EXP: "Earthquake Rebuild" - Mathematical Thinking and Learning via Architectural Design and Modeling

在这个网络学习：转变教育探索项目中，PI调查了如何帮助中学生同时发展数学理解、数学技能和数学性格。他们正在采取基于设计的教学方法，让学生练习他们通过建筑设计学到的数学。他们的软件环境被称为“地震重建”，将学习者设置在地震摧毁城市的虚拟环境中，他们必须使用几何和算术来做出建筑和城市规划决策，因为他们的目标是重建城市。在同样的软件背景下，调查人员正在纳入对性能数据进行不引人注目的收集和分析的手段，称为“隐形评估”，目的既是为了跟踪理解和能力的发展，也是为了提供适应性学习者支持。研究解决了系统设计中的实际问题，帮助学习者在解决现实世界问题和设计隐形评估的背景下深入学习内容和技能。研究还涉及数学学习中的概念性问题，特别关注非正式数学猜想的出现，并通过具体应用将其转化为正式的数学知识的方式。许多中学生未能培养出他们在劳动力市场上发挥生产力和成为公民所需的数学能力。更多的中学生完成了中学学业，却没有意识到数学与他们生活的现实世界之间的联系。这个项目的目的是解决这两个问题：促进中学生对数学的深入理解和能力，并让他们参与到他们的世界中来--看到数学在他们周围的自然和建筑环境中所扮演的角色。为了实现这些目标，调查人员正在设计一种软件环境，允许学生在使用中学数学重建被拆除的虚拟城市时，将严肃的游戏和学习结合起来。该系统旨在收集学生在后台的理解数据(称为“隐形评估”)，以便当学生参与该系统时，它可以帮助他们使用数学来重建虚拟城市中的建筑，更深入地学习他们正在使用的数学，并逐渐认识到数学和数学思维在高效地参与问题解决和设计活动中的有用性。调查人员将了解更多关于如何设计有助于学习者学习和欣赏数学的学习技术，如何在学生更系统地使用数学时学习数学，以及如何完成根据学生个人需求个性化学习技术所需的隐形评估类型。

In this Cyberlearning: Transforming Education Exploration project, the PIs investigate how to help middle schoolers simultaneously develop mathematics understanding, mathematics skill, and mathematics disposition. They are taking design-based pedagogical approach, having students practice the math they are learning through architectural design. Their software environment, called "Earthquake Rebuild," sets learners up in a virtual environment where an earthquake has demolished a city, and they must use geometry and arithmetic to make architectural and city planning decisions as they aim to rebuild the city. In this same context software context, the investigators are incorporating means of unobtrusive collection and analysis of performance data, called "stealth assessment," for purposes of both tracking development of understanding and capabilities and providing adaptive learner support. Research addresses practical issues in design of systems that help learners deeply learn content and skills in the context of solving real-world problems and in design of stealth assessments. Research also addresses conceptual issues in mathematics learning, specifically focusing on the ways that informal mathematical conjectures emerge and are transformed into formal mathematics knowledge through concrete application.Too many middle schoolers fail to develop the kinds of mathematics capabilities they will need to be productive in the workforce and to be engaged citizens. Even more middle schoolers complete middle school without appreciating the connections between mathematics and the real world they live in. The aim of this project is to address both of these issues: to promote deep mathematical understanding and capabilities among middle schoolers and to engage them in "mathematizing" their worlds -- seeing the roles mathematics plays in the natural and built environment around them. To achieve these goals, investigators are designing a software environment that allows students to combine serious play and learning as they use middle-school mathematics to reconstruct a demolished fictional city. The system is being designed to collect data about student understanding in the background (called "stealth assessment") so that as students engage with the system, it can help them use mathematics to rebuild the buildings in the fictional city, more deeply learn the mathematics they are using, and come to appreciate the usefulness of mathematics and mathematical thinking in engaging productively in problem solving and design activities. Investigators will learn more about how to design learning technologies that will help learners learn and appreciate mathematics, how mathematics is learned when students engage more systematically in using math, and how to accomplish the types of stealth assessment needed to personalize learning technologies to the needs of individual students.