Developing Teacher's Mathematical Knowledge for Teaching

尽管一再呼吁改善学术研究和提出更多基于经验的政策建议，但对教师学习的研究一直受到一些长期方法上的困难的困扰。最重要的是，这项研究受到了学者们能够测量的东西的限制：教师在在职或学习小组中出现的学习过程；在这些过程中产生的教师态度和信念；在某种程度上，教师的实践也会在这样的遭遇之后出现。然而，无法衡量的是贯穿所有这些可观察结果的一个组成部分，并最终证明了旨在改善教学的干预措施的最重要目标：教师对内容问题的知识和针对内容的教学方法。没有对这些知识的直接测量，研究人员几乎没有机会了解教师教育实践对其发展的贡献。在最近对教师准备的回顾中，Wilson， Floden和Ferrini-Mundy（2001）表明，在良好教学所需的内容以及教学与内容的理想结合方面，该领域的知识存在巨大差距。这种情况在专业发展知识方面同样薄弱（Wilson & Berne, 1999）。我们提出的这项研究旨在帮助纠正对教师学习缺乏纪律研究的问题。这项研究将利用最近在教学改进研究（Ball, Cohen & Rowan，主要调查人员）中开发的措施来确定有效的专业发展实践，并为该领域的评估人员和学者开辟新的方法。这些项目旨在挖掘对教师向学生提供高质量数学教学的能力至关重要的三个结构：教师理解小学数学基本主题的能力；教师运用数学知识解读学生思维的能力；以及教师在面对数学教学中常见问题时做出正确选择的能力。在这三个案例中，项目都是从数学教师面临的现实困境中提取出来的。本研究将在一项旨在提高教师数学知识及其教学水平的项目的纵向研究中使用这些指标，在大量教师参与专业发展、教师支持性课程材料和基于现场的创新举措之前、期间和之后对其进行跟踪。我们还将利用这个机会对我们的数学学习机会和教师教学知识的测量方法进行小型验证研究。最后，我们将采访和观察一小群教师，在他们参与数学专业强化发展之前，期间和之后，希望从教师的角度更好地了解，一个人可以学习什么以及如何学习数学内容来进行教学。

Despite repeated calls for improved scholarship and more empirically grounded policy recommendations, research into teacher learning has suffered from a number of chronic methodological difficulties. Most importantly, this research has been constrained by what scholars have been able to measure: the processes of teacher learning as they appear in in-services or study groups; teacher attitudes and beliefs which result from those processes; and, to some extent, teacher practices which emerge after such encounters. Left unmeasured, however, is a component which threads through all these observable outcomes and, ultimately, which proves the most significant target of interventions designed to improve teaching: teachers knowledge of content matter and content-specific teaching methods. Without direct measures of this knowledge, researchers have had few opportunities to learn which teacher education practices contribute to its development. In a recent review of teacher preparation, Wilson, Floden, and Ferrini-Mundy (2001) show the vast gaps in the field's knowledge of the content required for good teaching and of the ideal combination of pedagogical and content. The situation is equally weak with respect to knowledge about professional development (Wilson & Berne, 1999). The study we are proposing would aim to help redress the lack of disciplined study of teachers' learning.The study will take advantage of measures developed recently at the Study of Instructional Improvement (Ball, Cohen & Rowan, Principal Investigators) to identify effective professional development practices, and pioneers new methods for evaluators and scholars in this field.These items are designed to tap three constructs critical to teachers' capacity to deliver high-quality mathematics instruction to students: teachers ability to understand fundamental topics in elementary mathematics; teachers' ability to use mathematical knowledge to interpret students' thinking; and teachers' ability to make sound choices when faced with common problems of teaching mathematics. In all three cases, items are drawn from realistic dilemmas facing teachers of mathematics. The study will use these measures in a longitudinal study of programs designed to improve teachers' knowledge of mathematics and its teaching, tracking a large number of teachers before, during, and after their involvement with professional development, teacher-supportive curriculum materials, and innovative site-based initiatives. We will also use this opportunity to conduct a small validation study of our measures of mathematical learning opportunities and teachers' knowledge for teaching. Finally, we will interview and observe a small group of teachers before, during and after their participation in intensive mathematics professional development, hoping to better understand, from teachers' perspectives, what and how one can learn mathematics content for teaching.