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

这一拟议工作的中心思想是概念化教师知识的性质和发展，因为他们反过来又了解文化多样的城市中学的学生如何协商基于改革的数学课程的识字要求。我们提出三个核心主张作为这项拟议工作的理由。第一，学生和教师在改革中学课程中遇到的数学任务，就对学生和教师的识字要求而言，与传统课程相比有了重大转变。第二，城市环境中的学生，识字和数学成绩往往落后于其他环境中的学生，很有可能无法满足基于改革的课程和国家儿童运动委员会提出的通信标准所增加的识字要求。第三，中学数学教师在协调数学和识字之间的交叉点方面准备不足。在这项工作中，我们的驱动角度将是了解教师需要知道什么的性质，以支持学生的数学交流的方式，导致有效的代数学习的发展，并了解它是如何，这种知识是城市数学教师的社区之间开发。在这个项目中，我们将调查这些研究问题：教师如何理解学生使用代数语言的数学交流时，使用基于改革的数学课程在不同的，城市环境？教师如何理解数学交流中的代数语言，从而有效地进行代数教学？我们将使用质的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，使用基于改革的课程。我们将使用数学和识字性能的定量措施，以辨别教师的教学策略，出席课程的识字要求的相对有效性。 这项研究将解决重要的理论问题，在理解的基础结构的语言习得的代数思维和学习。 通过对教师学习和成长的数据分析，将有助于中学数学教师使用改革后的课程的理论问题和务实的问题。 该项目的广泛影响将是：（1）教师如何在他们准备不足的领域获得知识的模式和基本原则;（2）教师根据其识字需求分析数学任务及其背景的过程;（3）将其分析转化为实践的原则;（4）使用多媒体实践案例支持教师的方法的原则。

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