Investigating the Interrelated Development of Mathematics and Literacy in Urban Secondary Schools

本研究的中心思想是将教师知识的性质和发展概念化，因为教师反过来了解文化多样化的城市中学的学生如何协商以改革为基础的数学课程的识字要求。我们提出三个核心主张作为这项工作的基本原理。首先，在以改革为基础的中学课程中，学生和教师遇到的数学任务代表了传统课程在对学生和教师的识字要求方面的重大转变。其次，城市学生的读写能力和数学成绩往往落后于其他地区的学生，他们面临着无法满足基于改革的课程和NCTM提出的交流标准对读写能力日益增长的要求的巨大风险。第三，中学数学教师在调解数学与识字之间的交叉点方面准备不足。我们在这项工作中的驱动视角将是理解教师需要知道的本质，以支持学生以有效学习代数的方式发展数学交流，并理解这种知识是如何在城市数学教师社区中发展起来的。在这个项目中，我们将调查这些研究问题：教师如何理解学生在不同的城市环境中使用基于改革的数学课程时使用代数语言进行数学交流？教师对数学交流中代数语言的理解是如何发展的，从而导致代数的有效教学？我们将使用定性研究方法来探索数学交流的社会文化方面。这些分析将描述教师学习的性质和发展，在学生学习代数的背景下，采用改革为基础的课程。我们将使用数学和识字表现的定量测量来辨别教师教学策略的相对有效性，以满足课程的识字要求。本研究将探讨在代数思维和代数学习习得过程中语言的基本结构的重要理论问题。通过对实践产物的检验对教师学习和成长的数据进行分析，将有助于解决中学数学教师在使用改革后的课程方面的理论问题和实用问题。这个项目的更广泛的影响将是：(1)教师如何在他们准备不足的领域获得知识的模型和基本原则；(2)教师根据识字需求分析数学任务及其情境的过程；（三）将分析转化为实践的原则；(4)运用多媒体实践案例辅助教师教学的方法原则

The central idea in this proposed work is to conceptualize the nature and development of teachers' knowledge as they, in turn, learn about how students in culturally diverse urban secondary schools negotiate the literacy demands of reform-based mathematics curricula. We make three central claims as a rationale for this proposed work. First, the mathematical tasks that students and teachers encounter in the reform-based secondary school curricula represent a significant shift from traditional curricula in terms of the literacy demands they make on students and teachers. Second, students in urban settings, where literacy and mathematics achievement often lags behind achievement of students in other settings, are at great risk for not being able to meet the increased literacy demands of the reform-based curricula and of the communications standard put forward by the NCTM. Third, secondary mathematics teachers are underprepared to mediate the intersections between mathematics and literacy. Our driving perspective in this work will be to understand the nature of what teachers need to know to support students' development of mathematical communication in ways that lead to effective learning of algebra and to understand how it is that this knowledge is developed among a community of urban mathematics teachers. In this project, we will investigate these research questions:How do teachers understand student use of the language of algebra for mathematical communication when using reform-based mathematics curricula in diverse, urban settings?How do teachers' understandings about the language of algebra for mathematical communication develop in ways that lead to the effective teaching of algebra?We will use qualitative research methods to explore the sociocultural aspects of mathematics communication. These analyses will describe the nature and development of the teachers' learning, in the context of the students' learning of algebra, using reform- based curricula. We will use quantitative measures of mathematics and literacy performance to discern relative effectiveness of teachers' instructional strategies that attend to the literacy demands of the curricula. This study will address important theoretical issues in understanding the underlying structures of language in the acquisition of algebraic thinking and learning. The analyses of the data on the learning and growth of teachers through an examination of the artifacts of practice will contribute to theoretical issues as well as pragmatic issues in the use of reformed-based curricula by secondary mathematics teachers. The broader impact of this project will be: (1) a model and underlying principles for how teachers acquire knowledge in areas in which they are underprepared; (2) processes for teachers to analyze mathematical tasks and their contexts in terms of their literacy demands; (3) principles for transforming their analyses into practice; (4) principles for ways of using multimedia cases of practice to support teacher