Collaborative Research: Applying and Refining a Model for Dynamic, Discussion-Based Professional Development for Middle School Teachers about Fractions, Ratios and Proportions

合作研究：应用和完善中学教师关于分数、比率和比例的动态、基于讨论的专业发展模型

• 批准号: 2331772
• 负责人: Chandra Orrill
• 金额: $ 90.11万
• 依托单位: RETHINK LEARNING, INC.
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-06-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2331772&HistoricalAwards=false
• 关键词: Collaborative; Research; Applying; Refining; Model

This project explores the effectiveness of two different versions of professional development (PD) designed to enhance middle school mathematics teachers’ understanding of fractions and proportions, and their teaching of these mathematical concepts to students. The PD uses an approach that engages teachers with web-based apps that allow them to test and experiment with their mathematical ideas. The apps, combined with guiding questions that challenge teachers’ thinking about fractions and proportions, serve both to promote critical thinking about the concepts and to further developing their understandings of the concepts. The researchers will use an innovative approach, topic modeling, to examine the effectiveness of each of version of the PD. Topic modeling will allow the researchers to identify patterns in the language teachers use as they participate in the PD, and subsequently, to better understand the development of the understanding teachers develop. The project has promise to not only enhance teachers’ instruction on topics with which students have traditionally struggled, but also to demonstrate the viability of Topic Models as a means to measure learning using natural language—an approach that could potentially replace large-scale, multiple-choice tests as a measure of student learning with learning activities in the classroom. The project uses a design-based research approach to focus on three main goals: expansion of a pilot PD model to include fractions and proportions; testing of a conjecture about the PD model focused on supporting teachers in making connections between learning content in novel ways to developing pedagogical content knowledge (PCK) from their experiences; and implementing topic modeling as an assessment model for measuring changes in teachers’ participation in the PD. Topic models will be used as the primary assessment, rather than pencil and paper assessments, because of their alignment to the content and the PD approach, which is highly interactive and focused on conjecture testing. The use of topic modeling opens an opportunity for qualitative data to be used as an assessment tool rather than relying on assessment instruments that may not be aligned to the instruction. Proposed outcomes of this work include: a pool of mathematical tasks for teachers that support playful engagement with important mathematical ideas; a guide outlining a coherent 30-hour experience for teachers that engages in developing both content knowledge and PCK related to fractions, ratios, and proportions; evidence of the PD program’s effectiveness that relies on topic modeling to measure change in teachers’ participation and learning in the workshops; data on two different approaches to supporting teachers in linking content knowledge development to PCK development; and a coding framework that defines “robust” understanding of fractions related to referent units and invariance. All aspects of the PD will be grounded in the use of dynamic, web-based “toys” (apps) that have been designed to support the development of robust understandings of proportion and fraction concepts. Contributions to the field include the PD model, the robust understandings framework, and findings specific to the use of topic models. One such contribution will be further insight into the sample size necessary to use topic models for assessment, which will help the field better understand how to use this quantitative approach with relatively small qualitative data sets. The Discovery Research preK-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. 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 award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目探讨了两种不同版本的专业发展（PD）的有效性，旨在增强中学数学教师对分数和比例的理解，以及他们向学生教授这些数学概念的方法。这些应用程序允许他们测试和实验他们的数学思想，并结合挑战教师对分数和比例的思考的指导性问题，既可以促进对概念的批判性思考，又可以进一步发展他们对概念的理解。研究人员将采用创新方法，主题建模，以检查每个版本的 PD 的有效性 主题建模将使研究人员能够识别教师在参与 PD 时使用的语言模式，从而更好地了解教师开发的理解的发展。不仅有望加强教师对学生传统上难以理解的主题的教学，而且还能证明主题模型作为使用自然语言衡量学习的一种手段的可行性——这种方法有可能取代大规模的多项选择题测试作为学生学习活动的衡量标准该项目采用基于设计的研究方法，重点关注三个主要目标：扩展试点 PD 模型，以包括分数和比例；测试有关 PD 模型的猜想，重点支持教师在小说中的学习内容之间建立联系。从他们的经验中发展教学内容知识（PCK）的方法；以及实施主题模型作为衡量教师参与PD的变化的评估模型，而不是铅笔和纸质评估。他们与内容和内容的一致性PD 方法具有高度交互性，侧重于猜想测试，使用主题建模为定性数据用作评估工具提供了机会，而不是依赖于可能与本指令的建议结果不一致的评估工具。工作包括：为教师提供一系列数学任务，支持他们以有趣的方式参与重要想法；为教师概述了 30 小时的连贯经验，帮助他们发展与分数、比率和比例相关的内容知识和 PCK； PD 计划的有效性用于衡量教师在研讨会中的参与和学习变化的主题模型；支持教师将内容知识发展与 PCK 发展联系起来的两种不同方法的数据；以及定义与参考单位相关的分数的“稳健”理解的编码框架； PD 的所有方面都将基于动态、基于网络的“玩具”（应用程序）的使用，这些“玩具”旨在支持对比例和分数概念的深入理解。对该领域的贡献包括 PD 模型。 ， 这强大的理解框架以及针对主题模型使用的具体发现将进一步深入了解使用主题模型进行评估所需的样本量，这将有助于该领域更好地理解如何使用这种相对较小的定性方法。 Discovery Research preK-12 计划 (DRK-12) 旨在通过创新资源的研究和开发，显着增强 preK-12 学生和教师对科学、技术、工程和数学 (STEM) 的学习和教学。中的模型和工具。 DRK-12 计划建立在 STEM 教育的基础研究和先前的研究和开发工作的基础上，为拟议项目提供理论和实证依据。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响进行评估，被认为值得支持审查标准。