Developing Teacher's Mathematical Knowledge for Teaching

尽管一再呼吁改善奖学金和更多的经验为基础的政策建议，研究教师学习遭受了一些长期的方法上的困难。最重要的是，这项研究受到了学者们所能衡量的：教师学习的过程，因为他们出现在服务或研究小组;教师的态度和信念，从这些过程中产生的，并在一定程度上，教师的做法后，出现这样的遭遇。然而，有一个组成部分没有得到衡量，它贯穿所有这些可观察到的结果，并最终证明是旨在改善教学的干预措施的最重要目标：教师对内容问题和针对具体内容的教学方法的了解。如果没有直接的措施，这方面的知识，研究人员很少有机会了解教师教育的做法有助于其发展。 在最近对教师准备的回顾中，Wilson，Floden和Ferrini-Mundy（2001）显示了该领域对良好教学所需内容的知识以及教学法和内容的理想结合的巨大差距。关于专业发展的知识也同样薄弱（Wilson Berne，1999年）。我们建议进行的研究，旨在纠正缺乏对教师学习的纪律性研究的问题。这项研究将利用最近在教学改进研究（首席研究员鲍尔、科恩&·罗文）中开发的措施，以确定有效的专业发展做法，并为该领域的评估者和学者开创了新的方法。这些项目旨在挖掘三个对教师提供高质量教学能力至关重要的结构，优质数学教育：教师对小学数学基本课题的理解能力;教师运用数学知识解释学生思维的能力;以及教师在面对数学教学中常见问题时作出正确选择的能力。在所有这三种情况下，项目都来自数学教师面临的现实困境。 这项研究将使用这些措施，旨在提高教师的数学知识和教学的方案的纵向研究，跟踪大量的教师之前，期间和之后，他们参与的专业发展，教师支持的课程材料，和创新的网站为基础的举措。我们亦会借此机会，就数学学习机会和教师教学知识的量度方法，进行一项小型的验证研究。最后，我们将采访和观察一小群教师之前，期间和之后，他们参与密集的数学专业发展，希望更好地了解，从教师的角度来看，什么和如何学习数学教学内容。

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.