Developing Teacher's Mathematical Knowledge for Teaching

尽管一再呼吁改善学术水平，提出更有经验的政策建议，但对教师学习的研究却遭遇了一些长期的方法论困难。最重要的是，这项研究受到了学者们所能衡量的因素的限制：教师在在职或学习小组中出现的学习过程；这些过程产生的教师态度和信念；以及在某种程度上，在这种接触之后出现的教师实践。然而，没有衡量的是贯穿所有这些可观察到的结果的一个组成部分，最终证明了旨在改善教学的干预措施的最重要目标：教师对内容问题和具体内容教学方法的知识。如果没有对这种知识的直接测量，研究人员几乎没有机会了解哪些教师教育实践有助于这种知识的发展。在最近一篇关于教师准备的综述中，威尔逊、弗洛登和费里尼-芒迪(2001)指出，该领域在良好教学所需的内容以及教学和教学的理想结合方面的知识存在巨大差距。在有关专业发展的知识方面，情况同样薄弱(Wilson&amp；Berne，1999)。我们建议的这项研究旨在帮助纠正对教师学习缺乏有纪律的研究。这项研究将利用教学改进研究(Ball，Cohen&Amp；Rowan，首席调查员)最近开发的措施来确定有效的专业发展实践，并为这一领域的评估者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；教师使用数学知识解释学生思维的能力；以及教师在面临常见的数学教学问题时做出正确选择的能力。在所有三个案例中，题目都是从数学教师面临的现实困境中提取出来的。这项研究将使用这些方法对旨在提高教师的数学知识及其教学知识的项目进行纵向研究，跟踪大量教师在参与专业发展、教师支持性课程材料和创新的现场倡议之前、期间和之后的情况。我们还将利用这个机会对我们衡量数学学习机会和教师教学知识的指标进行一项小型的验证性研究。最后，我们将在参与数学专业集约化发展之前、期间和之后对一小群教师进行访谈和观察，希望从教师的角度更好地了解一个人可以学习什么和如何学习数学内容，以供教学。

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.