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, Celedon-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 sociocultural theory. Of particular interest to the field of bilingual education is the way students engage with CGI problems when the problems have been contextualized within students' native language and culture (Cummins, 2001; Secada & De La Cruz, 1996). Additionally, this study demonstrates how bilingual students use two languages, Spanish and English, to explain their mathematical thinking and describe their problem solving strategies.
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机译：这项研究探索了母语为西班牙语的小学拉丁裔/ o学生在双语教室中学习的情况，而他们大部分的数学教学都使用西班牙语。以社会文化理论为指导，强调语言与概念发展之间的重要联系（Mahn，2008； Sfard，2001； Van Oers，2001； Zack＆Graves，2001），以及认知指导理论[CGI]（木匠） ，安塞尔（Ansell），弗兰克（Franke），芬妮玛（Fennema）和韦斯贝克（Weisbeck），1993；卡彭特（Carpenter），芬尼玛（Fennema）和弗兰克（Franke），1996；卡彭特（Carpenter），芬尼玛（Fennema）和弗兰克（Franke），1999；卡彭特（Fennema），弗兰克（Franke），李维＆恩普森（Levi＆Empson），1999；芬纳玛（Fennema），弗兰克（Franke），Carpenter＆Carey，1993；特纳（Turner） （Celedon-Pattichis和Marshall，2008年），收集了有关学生解决CGI问题并说明他们对解决方案的想法的开发能力的数据。分析中使用了扩展的数学解释和话语概念，该分析超出了学生的语言范围，包括了他们的手势，他们选择的用于解决问题的工具以及他们的绘画和方程式（Gee＆Green，1998； Moschkovich，2002）。这项定性，纵向的研究是基于对四个学生在学校学习的头三年的个别CGI访谈而进行的，并遵循扎根的理论传统（Creswell，1998； Glaser＆Strauss，1980），以发现他们数学思维的主题。这项研究的总体动机是公平的一种，广泛的方法论旨在鼓励双语教室中讲西班牙语的墨西哥移民学生获得高质量的数学学习环境（Secada＆De La Cruz，1996）。这项研究的开创性发现增加了关于年轻学生如何理解数学单词问题中数字的文献（Fuson，1988）。研究结果表明，学生正在以根本不同的方式理解数字，并对CGI理论，数学教学和社会文化理论具有重大意义。在双语教育领域中，特别令人感兴趣的是当问题已经在学生的母语和文化中进行情境化时，学生如何参与CGI问题（Cummins，2001； Secada和De La Cruz，1996）。此外，本研究还演示了双语学生如何使用西班牙语和英语两种语言来解释他们的数学思维和描述他们的问题解决策略。
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