In particular, in English-only mathematics classes, children are likely to have difficulty reading and comprehending text, reading word problems, and giving written or oral justifications of their problem-solving strategies in English (Clarkson and Galbrath 1992; Cuevas 1984; Cummins 1984; Moschkovich 2000; Ron 1999). A language barrier should not be mistaken for a learning problem or a deficit. English-speaking peers of ELLs should also avoid assigning them lower social and academic status because of nonnative language skills and perceived inability to perform well on social and academic tasks (Cohen et al. 2004).
Diane Torres-Velasquez and Gilberto Lobo
Culturally responsive teaching is a dynamic form of teaching that builds on and supports students' home culture. The strategies that we recommend in this article for English Language Learners (ELL) are based on research or classroom experience. We provide real-life examples of how the second author, Gilberto Lobo, implements these ideas in the context of data analysis.
Students who are computationally fluent can solve problems accurately, efficiently, and with flexibility. These students draw on a repertoire of strategies when solving problems, and their choice of strategies often depends on the type of problem they are solving and the numbers involved. Computational fluency is rooted in an understanding of arithmetic operations, the base-ten number system, and number relationships. Communicating mathematical ideas is fundamental to developing computational fluency. When students share their solution strategies with others, they learn that there are many ways to solve problems and that some strategies are more efficient than others.