Enhancing Mathematics Curricula and Instruction to Facilitate Latino English Language Learners’ Success: A Case Study of Juan

• In Event: Reexamining the Links Between Curriculum and Instruction for Latina/o Mathematics Learners

Abstract

Juan’s third grade teacher participated in an intervention study focused on enhancing curriculum and instruction to support Latino English Language Learners. Juan filmed 25 math lessons during the academic year using a head-mounted camera to capture how he responded to the curriculum and instructional supports. Six different children wore cameras in each lesson so that all the children in the classroom participated in filming math lessons. (See Figure 1 for example of student wearing a head-mounted camera.)



Figure 1: Student filming a mathematics lesson using a head-mounted camera

The study was based on a situated-sociocultural perspective where learning is viewed as social activity, situated in an environment (i.e., the aggregate of the surrounding objects, conditions, and influences) as well as in the context of interactions (i.e., reciprocal exchanges) with people (i.e., teachers and students) and cultural signs and tools (i.e., language, curricula, manipulatives), and guided by a more-experienced other (Mercer, 1995; Resnick, 1988; Rogoff & Lave, 1984; Vygotsky, 1978). Through social interactions over a sustained period of time, students come to share common ways of thinking and communicating. Moschkovich (2002) argues that this perspective is “useful for avoiding deficiency models of bilingual learners, developing detailed descriptions of the resources that students use to communicate mathematically, and helping teachers build on these resources during instruction” (p. 191).

The study was framed using a conceptual model based on the ideas discussed by Cohen, Raudenbush, and Ball (2003) (see Figure 2) where organization, coordination, and use of resources influence classroom social processes which in turn influence student outcomes. Therefore, at the classroom level, we need to influence the resources, organization and coordination of those resources, as well as the social processes. Ultimately, expectations, norms, and participation influence student outcomes. If students do not engage and participate, then their learning is hindered. Therefore, it is important to identify and address what hinders participation.

Figure 2:Conceptual Model

Data sources included: Two interviews with Juan’s parents, audio records of 20 one-hour meetings and interviews with Juan’s teacher throughout the school year, audio and video records of 25 math lessons, copies of Juan’s mathematical work, results on standardized tests, and Juan’s performance on math pre-and post tests.

Juan achieved tremendous growth on a pre-post mathematics test in English and also in Spanish (see Table 1).


Juan Math Test
Pre-Test Post-Test
English 19% (4/21) 95% (20/21)
Spanish 33% (7/21) 86% (18/21)
Table 1: Juan’s performance on pre- and post mathematics tests in English and Spanish

In addition, he demonstrated increased participation in small and whole-group discussions with his peers and teacher, and improved his performance on individual mathematical work during the year. For example, initially Juan refused to discuss his mathematical thinking in front of his peers. However, within three months Juan began presenting his mathematical solutions in front of the entire class demonstrating growth in both mathematics and language skills. The purpose of this paper is to describe the curriculum enhancements and instructional supports that facilitated Juan’s mathematical participation, communication, and learning.

Authors

• Kathryn B. Chval, University of Missouri - Columbia

• Rachel J. Pinnow, University of Missouri

• Amanda Thomas, University of Missouri