CAREER: Covariational and Algebraic Reasoning: A New Path to Algebra

对于许多学生来说，代数带来了具有长期经济和社会影响的挑战，因为代数可以成为未来STEM课程和职业的看门人。因此，对于K-12教育来说，支持所有学生发展代数知识至关重要。协变推理，或者说当量一起变化时对关系进行推理的能力，是一种思维方式，可以为学生建立更抽象的代数知识提供基础。这项研究为在学生发展代数知识、协变推理和新的教育技术创造一条进入代数的新道路的交汇点进行教学和研究奠定了基础。这条道路可以帮助消除历来限制获得数学和STEM课程和职业的障碍。为了将这一新途径发展到代数中，该项目扩展了之前的研究，探索中学生如何通过协变推理来发展对代数至关重要的概念的理解。两个研究问题指导着这个项目：(I)中学生的协变推理如何成为他们发展代数推理和知识的基础？(Ii)学生通过协变推理发展代数推理和知识的一般途径是什么？该项目通过在中学生中实施多个阶段的小组和基于全班设计的研究周期来解决这些问题。每个阶段都将通过描述个别学生通过协变推理建立代数知识的方式，对学生的学习产生新的见解。比较和对比个别学生的进步将有助于阐明学生通过协变推理发展他们的代数知识时所经历的一般路径。在每个阶段，该项目将反复生成和测试位于免费、公开可用的Desmos平台上的任务，以创建一系列以研究为基础的Desmos活动，包括教师支持材料，这些活动一直有效地支持学生的代数和协变推理。这些努力还将允许开发设计动态数字任务的原则，以支持学生的协变推理和代数学习。该奖项的部分资金来自《2021年美国救援计划法案》(Public Law 117-2)。该奖项的部分资金来自发现研究预科-12项目(DRK-12)，该项目旨在通过研究和开发创新资源、模型和工具，显著提高预科-12学生和教师的科学、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经验上的证明。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

For many students, algebra presents challenges that have long-term economic and social impacts, as algebra can serve as a gatekeeper for future STEM coursework and careers. Thus, it is critical for K-12 education to support all students in developing algebraic knowledge. Covariational reasoning, or the ability to reason about relationships as quantities change together, is one way of thinking that can provide a foundation for students to build their more abstract algebraic knowledge. The research builds a foundation for integrating education and research at the intersection of students’ developing algebraic knowledge, covariational reasoning, and new educational technologies to create a new path into algebra. This path can help remove barriers that have historically restricted access to mathematics and STEM coursework and careers. To develop this new path into algebra, the project extends prior research exploring how middle-school students can reason covariationally to develop understandings for ideas critical to algebra. Two research questions guide the project: (i) How can middle-school students’ covariational reasoning serve as a foundation for their development of algebraic reasoning and knowledge? (ii) What general paths support students to develop algebraic reasoning and knowledge via their covariational reasoning? The project addresses these questions by enacting multiple phases of small-group and whole-class design-based research cycles with middle-school students. Each phase will produce new insights into students’ learning by characterizing ways individual students build their algebraic knowledge via their covariational reasoning. Comparing and contrasting individual students’ progressions will support the articulation of general paths students progress through as they develop their algebraic knowledge via their covariational reasoning. In each phase, the project will iteratively generate and test tasks situated in the free, publicly-available, Desmos platform to create a research-based sequence of Desmos activities, including teacher support materials, that have been effective in supporting students’ algebraic and covariational reasoning. These efforts will also allow for the development of principles for designing dynamic digital tasks to support students’ covariational reasoning and algebra learning.This award is funded by in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The award is also funded in part by the Discovery Research preK-12 program (DRK-12) which 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 projectsThis 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.