Developing and Validating a Scalable, Classroom-focused Measure of Usable Knowledge for Teaching Mathematics: The Classroom Video Analysis Instrument

人们普遍认为，对教师来说，有效地教授拥有丰富知识的学生很重要，但还不够。为了有利于教学和学生的学习，教师需要能够在实际的教学情境和教学任务中获取和灵活使用他们在课堂上的知识。然而，评估教师有用知识的措施仍然很少。关于教师作为教师预备课程和专业发展的一部分所获得的知识是如何变得有用的，它是如何随着时间的推移而发展的，以及教师如何在教学过程中使用它，我们仍然知之甚少。为了满足这一项目中的两种评估需求，该项目将开发一套可扩展的、以课堂为重点的有用数学教学知识的衡量标准，并与国家标准保持一致。新措施将扩展课堂视频分析方法，通过使视频剪辑和评估任务符合标准，扩展基于教师分析和回应真实课堂教学短视频片段的能力的课堂视频分析方法。这些新的措施将在网上公布，对于研究人员、政策制定者和学区来说，将是一个有价值的工具，用于监测教师随时间推移的知识，并衡量教师为实施国家数学标准所做的准备。这些措施还将对有用的知识和知识的使用提供新的见解，并提出亟需的教师知识理论。最后，该项目扩展和完善了一种有希望的评估方法，该方法可适用于任何未来的内容框架或标准，也可用于其他以实践为基础的知识领域的工具开发。探索研究K-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具(RMT)，显著提高K-12学龄前学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发努力的基础上，这些研究和开发工作为拟议的项目提供了理论和经验证明。该项目还得到了NSF的EHR核心研究(ECR)计划的支持。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。该项目将开发一种可扩展的、以课堂为中心的有用数学教学知识的衡量标准，通过课堂视频分析衡量(CVA-M))在三个内容领域：(A)4年级和5年级的分数，(B)6年级和7年级的比例和比例；和(C)6年级和7年级的变量、表达和方程。该项目将检查新条目和量表的心理测量学特性，包括分数的可靠性，并收集关于内容、实质、结构和外部效度的证据，以评估CVA-M的整体结构效度。该项目建立在一种创新的、前景看好的评估方法的基础上，该方法使用真实课堂教学的视频剪辑，要求教师观看和分析这些视频剪辑，以获取他们有用的知识。教师从不同的评估任务中分析视频剪辑中显示的教学情景，这些评估任务反映了真实的教学任务，例如诊断学生思维、生成具有数学目标的教师问题，或将特定内容和数学练习与剪辑中显示的教学情景相关联。为了制定这三个尺度，视频剪辑将被映射到国家级内容和数学实践标准。评估任务和标准也将与这些标准保持一致。为了创建题目，视频剪辑将与要求提供书面答案、多项选择或评分标准的分析提示相结合。为了使需要由训练有素的评分员评分的构建的回答项目更容易在规模上使用，将使用计算方法来开发分类器来自动评分。运用因素分析、经典测验理论和项目反应理论对新的CVA-M项目和量表的心理测量学特性进行了分析。将进行一系列的有效性调查。教师在新的CVA-M量表上的分数将与他们在另一种教师知识测量工具--教学数学知识(MKT)工具上的分数进行比较，并将通过将教师的CVA-M分数与学生的学习联系起来，将教师的CVA-M分数与学生的标准化测试分数联系起来，以探索每个量表相对于学生学习的预测有效性。

There is widespread agreement that for teachers to effectively teach their students having lots of knowledge is important, but not enough. To benefit instruction and student learning, teachers need to be able to access and flexibly use their knowledge in the classroom in actual teaching situations and teaching tasks. Yet, measures to assess teachers' usable knowledge have remained scarce. We still know little about how the knowledge teachers acquire as part of teacher preparation courses and professional development becomes usable, how it develops over time, and how teachers use it in the process of teaching. To address both assessment needs in this project, The project will develop a set of scalable, classroom-focused measures of usable mathematics teaching knowledge that are aligned with state standards. The new measures will extend the classroom video analysis approach, which is based on teachers' ability to analyze and respond to teaching episodes shown in short video clips of authentic classroom instruction, by aligning video clips and assessment tasks to standards. The new measures, which will be made available online, will be a valuable tool for researchers, policy makers, and school districts to monitor teacher knowledge over time and to gauge teacher preparedness for implementing state standards in mathematics. The measures will also provide new insights into usable knowledge and knowledge use and advance a much-needed theory of teacher knowledge. Finally, the project extends and refines a promising assessment methodology that can be adapted to any future content frameworks or standards and that can also be used for instrument development in other practice-based knowledge domains. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This project is also supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.The project will develop a scalable, classroom-focused measure of usable mathematics teaching knowledge that is aligned with the state standards through a classroom video analysis measure (CVA-M)) in three content areas: (a) fractions for grades 4 and 5, (b) ratio and proportions for grades 6 and 7; and (c) variables, expressions, and equations for grades 6 and 7. The project will examine the psychometric properties of the new items and scales, including the reliability of scores, and collect evidence on content, substantive, structural, and external aspects of validity to evaluate the overall construct validity of the CVA-M. The project builds on an innovative and promising assessment methodology that uses video clips of authentic classroom instruction that teachers are asked to view and analyze to elicit their usable knowledge. Teachers analyze the teaching episodes shown in the video clips from different assessment tasks that reflect authentic teaching tasks, such as diagnosing student thinking, generating mathematically targeted teacher question, or relating specific content and mathematical practices to teaching episodes shown in the clips. To develop each of the three scales, video clips will be mapped to state level content and mathematical practice standards. Assessment tasks and rubrics will also be aligned with these standards. To create items, video clips will be combined with analysis prompts that ask for a written answer, multiple-choice or rating scales. To make the constructed response items, which need to be scored by trained raters, easier to use at scale, computational approaches will be employed to develop classifiers to automate scoring. Using responses from large samples of teachers, the psychometric properties of the new CVA-M items and scales will be analyzed using factor analysis, classical test theory and item response theory. A series of validity investigations will be conducted. Teachers' scores on the new CVA-M scales will be compared to their scores on another measure of teacher knowledge, the Mathematics Knowledge for Teaching (MKT) instrument, and each scale's predictive validity will be explored vis-a-vis student learning by relating teachers' CVA-M scores to their students' learning as measured by a pre-post quiz and by students' standardized test scores.