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

该项目旨在通过让学生参与到生动的对比案例中来，支持学生在中学几何教学和学习中取得更好的成果。动画对比的情况是一组两个工作的例子，为相同的几何问题，以不同的方式接近。动画展示了学生在解决问题时的视觉动作和注释。学生被要求比较和讨论这些方法。这种基于理论的方法扩展了认知科学家和数学教育家的工作，他们已经证明这种方法有助于学生学习代数。该项目将在一个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。该研究将测量学生在接触材料后对几何的程序和概念知识的变化，并将探索教师在课堂上实施材料的方式。这项工作尤其重要，因为几何在数学教育中是一个未被充分研究的领域，在中学水平的国家和国际评估中，几何一直被认为是学生得分最低的数学内容领域。本项目借鉴了前人的研究成果，这些成果记录了比较对学生代数学习的影响。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，这种方法可以促进灵活性，增强概念知识和程序流畅性。更具体地说，这种方法允许学生在解决问题的背景下比较数学论证的有效性和效率。一项对几何中非动画对比案例的初步试点研究显示了通用方法的前景，并表明动画案例有可能使学生获得更大的学习收益。本研究将考察动画案例在多大程度上提高了学生的几何概念和程序知识，并确定与知识变化有关的因素。项目团队将根据先前代数工作的设计原则开发24个工作实例对比案例。这些材料将在第一个周期的四个治疗教室实施，修改，然后在八个治疗教室实施。学生的书面作业将与课堂讨论和学生小组访谈的性质数据一起收集。教师对课程的看法也将被收集，以支持修订和加强教材。学生几何知识的评估将采用具有证明有效性和可靠性的测量方法来衡量学生学习的变化。探索研究preK-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具，显著提高preK-12学生和教师对科学、技术、工程和数学（STEM）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工作的基础上，为拟议的项目提供了理论和实证依据。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.