Developing a Practice-Based Theory of Mathematical Knowledge for Teaching

本研究旨在探讨小学教师需要了解和欣赏的数学内容，以及在教学中如何使用这些理解和欣赏。两个持久的问题是当代努力提高数学教学的核心：o什么数学知识是由数学教学工作所必需的？ 在数学教学工作中，数学知识在哪里以及如何产生，以及它如何有用和使用？ 在这项工作中，数学知识是如何与其他知识和情感交织在一起的？在“知识”一词中，项目包括内容（例如，主题，定理，定义，算法）以及实践和敏感性。这可能意味着什么，以及需要什么，小学教师以尊重学生和数学的方式教学。作为一名小学教师，拥有“数学完整性”意味着什么？ 该项目还将寻求定位小学教学的数学方面--任务、时刻和挑战--教师能听到、看到、做什么和说什么取决于数学知识。该项目不是通过检查课程框架或教师应该教什么的标准来提出这些问题，而是在实践中工作。我们的调查首先要调查的教学和学习数学的做法，以及数学本身的做法。这项工作的核心是一个大型的纵向NSF资助的数据库，记录了1989年至1990年期间鲍尔三年级公立学校教学的整整一年。 通过分析这些详细的实践记录，我们寻求发展理论的数学知识，因为它是所需要的，并在教学中使用，考虑教学随着时间的推移，检查教师的工作，在整个学年发展数学和他们的学生。 该项目的成果将包括对小学教学中所涉及的数学的详细分析，以及关于数学内容的性质和用途、实践和日常教学工作中的情感的扎根理论。 书面产品将针对对这项工作感兴趣的不同受众。

This project seeks to examine what it is about mathematics that elementary teachers need to know and appreciate, and where and how in teaching such understandings and appreciation are used. Two enduring questions are at the heart of contemporary efforts to improve mathematics instruction:o What mathematical knowledge is entailed by the work of teaching mathematics? o Where and how is mathematical knowledge entailed, and how would it be useful and used, within the work of teaching mathematics? How is mathematical knowledge intertwined with other knowledge and sensibilities in the course of that work?Within the term "knowledge" the project includes content (e.g., topics, theorems, definitions, algorithms) as well as practices and sensibilities. What it might mean, and what it would take, for elementary teachers to teach in ways that are respectful of both students and the mathematics. What could it mean to have "mathematical integrity" as an elementary teacher? The project will also seek to locate the mathematical aspects of elementary teaching -- the tasks, moments, and challenges -- where what a teacher can hear, see, do, and say depends on mathematical knowledge.Rather than asking these questions by examining curriculum frameworks or standards of what teachers are supposed to teach, the project works in and from practice. Our investigations take us first into investigations of the practices of teaching and learning mathematics, as well as into the practices of mathematics itself. Central to this work is a large longitudinal NSF-funded database, documenting an entire year of Ball's third grade public school teaching during 1989-90. By analyzing these detailed records of practice, we seek to develop theory of mathematical knowledge as it is entailed by and used in teaching, to consider instruction over time, examining the work of teachers in developing mathematics and their students across the school year. Products of this project will include detailed analyses of the mathematics entailed in elementary school teaching, as well as grounded theory about the nature and uses of mathematical content, practice, and sensibilities in the day-to-day work of teaching. Written products will target different audiences with interests in this work.