Using Animated Contrasting Cases to Improve Procedural and Conceptual Knowledge in Geometry

使用动画对比案例来提高几何的程序和概念知识

基本信息

批准号：
1907745
负责人：
Erin Krupa
金额：
$ 44.95万
依托单位：
North Carolina State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907745&HistoricalAwards=false
关键词：
Using Animated Contrasting Cases Improve

项目摘要

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. Animated contrasting cases are a set of two worked examples for the same geometry problem, approached in different ways. The animations show the visual moves and annotations students would make in solving the problems. Students are asked to compare and discuss the approaches. This theoretically-grounded approach extends the work of cognitive scientists and mathematics educators who have shown this approach supports strong student learning in algebra. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms. This work is particularly important as geometry is an understudied area in mathematics education, and national and international assessments at the middle school level consistently identify geometry as a mathematics content area in which students score the lowest.This project draws on prior work that documents the impact of comparison on students' learning in algebra. Providing students with opportunities to compare multiple strategies is recommended by a range of mathematics policy documents, as research has shown this approach promotes flexibility and enhances conceptual knowledge and procedural fluency. More specifically, the approach allows students to compare the effectiveness and efficiency of mathematical arguments in the context of problem solving. An initial pilot study on non-animated contrasting cases in geometry shows promise for the general approach and suggests that animating the cases has the potential for stronger student learning gains. This study will examine the extent to which the animated cases improve students' conceptual and procedural knowledge of geometry and identify factors that relate to changes in knowledge. The project team will develop 24 worked example contrasting cases based on design principles from the prior work in algebra. The materials will be implemented in four treatment classrooms in the first cycle, revised, and then implemented in eight treatment classrooms. Students' written work will be collected along with data on the nature of the classroom discussions and small-group interviews with students. Teachers' perspectives on lessons will also be collected to support revision and strengthening of the materials. Assessments of students' geometry knowledge will be developed using measures with demonstrated validity and reliability to measure changes in student learning.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.

该项目旨在通过让学生参与动画对比的工作示例中的学生来支持中级的几何学教学和学习中更强大的学生成果。动画对比案例是两个以不同方式接近相同几何问题的两个工作示例。动画显示了学生在解决问题时所做的视觉动作和注释。要求学生比较和讨论这些方法。这种理论上的方法扩展了认知科学家和数学教育者的工作，他们表明这种方法支持代数的强大学生学习。该项目将在数字平台上设计一系列动画几何课程材料，要求学生比较解决相同几何问题的不同方法。该研究将衡量学生与材料交战后的几何学的程序和概念知识的变化，并将探索教师在教室中实施材料的方式。这项工作尤其重要，因为几何学是数学教育领域的一个研究领域，中学一级的国家和国际评估始终将几何形状确定为学生评分最低的数学内容领域。该项目借鉴了先前的工作，这些项目记录了比较代数中学生学习的影响。一系列数学政策文件建议为学生提供比较多种策略的机会，因为研究表明这种方法促进了灵活性并增强了概念知识和程序流利性。更具体地说，该方法允许学生在解决问题的背景下比较数学论点的有效性和效率。一项关于几何形状中未取消对比的病例的初步试点研究表明了对总体方法的希望，并表明对案例进行动画有可能获得更强的学生学习收益。这项研究将研究动画案例改善学生对几何学的概念和程序知识的程度，并确定与知识变化有关的因素。项目团队将根据代数的现有工作的设计原理开发24个工作示例对比案例。这些材料将在第一个周期中在四个治疗教室中实施，然后修订，然后在八个治疗教室中实施。学生的书面工作以及有关课堂讨论的性质和与学生的小组访谈的性质的数据。还将收集教师对课程的观点，以支持修订和加强材料。使用具有证明有效性和可靠性的措施来衡量学生学习的变化的措施的评估。发现PreK-12计划（DRK-12）试图通过创新资源，模型和工具的研究和开发来显着增强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，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来进行评估的。