DIP: Graphical Model Construction by System Decomposition: Increasing the Utility of Algebra Story Problem Solving

DIP：通过系统分解构建图形模型：增加代数故事解决问题的效用

• 批准号: 1628782
• 负责人: Kurt VanLehn
• 金额: $ 134.63万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1628782&HistoricalAwards=false
• 关键词: DIP; Graphical; Model; Construction; System

The Cyberlearning and Future Learning Technologies Program funds efforts that will help envision the next generation of learning technologies and advance what we know about how people learn in technology-rich environments. Development and Implementation (DIP) Projects build on proof-of-concept work that shows the possibilities of the proposed new type of learning technology, and PI teams build and refine a minimally-viable example of their proposed innovation that allows them to understand how such technology should be designed and used in the future and that allows them to answer questions about how people learn, how to foster or assess learning, and/or how to design for learning. This project studies a new genre of learning technology that may remove a notorious bottleneck in STEM education: mathematical model construction. These days, computers can solve complex mathematical problems, but humans must still define the problem for the computer, which is called constructing a model of a system. Many students can learn procedural skills, such as solving a quadratic equation, but constructing a model frustrates them because there is no procedure. This effectively stops their progress in math and blocks their entry to STEM professions. That may be why model construction is one of the few practices that appears in both math (CCSSM) and science (NGSS) standards. The key innovation for solving these problems is a new genre of learning technology based on two ideas. First, it emphasizes decomposing the given system description into subsystems. Second, although the final model is a set of algebraic equations, the model is first constructed as a node-link graph that shows which quantities are connected to which relationships. This notation is called TopoMath.TopoMath builds on prior success with the Dragoon intelligent tutoring system, and represents a revision of that system to support a novel graphical representation to allow learners to recognize distinct problem-solving schemata. Stealth assessment using Bayesian Knowledge Tracing will allow feedback on student submitted models in response to word problems in modelling. When a model is represented as a TopoMath graph, it can usually be drawn such that distinct subsystems correspond to distinct subgraphs. This makes it easier for students to understand the relationship between the model and the system that is represents. Moreover, when constructing a model by decomposing a system into subsystems, blank areas in the TopoMath graph suggest which subsystems still need to be modeled. Students can learn model construction schemas by comparing and generalizing systems that have visually similar TopoMath models so that when constructing a model by decomposing a system into subsystems, if a schema matches a subsystem, then a whole section of the model can be filled in without further decomposition. These are just a few of the synergies of combining system decomposition and TopoMath's graphical representation of mathematical models. This project will explore sequences of TopoMath learning activities with the goal of bringing students to model construction mastery with just 20 hours of instruction. The instruction will be developed in the context of remedial college math classes that are equivalent to high school algebra 2 classes. The instruction will include individual, small group and whole class activities using the TopoMath technology. Qualitative analysis of verbal protocols will be undertaken using the Knowledge-Learning-Instruction framework both for system evaluation, and to better understand the processes of learning in model construction that are supported by the system's representations and scaffolds for modeling.

网络学习和未来的学习技术计划资助的工作将有助于设想下一代学习技术，并促进我们对人们在技术丰富的环境中学习的了解。开发和实施（DIP）项目以概念证明的作品为基础，该工作显示了拟议的新型学习技术的可能性，PI团队建立和完善了他们提出的创新的最低限制的示例，使他们能够在未来设计和使用此类技术，并允许他们如何回答有关人们学习，如何培养或评估学习，或评估学习，以及如何设计，或设计如何进行学习，或设计如何进行学习。 该项目研究了一种新的学习技术类型，可以消除STEM教育中臭名昭著的瓶颈：数学模型构建。 如今，计算机可以解决复杂的数学问题，但是人类仍必须定义计算机的问题，该计算机称为构建系统模型。 许多学生可以学习程序技能，例如解决二次方程式，但是建造模型会使他们感到沮丧，因为没有程序。 这有效地阻止了他们在数学方面的进步，并阻止了他们进入STEM专业的。 这可能就是为什么模型构建是数学（CCSSM）和科学（NGSS）标准中出现的少数实践之一的原因。 解决这些问题的关键创新是基于两个想法的学习技术的新类型。 首先，它强调将给定的系统描述分解为子系统。 其次，尽管最终模型是一组代数方程，但该模型首先构造为节点链接图，该图显示了哪些数量已连接到哪个关系。 该符号称为topomath.topomath在龙龙智能辅导系统的先前成功基础上，代表对该系统的修订，以支持新颖的图形表示，以允许学习者识别出不同的问题解决方案。使用贝叶斯知识追踪的隐形评估将允许对学生提交的模型的反馈，以应对建模中的单词问题。当模型表示为topomath图时，通常可以绘制它，以使不同的子系统对应于不同的子图。 这使学生更容易理解代表模型与系统之间的关系。 此外，当通过将系统分解为子系统来构建模型时，Topomath图中的空白区域表明，仍需要对哪些子系统进行建模。 学生可以通过比较和概括具有视觉上相似的Topomath模型的系统来学习模型构建模式，以便在将系统分解为子系统中构建模型时，如果模式与子系统匹配，则可以填充整个模型的整个部分而无需进一步分解。 这些只是组合系统分解和Topomath的数学模型图形表示的一些协同作用。 该项目将探索Topomath学习活动的序列，目的是使学生仅需20个小时的教学才能模拟构建构建精通。 该指令将在补救学院数学课程的背景下开发，该课程等同于高中代数2类。 该指令将使用Topomath技术包括个人，小组和整个班级活动。将使用知识学习的实施框架进行系统评估的定性分析，以便更好地了解模型构建中的学习过程，这些过程得到了系统的表示和建模的脚手架的支持。