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Generalization Across Multiple Mathematical Areas: Studies of Classrooms and Teaching

跨多个数学领域的概括：课堂和教学研究

基本信息

批准号：
1920538
负责人：
Amy Ellis
金额：
$ 149.99万
依托单位：
University of Georgia Research Foundation Inc
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-10-01 至 2025-09-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1920538&HistoricalAwards=false
关键词：
Generalization Across Multiple Mathematical Areas

项目摘要

With funding from the EHR Core Research Program, this project will investigate how productive mathematical generalization can be supported in whole-classroom settings. Generalization is the ability to recognize patterns in relationships between numbers. An example of generalization is recognizing that 2 + 3 = 5, and generalizing that adding any even number to any odd number will produce an odd number. Generalization is a critical component of mathematical reasoning. As a result, researchers and policymakers recommend that it should be central to the education of all students at all grade levels. However, acting on this recommendation poses serious challenges, given the limited research base about students' difficulties in making appropriate generalizations and the challenges teachers face in supporting generalization in the classroom. This project aims to help address this gap by focusing on math classes from Grade 6 through college. To do so, the project team will investigate students' generalizations, as well as the strategies that affect their ability to develop generalization skills in algebra, advanced algebra, trigonometry, calculus, and combinatorics. The project will build a framework to describe and understand research-informed, classroom-based strategies for fostering generalization at the whole-classroom level with practicing teachers and instructors of undergraduate mathematics courses. The project has two objectives: (1) systematically investigate the current state of classroom generalization, identifying existing supports for students' generalizing; and (2) examine the ways in which teachers/instructors can be supported to foster productive mathematical generalization. The study implements a classroom-based design experiment model, leveraging classroom observations and videotaped professional development sessions in a two-phase methodology, with the second phase building on the first phase. The research activities will produce a set of findings about the relationships between instructional supports for generalizing and the nature of student generalizations, thus contributing to theory and a deeper understanding of generalization as it occurs in the context of typical instruction across multiple domains.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.

在EHR核心研究计划的资助下，该项目将研究如何在整个课堂环境中支持富有成效的数学概括。概括是识别数字之间关系模式的能力。推广的一个例子是认识到2 + 3 = 5，并推广到任何偶数加任何奇数都会产生奇数。泛化是数学推理的重要组成部分。因此，研究人员和政策制定者建议，它应该是所有年级所有学生教育的核心。然而，鉴于关于学生在作出适当概括方面的困难的研究基础有限，以及教师在课堂上支持概括方面面临的挑战，因此，就这一建议采取行动构成了严重的挑战。该项目旨在通过关注从六年级到大学的数学课程来帮助解决这一差距。为了做到这一点，项目团队将调查学生的概括，以及影响他们在代数，高等代数，三角，微积分和组合数学中发展概括技能的能力的策略。该项目将建立一个框架，以描述和理解研究为基础的，以课堂为基础的战略，以促进在整个课堂水平的概括与实践教师和本科数学课程的讲师。该项目有两个目标：（1）系统地调查课堂概括的现状，确定现有的支持学生的概括;（2）研究如何支持教师/教师促进生产性数学概括。本研究实施了一个基于课堂的设计实验模型，利用课堂观察和录像专业发展会议在两个阶段的方法，第二阶段的建设上的第一阶段。研究活动将产生一系列关于概括的教学支持与学生概括性质之间关系的发现，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评估来支持。影响审查标准。

项目成果

期刊论文数量（32）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Leveraging combinatorial and quantitative reasoning to support the generalization of advanced algebraic identities

利用组合和定量推理来支持高级代数恒等式的推广

DOI：
发表时间：
2020
期刊：
International Congress on Mathematical Education to the Topic Study Group on the Teaching and Learning of Discrete Mathematics
影响因子：
0
作者：
Tillema, E.S.
通讯作者：
Tillema, E.S.

Scaling-continuous variation: supporting students’ algebraic reasoning

尺度连续变化：支持学生的代数推理

DOI：
10.1007/s10649-020-09951-6
发表时间：
2020
期刊：
Educational Studies in Mathematics
影响因子：
3.2
作者：
Ellis, Amy;Ely, Robert;Singleton, Brandon;Tasova, Halil
通讯作者：
Tasova, Halil

). A serendipitous mistake: How one teacher’s beliefs and knowledge mediated her in-the-moment instruction

）。

DOI：
发表时间：
2021
期刊：
Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
影响因子：
0
作者：
Tasova, H. I.;Ellis, A.;Hamilton, M.;Moore, K. C.;Waswa, A.;Çelik, A Ö;Ying, Y.
通讯作者：
Ying, Y.

Productive mathematical meanings as a guide to analyzing algebra textbooks

富有成效的数学意义作为分析代数教科书的指南

DOI：
发表时间：
2021
期刊：
Forty Third Annual Meeting of the International Group for Psychology of Mathematics Education in North America
影响因子：
0
作者：
Burch, L.J.;Tillema, E.S.;Cox, J.;Sianturi, I.;Yavus, S.
通讯作者：
Yavus, S.

The role of lines and points in the construction of emergent shape thinking

线和点在构建涌现形状思维中的作用

DOI：
发表时间：
2021
期刊：
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
影响因子：
0
作者：
Tasova, H.I.;Liang, B.;Moore, K.C.
通讯作者：
Moore, K.C.

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Amy Ellis其他文献

Association of Drug Burden Index With Measures of Cognitive Function Among Older Adults

DOI：
10.1093/cdn/nzab033_011
发表时间：
2021-06-01
期刊：
Conference abstract
影响因子：
作者：
Janie DiNatale;Kristi Crowe-White;Amy Ellis;Joy Douglas;Ian McDonough;Kristine Yaffe
通讯作者：
Kristine Yaffe

P21 Determinants of Low-Income Older Adults' Intention to Consume Fruits and Vegetables

DOI：
10.1016/j.jneb.2019.05.397
发表时间：
2019-07-01
期刊：
Conference abstract
影响因子：
作者：
Seung Eun Jung;Yeon Ho Shin;Jinyoung Im;Janice Hermann;Amy Ellis;Kristi Crowe-White
通讯作者：
Kristi Crowe-White

The role and use of examples in learning to prove

DOI：
10.1016/j.jmathb.2017.06.002
发表时间：
2019-03-01
期刊：
Research article
影响因子：
作者：
Eric Knuth;Orit Zaslavsky;Amy Ellis
通讯作者：
Amy Ellis

The Impact of the Community Partnership Schools Model Community School on Graduation and Attendance Rates in One Florida High School.

社区合作学校示范社区学校对佛罗里达州一所高中毕业率和出勤率的影响。

DOI：
发表时间：
2019
期刊：
影响因子：
0
作者：
Amy Ellis
通讯作者：
Amy Ellis

P23-024-23 The Drug Burden Index Is Associated With Measures of Cognitive Function Among Older Adults in the Health, Aging, and Body Composition Study

DOI：
10.1016/j.cdnut.2023.100136
发表时间：
2023-07-01
期刊：
Conference abstract
影响因子：
作者：
Janie DiNatale;Kristi Crowe-White;Joy Douglas;Amy Ellis;Matthew Growdon;Kristine Yaffe
通讯作者：
Kristine Yaffe