Collaborative Research: Fostering conceptual understanding and skill with an intelligent tutoring system for equation solving

协作研究：通过求解方程的智能辅导系统培养概念理解和技能

• 批准号: 1760947
• 负责人: Martha Alibali
• 金额: $ 52.4万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-06-01 至 2023-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1760947&HistoricalAwards=false
• 关键词: Collaborative; Research; Fostering; conceptual; understanding

This Education and Human Resources Core Research project addresses a persistent challenge in designing effective mathematics instruction: how to foster deep learning of concepts and skills, with strong connections among them. This challenge arises especially in middle school and high school algebra; far too often, students in algebra courses come away with only a moderate level of skill at procedures (e.g., equation solving) with almost no conceptual understanding of why these procedures work. This lack of deep understanding is unfortunate, because algebra is an important stepping stone to advanced mathematics as well as to future educational and employment opportunities. Thus, there is a great need for algebra instruction that helps students acquire well-integrated knowledge of key concepts and problem-solving procedures. This project tackles this issue using, as a platform, a software-based intelligent tutoring system that will extend an existing tutoring system for algebra. The new, enhanced tutoring system will support both practice in solving equations and new conceptually-oriented algebra activities. It will provide detailed and targeted guidance that adapts to individual students' errors, strategies, and developing algebra knowledge. Lab-based and classroom studies will investigate three key questions: (1) What mix of conceptual and procedural activities best helps students acquire deep skill and conceptual knowledge of algebra? (2) How frequently should students shift back and forth between the two types of activities? (3) How effective is the new tutoring system compared to commonly-used software, namely, Khan Academy, or a standard intelligent tutoring system that provides procedural practice only? The project will lead to new knowledge about how to create effective instruction for middle school and high school algebra, together with new intelligent tutoring software that embodies this knowledge.Based on past research, it is commonly accepted that in many domains, gains in conceptual knowledge can lead to gains in procedural knowledge, and vice versa. Further, there is some evidence that instruction that shifts back and forth between conceptually-oriented activities and procedurally-oriented activities is especially effective. However, it is not yet known what sorts of activities best support the development of conceptual knowledge, or how they should be integrated with activities that target learning of procedures so that students might make connections between the two. To address these issues, the project will extend existing tutoring system for equation solving (called Lynnette) with conceptual activities, based on past research that suggests that worked examples, self-explanation, visual representations (namely, bar diagrams), and activation of prior knowledge can be effective for promoting gains in conceptual knowledge. In doing so, this will leverage an established technical infrastructure for intelligent tutoring systems research and development, called CTAT/Tutorshop. The project will conduct two lab studies and two classroom studies to investigate what mix of conceptually-oriented activities is the most effective complement to the system's current set of procedurally-oriented activities, how frequently students should shift back and forth between procedurally- and conceptually-oriented activities, and how effective the resulting tutoring system is, compared to two control conditions in which students work with commonly used types of software for algebra learning (Khan Academy and Lynnette). The project will generate new knowledge about how to design effective instruction that helps students acquire well-integrated conceptual and procedural knowledge that is effective in real educational settings. This knowledge could lead to better, more conceptually-oriented instruction in algebra, and it has the potential to improve instruction in other STEM learning environments. The project will also create a new intelligent tutoring system for algebra that is much more effective than current systems. The system will be made available to teachers and schools free of charge.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.

这个教育和人力资源核心研究项目解决了设计有效的数学教学的持续挑战：如何促进概念和技能的深度学习，并在它们之间建立强有力的联系。这一挑战尤其出现在初中和高中代数中;通常，代数课程的学生在程序方面只有中等水平的技能（例如，方程求解），几乎没有概念上的理解，为什么这些程序的工作。这种缺乏深刻理解是不幸的，因为代数是一个重要的垫脚石，高等数学以及未来的教育和就业机会。因此，有一个伟大的需要代数教学，帮助学生获得良好的综合知识的关键概念和解决问题的程序。这个项目解决这个问题，作为一个平台，基于软件的智能辅导系统，将扩展现有的代数辅导系统。新的，增强的辅导系统将支持在解决方程和新的概念为导向的代数活动的实践。它将提供详细和有针对性的指导，以适应个别学生的错误，策略和发展代数知识。基于实验室和课堂的研究将探讨三个关键问题：（1）什么样的概念和程序活动的组合最能帮助学生获得代数的深层技能和概念知识？(2)学生在这两种活动之间来回转换的频率应该是多少？(3)新的辅导系统与常用的软件，即可汗学院，或只提供程序练习的标准智能辅导系统相比，效果如何？该项目将带来关于如何为初中和高中代数创建有效教学的新知识，以及体现这种知识的新智能辅导软件。根据过去的研究，人们普遍认为，在许多领域，概念知识的获得可以导致程序知识的获得，反之亦然。此外，有一些证据表明，在概念导向活动和程序导向活动之间来回转换的教学特别有效。然而，目前还不知道什么样的活动最能支持概念知识的发展，或者它们应该如何与以学习程序为目标的活动相结合，以便学生可以在两者之间建立联系。为了解决这些问题，该项目将扩展现有的辅导系统方程求解（称为Lynnette）的概念活动，根据过去的研究表明，工作的例子，自我解释，视觉表示（即，条形图），和激活的先验知识可以有效地促进概念知识的增益。在这样做的过程中，这将利用一个成熟的技术基础设施，为智能辅导系统的研究和开发，称为CTAT/Tutorshop。该项目将进行两项实验室研究和两项课堂研究，以调查什么样的概念导向活动组合是对系统当前程序导向活动的最有效补充，学生应该在程序导向和概念导向活动之间来回转换的频率，以及由此产生的辅导系统的有效性，与两个控制条件相比，学生使用常用类型的代数学习软件（Khan Academy和Lynnette）。该项目将产生关于如何设计有效教学的新知识，帮助学生获得在真实的教育环境中有效的综合概念和程序知识。这些知识可以导致更好的，更以概念为导向的代数教学，它有可能改善其他STEM学习环境中的教学。该项目还将创建一个新的代数智能辅导系统，比目前的系统更有效。该系统将免费提供给教师和学校。该奖项反映了NSF的法定使命，并被认为值得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。

项目成果

Students’ self-regulated use of diagrams in a choice-based intelligent tutoring system

学生在基于选择的智能辅导系统中自我调节图表的使用

• 发表时间: 2022
• 期刊: ICLS 2022
• 作者: Nagashima, T.;Tseng, S.;Ling, E.;Bartel, A. N.;Vest, N. A.;Silla, E. M.;Alibali, M. W.;Aleven, V.
• 通讯作者: Aleven, V.

Promoting students’ self-regulated choices in learning with visual representations in intelligent tutoring software

通过智能辅导软件中的视觉表现促进学生在学习中的自我调节选择

• 发表时间: 2023
• 期刊: Proceedings of the Annual Meeting for the International Society of the Learning Sciences (ISLS2023
• 作者: Nagashima, T.;Zheng, B.;Tseng, S.;Ling, E.;Aleven, V.
• 通讯作者: Aleven, V.

Pedagogical Affordance Analysis: Leveraging Teachers’ Pedagogical Knowledge to Elicit Pedagogical Affordances and Constraints of Instructional Tools

教学可供性分析：利用教师的教学知识来得出教学工具的教学可供性和限制

• 发表时间: 2020
• 期刊: 14th International Conference of the Learning Sciences (ICLS
• 作者: Nagashima, T.;Yang, K.;Bartel, A.;Silla, E.;Vest, N.;Alibali, M.;Aleven, V.
• 通讯作者: Aleven, V.

Using anticipatory diagrammatic self-explanation to support learning and performance in early algebra

使用预期的图表自我解释来支持早期代数的学习和表现

• DOI: 10.22318/icls2021.474
• 发表时间: 2021
• 期刊: Annual Meeting of the International Society of the Learning Sciences–ISLS 2021.
• 作者: Nagashima, T.;Bartel, A. N.;Yadav, G.;Tseng, S.;Vest, N. A.;Silla, E. M.;Alibali, M. W.;Aleven, V.
• 通讯作者: Aleven, V.

How does sustaining and interleaving visual scaffolding help learners? a classroom study with an intelligent tutoring system

维持和交错的视觉脚手架如何帮助学习者？

• 发表时间: 2022
• 期刊: Proceedings of the 44th Annual Conference of the Cognitive Science Society
• 作者: Nagashima, T.;Ling, E.;Zheng, B.;Bartel, A. N.;Silla, E. M.;Vest, N. A.;Alibali, M. W.;Aleven, V.
• 通讯作者: Aleven, V.