CAREER: Grasping Understandings of Students Mathematical and Perceptual Strategies Using Real-Time Teacher Orchestration Tools

在美国，许多初中生和高中生的代数水平还不够熟练。在求解代数表达式和方程时，学生不仅需要执行程序，还需要识别数学结构，注意重要的感知线索，并决定在特定问题背景下哪些步骤最合适或最有成效。数学教师通过向学生提供高质量的反馈、指导、话语和机会，对支持和提高学生的数学成绩至关重要。然而，许多教师努力寻找一种基于代数的教学工具，这些工具可以有效地提供一种手段来挑战学生的概念性思维，让他们的学生参与其中，实时有效地审查学生的作业，并更好地支持他们的教学。该项目专注于设计、开发和使用新的以代数为重点的教师工具，这些工具使用人工智能(AI)有效地向教师提供有关学生数学问题解决步骤、行为、错误和实时学习的详细信息。潜在的假设是，如果教师通过实时分析得到关于学生感知和数学过程的详细信息和反馈，教师将更好地注意到并解释学生的挣扎。反过来，教师将能够做出更好的决定，并为更广泛的学生区分他们的教学。主要的研究问题是确定教师在使用人工智能支持的工具时是否能够更好地发现、关注、解释和做出可行的决定。研究人员将在这项为期五年的项目中开展一系列活动。首先，为了确定什么行为最能预测学习，将使用统计和学习分析方法分析学生解决问题所产生的日志文件数据库。接下来，研究人员将利用机器学习方法创建自动检测器，捕捉有效的数学策略、错误和注意力的使用，从而改善学习。第三，该项目将与教师一起使用基于设计的研究来共同设计、开发和制作人工智能支持的教师工具的原型。这些工具提供了有关学生数学和感知过程的关键信息，并帮助教师快速确定学生在数学知识方面存在哪些差距。研究人员将进行基于课堂的观察和采访，以检查教师的教学和学生的理解可能如何通过实时工具和反馈来改变。该项目的成果将推动学习科学、计算数据科学、人机交互和数学教育领域的理论和基础研究，并为数学策略的自动检测和课堂编排提供新的见解。技术和教育议程还提供了跨学科研究和实践培训的机会，以及研究生、博士后、教师和学生之间的合作。该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many middle and high school students in the United States do not reach proficiency in algebra. When solving algebraic expressions and equations, students not only need to perform procedures, but also identify mathematical structure, attend to important perceptual cues, and make decisions about which steps are most appropriate or productive in a particular problem context. Math teachers are critical to supporting and improving students’ math achievement by providing high-quality feedback, instruction, discourse, and opportunities to their students. However, many teachers struggle to find algebra-based teaching tools that efficiently provide a means to challenge students to think conceptually, keep their students engaged, review student work efficiently in real-time, and better support their instruction. This project focuses on the design, development, and use of new algebra-focused teacher tools that use artificial intelligence (AI) to efficiently provide teachers with detailed information about their students’ math problem solving steps, behaviors, errors, and learning in real-time. The underlying hypothesis is that if teachers are given detailed information and feedback about their students’ perceptual and mathematical processes using real-time analytics, teachers will better notice and interpret student struggles. In turn, teachers will be able to make better decisions and differentiate their instruction for a broader range of students.The main research question is to determine whether teachers are better able to detect, attend to, interpret, and make actionable decisions when using the AI-supported tool. Researchers will conduct a sequence of activities during this five-year project. First, to determine what behaviors best predict learning, a database of log files generated from students solving problems will be analyzed using statistical and learning analytics methods. Next, researchers will utilize machine learning approaches to create automated detectors that capture the use of effective math strategies, errors, and focus that has led to improved learning. Third, the project will use design-based research alongside teachers to co-design, develop, and prototype AI-supported teacher tools. The tools provide critical information about students’ mathematical and perceptual processes and help teachers quickly identify what gaps students have in their math knowledge. The researchers will conduct classroom-based observations and interviews to examine how teachers’ instruction and students’ understanding might be altered with the real-time tools and feedback. The outcome of the project will advance theories and foundational research in the fields of learning science, computational data science, human-computer interaction, and math education, as well as offer new insights into automatic detection of mathematical strategies and classroom orchestration. The technical and educational agendas also provide opportunities for interdisciplinary research and practical training and collaboration between graduate students, postdocs, teachers, and students. This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).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.