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对这些数学概念的教学。 PD使用一种方法，该方法使教师使用基于Web的应用程序，使他们可以测试和尝试其数学思想。这些应用程序与指导性问题相结合，挑战教师对分数和属性的思考，既可以促进对概念的批判性思考，并进一步发展他们对概念的理解。研究人员将使用一种创新的方法，主题建模来检查每个版本的PD的有效性。主题建模将使研究人员能够在教师参与PD时使用语言中使用的模式，并随后更好地了解教师发展的理解发展。该项目有望不仅可以增强教师对传统上苦苦挣扎的主题的指导，而且还可以证明主题模型的可行性，以此作为使用自然语言进行学习的一种手段，这种方法可能会替代大型，多项选择测试，以替代课堂学习活动来衡量学生的学生学习。该项目使用基于设计的研究方法来关注三个主要目标：扩展飞行员PD模型以包括分数和比例；测试有关PD模型的猜想，重点是支持教师以新颖的方式与学习内容之间建立联系，从而从他们的经验中发展教学内容知识（PCK）；并将主题建模作为评估模型，以衡量教师参与PD的变化。主题模型将用作主要评估，而不是铅笔和纸质评估，因为它们与内容和PD方法的一致性，这是高度互动性的，并且专注于会议测试。主题建模的使用为定性数据用作评估工具提供了机会，而不是依靠可能与指令不符的评估工具。这项工作的拟议结果包括：为教师提供的数学任务库，以支持重要的数学思想嬉戏互动；指导教师概述了30小时连贯的经验，该教师参与开发与分数，比率和比例有关的内容知识和PCK； PD计划有效性的证据依赖于主题建模来衡量教师参与和学习讲习班的变化；关于支持教师将内容知识发展与PCK开发联系起来的两种不同方法的数据；以及一个定义与参考单元和不变性相关的分数的“强大”理解的编码框架。 PD的所有方面都将基于使用动态的，基于Web的“玩具”（应用程序），这些“玩具”（应用程序）旨在支持对比例和分数概念的强大理解的发展。对该领域的贡献包括PD模型，强大的理解框架以及特定于主题模型的发现。这样的贡献将进一步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了解如何使用相对较小的定性数据集使用这种定量方法。 Discovery Research PreK-12计划（DRK-12）试图通过研究和开发创新资源，模型和工具的研究和开发，从而显着增强PreK-12学生和教师的科学，技术，工程和数学（STEM）的学习和教学。 DRK-12计划中的项目基于STEM教育和先前的研发工作的基础研究，为拟议项目提供了理论和经验的理由。该奖项反映了NSF的法定任务，并通过基金会的智力优点和更广泛的影响审查标准，通过评估来诚实地支持支持。