Measuring Mathematical Knowledge for Teaching: Evaluation Module Development and Dissemination

衡量教学数学知识：评估模块的开发和传播

• 批准号: 0535816
• 负责人: Merrie Blunk
• 金额: --
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0535816&HistoricalAwards=false
• 关键词: Measuring; Mathematical; Knowledge; Teaching; Evaluation

Intellectual Merit:This proposal draws on existing efforts to develop measures of elementary and middle schoolmathematical knowledge for teaching. Different from conventional assessments of mathematicalknowledge (e.g., the SAT or Woodcock-Johnson assessment), these measures investigate the specialmathematical knowledge teachers use to work in classrooms with students. For instance, these measuresassess not only whether teachers know that 1 3/4 1/2 = 3 1/2, but also whether they can explain whatthis equation means, can construct a concrete representation or word problem which corresponds to it, andcan understand and generalize from an unusual solution method for this problem. This proposal respondsto a number of challenges that have arisen while disseminating these measures to researchers.Currently, the Learning Mathematics for Teaching project (LMT) disseminates pre-piloted forms andtechnical information for evaluating teacher learning in K-8 number and operations, pre-algebra andalgebra, and geometry. Teacher learning opportunities, however, frequently focus on more narrowlydefined topic areas for instance, rational number concepts and operations. Yet items capturing teacherknowledge of rational number compose only one component of LMT's number concepts and operationsmeasures. Because these current measures include other topics, they are unlikely to be appropriatelysensitive to the content and effects of such professional development.In response, this proposal argues for the construction of evaluation modules designed to be sensitive toand allow research and evaluation in the following areas: rational numbers; proportional reasoning;geometry; data analysis and probability. In all but the last topic area, for which LMT will create anentirely new set of items, the project will review and supplement existing items, create a form composedof items that capture key teacher competencies in these areas, pilot this form, then compose technicalmaterials that support these modules' use. These technical materials will include two parallel forms andpre-equated raw-score-to-standardized-score conversion tables, to facilitate straightforward scoring.This proposal also describes plans to improve the quality of dissemination training by exploring thenature of problems that arise when outside evaluators use these measures, and describes work to improvemeasures of teachers' knowledge of student learning around content.Intellectual MeritThis proposal grows from a well-established measures development project. At every step in this project'shistory, the provision of high-quality measures has coincided with and in some ways, depended upon progress in building theory about content knowledge for teaching mathematics, and exploring new areasin measurement design and scaling. This will be the case in the work proposed here, as well.Broader ImpactThis proposal enhances the infrastructure for research on teacher learning. These measures can be used toevaluate teachers' learning in pre-service teacher education programs; to make comparisons betweenpreparation in traditional teacher education programs and alternative routes to certification; to judge theefficacy of professional development aimed at improving teachers' content knowledge for teaching; andto estimate the effects of curriculum materials designed to improve teachers' knowledge of mathematicsand students. These measures are accessible to users with limited technical expertise, comparable acrossprograms and approaches to professional development, and of high technical quality.

智力价值：这项建议借鉴了现有的努力，为教学开发小学和中学数学知识的衡量标准。与传统的数学知识评估(如SAT或Woodcock-Johnson评估)不同，这些措施调查教师在课堂上与学生一起工作时使用的专业数学知识。例如，这些测量不仅评估教师是否知道1 3/4 1/2=3 1/2，而且还评估他们是否能够解释这个方程的含义，是否能够构造与之相对应的具体表示或应用题，是否能够理解和概括这一问题的一种不寻常的解决方法。这项建议回应了在向研究人员传播这些措施时出现的一些挑战。目前，教学数学学习项目(LMT)传播预先试行的表格和技术信息，以评估教师在K-8数字和运算、预代数和代数以及几何方面的学习。然而，教师的学习机会往往集中在更狭隘的主题领域，例如有理数概念和运算。然而，捕捉教师有理数知识的项目只构成了LMT的数字概念和运算测量的一个组成部分。由于这些目前的措施包括其他主题，它们不太可能对这种专业发展的内容和影响适当地敏感。对此，本提案主张建立对以下领域敏感的评价模块，并允许在以下领域进行研究和评价：有理数；比例推理；几何；数据分析和概率。除了最后一个主题区域，LMT将为其创建一组全新的项目，该项目将审查和补充现有项目，创建一个由项目组成的表格，以捕捉这些领域的关键教师能力，试验该表格，然后编写支持这些模块使用的技术材料。这些技术材料将包括两个平行的表格和预先相等的原始分数到标准化分数的转换表，以便于直接评分。本建议还描述了通过探索外部评估者使用这些措施时出现的问题的性质来提高传播培训质量的计划，并描述了改善教师对学生学习内容的了解的工作。智力价值本建议源于一个成熟的措施开发项目。在这个项目历史上的每一步，高质量措施的提供都与为数学教学建立内容知识的理论以及在测量设计和尺度方面探索新领域的进展不谋而合，并在某种程度上依赖于这一进展。在这里提出的工作中也是如此。布罗德影响这项建议加强了关于教师学习的研究的基础设施。这些措施可用于评估教师职前教育计划中的教师学习情况；比较传统教师教育计划中的准备和获得认证的替代途径；判断旨在提高教师教学内容知识的专业发展的有效性；以及评估旨在提高教师和学生的数学知识的课程材料的效果。只有有限的技术专长、可与之媲美的各种专业发展方案和方法以及高技术质量的用户才能使用这些措施。