# CEMELA's Theoretical Framework

A sociocultural perspective is the guiding theoretical paradigm for CEMELA and permeates the Center activities from research to teacher education. This perspective emphasizes the social and cultural dimensions of teaching and learning mathematics, while remaining compatible with current interpretations of constructivist approaches to teaching. The educational circumstances of Latinos are sufficiently different from other racial and ethnic groups that they cannot be addressed adequately under one umbrella of diversity nor with general "good" teaching approaches. Affiliation to Spanish regardless of their proficiency in the language sets Latinos/as apart from other major minority groups (Suárez-Orozco and Páez, 2002). To improve Latinos' education, research points to the need to capitalize on language and culture (Garcia, 1993). This is CEMELA's mission. The work in the Center will focus on mathematics education and its relation to the two main areas - community knowledge (culture) and language.

### Building on Community knowledge

Among the most significant work on Latinos/as is the project Funds of Knowledge for Teaching (FKT) conducted by Moll and his colleagues (e.g., González, 1995; Moll, Amanti, Neff, & González, 1992), whose premise is that low-income Latino/a families and communities have linguistic and cultural resources that can support children's learning in school; these resources, however, are frequently overlooked because of various factors including teachers' lack of understanding of the resources, unproductive social perceptions related to differences in language and culture, and different cultural expectations of the role of schools and parents (Henry, 1996; Villenas, 2001). Through project Bridge, Civil and her colleagues extended the work of FKT to investigate linguistic and cultural resources related to mathematics (Civil & Andrade, 2002; González, Andrade, Civil, & Moll, 2001). They provide ethnographic evidence that Latino/a children engage in out-of-school activities that are mathematically rich and culturally based (e.g., commercial transactions at "swap meets" or house construction tasks). Research on the effects of FKT's mathematics workshops for parents demonstrated that they valued mathematical explorations that built on their interests (e.g., wanting to learn algebra to help their children) and on their cultural knowledge (e.g., exploring symmetry in the context of a Mexican craft) (Civil & Andrade, 2003). These workshops, as well as recent classroom observations with parents (Civil & Quintos, 2002; Civil, Quintos, & Bernier, 2003), point to the need for more research into Latino/a parents' beliefs about the teaching and learning of mathematics.

### Teaching Mathematics to English Language Learners

Standards-based mathematics instruction emphasizes the need for students to be able to read mathematics and explain their mathematical thinking (orally and in writing). This shift might have a profound impact on Latino/a students' learning because a significant number are English language learners (ELLs). Thus, this potential impact is a crucial question to address empirically. The increased expectation for Latino/a ELL students to participate in public conversations might increase the possibilities that these students will be assessed as deficient in mathematics because of their oral language skills or reading levels in English. Alternatively, an emphasis on explanations and mathematical reasoning might provide more opportunities for these students to participate in purposeful and contextual conversations with others, creating an environment that supports both language and conceptual development. Research has only recently begun to consider mathematical discourse in classrooms with Latino/a students (Brenner, 1998; Khisty, 1995; Morales, 2003; Moschkovich, 1999; 2002). Much more research is needed to identify the language resources Latinos bring to mathematics learning and problem solving, especially for topics other than arithmetic, such as algebra, geometry, proportional reasoning, and data analysis.

Teachers' use of language has a major influence on ELLs' mathematics learning (Celedón-Pattichis, 2003; Khisty, McLeod, & Bertilson, 1990; Khisty, 1995). Studies of effective teachers of mathematics with Latinos/as (Khisty, 2001; Chval & Khisty, 2001) found that these teachers use the primary language to clarify meanings and modify their talk and use it as a pedagogical tool to develop conceptual understandings. Moreover, evidence exists that Latino/a students do better when teachers attend to the development of both oral and written academic second language proficiencies within mathematics instruction (Chval, 2001; Khisty & Chval, 2002). Research in second language acquisition describes strategies for teaching in English so that content instruction is comprehensible to ELLs (Echevarria, Vogt, & Short, 2000; Snow & Britton, 1998).

In summary, in order to address the needs of Latino/a students, mathematics educators should have a better understanding of the interactions among mathematics learning, language, and culture (especially community knowledge). Only then can we begin to address instructional and policy questions in a principled way. Research questions that need further investigation and will be central to CEMELA's work, include 1) how to use Latinos' community knowledge to support standards-based mathematics instruction; 2) how changes in mathematics instruction affect parents' connections and contributions to schooling; 3) how teachers come to understand and utilize talk and content-based ESL strategies in mathematics; 4) how home language and English interact to impact academic discourse in mathematics, instruction, and student learning; 5) how students' bilingualism can be used as an asset in the development of conceptual understanding in mathematics; 6) how mathematics curricula in English, Spanish, or both languages affect mathematics learning and teaching; and 7) how policies (e.g., assessment, students' placement) impact mathematics learning and teaching for low-income Latinos.