CAREER: Covariational and Algebraic Reasoning: A New Path to Algebra
职业:协变和代数推理:通向代数的新途径
基本信息
- 批准号:2142000
- 负责人:
- 金额:$ 88.5万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2022
- 资助国家:美国
- 起止时间:2022-07-01 至 2027-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
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.
对于许多学生来说,代数提出了具有长期经济和社会影响的挑战,因为代数可以作为未来STEM课程和职业的守门人。因此,K-12教育支持所有学生发展代数知识至关重要。协变推理,或推理关系的能力,因为数量一起变化,是一种思维方式,可以为学生提供一个基础,建立他们更抽象的代数知识。这项研究为整合教育和研究奠定了基础,在学生发展代数知识,协变推理和新的教育技术的交叉点,以创建一个新的途径进入代数。这条道路可以帮助消除历史上限制获得数学和STEM课程和职业的障碍。为了将这条新的道路发展到代数中,该项目扩展了先前的研究,探索中学生如何通过协变推理来理解代数的关键思想。两个研究问题指导该项目:(一)如何才能中学生的协变推理作为他们的代数推理和知识的发展的基础?(ii)什么一般路径支持学生发展代数推理和知识,通过他们的协变推理?该项目通过制定多个阶段的小组和全班设计为基础的研究周期与中学生解决这些问题。每个阶段将产生新的见解,学生的学习特点的方式,个别学生建立他们的代数知识,通过他们的协变推理。比较和对比个别学生的进展将支持一般路径的衔接学生的进展,因为他们通过他们的协变推理发展他们的代数知识。在每个阶段,该项目将迭代地生成和测试位于免费,公开的Desmos平台上的任务,以创建基于研究的Desmos活动序列,包括教师支持材料,这些材料有效地支持学生的代数和协变推理。这些努力也将允许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的发展。该奖项是根据2021年美国救援计划法案(公法117-2)的部分资助。该奖项还部分由发现研究preK-12计划(DRK-12)资助,该计划旨在通过研究和开发创新资源,模型和工具,显着提高preK-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教育的基础研究以及为拟议项目提供理论和经验依据的先前研究和开发工作的基础上。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智力价值和更广泛的影响审查标准进行评估来支持。
项目成果
期刊论文数量(0)
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Teo Paoletti其他文献
Comparative and restrictive inequalities
比较性和限制性不平等
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Teo Paoletti;Irma E. Stevens;Madhavi Vishnubhotla - 通讯作者:
Madhavi Vishnubhotla
Exploring the Prevalence of Covariational Reasoning Across Mathematics and Science Using TIMSS 2011 Assessment Items
使用 TIMSS 2011 评估项目探索数学和科学中协变推理的普遍性
- DOI:
10.1007/s10763-023-10353-2 - 发表时间:
2023 - 期刊:
- 影响因子:2.2
- 作者:
Allison L. Gantt;Teo Paoletti;Julien Corven - 通讯作者:
Julien Corven
A Local Instruction Theory for Emergent Graphical Shape Thinking: A Middle School Case Study
突发图形形状思维的局部教学理论:中学案例研究
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:2.8
- 作者:
Teo Paoletti;Allison L. Gantt;Julien Corven - 通讯作者:
Julien Corven
The parametric nature of two students’ covariational reasoning
两个学生协变推理的参数性质
- DOI:
10.1016/j.jmathb.2017.08.003 - 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
Teo Paoletti;K. Moore - 通讯作者:
K. Moore
Pre-service teachers’ figurative and operative graphing actions
职前教师的形象和操作性绘图动作
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:1.7
- 作者:
K. Moore;Irma E. Stevens;Teo Paoletti;Natalie L. F. Hobson;Biyao Liang - 通讯作者:
Biyao Liang
Teo Paoletti的其他文献
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{{ truncateString('Teo Paoletti', 18)}}的其他基金
Collaborative Research: Middle School Students Graphing From the Ground Up
合作研究:中学生从头开始绘图
- 批准号:
2200777 - 财政年份:2022
- 资助金额:
$ 88.5万 - 项目类别:
Standard Grant
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Learning activities facilitating students' constructions of objects of thought in school mathematics: A case of learning on covariational and functional relations
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- 批准号:
25350190 - 财政年份:2013
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$ 88.5万 - 项目类别:
Grant-in-Aid for Scientific Research (C)