Exploring the Mathematical Thinking of Bilingual Primary-Grade Students: CGI Problem Solving From Kindergarten Through 2nd Grade

This study explores the mathematical thinking of native Spanish-speaking, primary-grade Latina/o students learning in bilingual classrooms where the majority of their mathematics instruction has been in Spanish. Guided by sociocultural theory, which emphasizes the important connection between language and conceptual development (Mahn, 2008; Sfard, 2001; Van Oers, 2001; Zack & Graves, 2001), and the theory and methods of Cognitively Guided Instruction [CGI] (Carpenter, Ansell, Franke, Fennema & Weisbeck, 1993; Carpenter, Fennema & Franke, 1994; Carpenter, Fennema & Franke, 1996; Carpenter, Fennema, Franke, Levi & Empson, 1999; Fennema, Franke, Carpenter & Carey, 1993; Turner, Celedón-Pattichis & Marshall, 2008), data were collected on students developing abilities to solve CGI problems and explain their thinking about their solutions. An expanded notion of mathematical explanations and discourse was used in the analysis that goes beyond student language to include their gestures, the tools they selected as problem solving aids, and their drawings and equations (Gee & Green, 1998; Moschkovich, 2002). This qualitative, longitudinal study is based on individual CGI interviews with four students over the course of their first three years in school and follows a grounded theory tradition (Creswell, 1998; Glaser & Strauss, 1980) to uncover themes in their mathematical thinking. The overarching motivation for this research was one of equity where the broader methodology sought to encourage a high-quality mathematics learning environment for Spanish-speaking, Mexican immigrant students in bilingual classrooms (Secada & De La Cruz, 1996). Groundbreaking findings from this study add to the literature on how young students make sense of the numbers in mathematical word problems (Fuson, 1988). The findings demonstrate that students are making sense of the numbers in fundamentally different ways and carry major implications for CGI theory, mathematics teaching and learning, and s