Learning Trajectories in Grades K-2 Children's Understanding of Algebraic Relationships

K-2年级儿童对代数关系的理解的学习轨迹

• 批准号: 1415509
• 负责人: Maria Blanton
• 金额: $ 44.99万
• 依托单位: TERC Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-15 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1415509&HistoricalAwards=false
• 关键词: Learning; Trajectories; Grades; Children; Understanding

Algebra is a central concern in school mathematics education. Its historical gatekeeper role in limiting students' career and life choices is well documented. In recent years, the response has been to reframe algebra as a K-12 endeavor. To this end, research on children's algebraic thinking in grades 3-5 shows that students can begin to understand algebraic concepts in elementary grades that they will later explore more formally. However, there is much that is unknown about how children in grades K-2 make sense of algebraic concepts appropriate for their age. This project aims to understand specific ways in which grades K-2 children begin to think algebraically. It will identify how children understand mathematical relationships, how they represent the relationships they notice, and how they use these relationships as building blocks for more sophisticated thinking. The project will use classroom-based research to teach children about important algebraic concepts and to carefully explore how children come to understand these concepts. The primary goal is to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops will provide a critical foundation for designing curricula, developing content standards, and informing educational policies, all in ways that can help children become successful in algebra and have wider access to STEM-related careers.While college and career readiness standards point to the role of algebra beginning in kindergarten, the limited research base in grades K-2 restricts algebra's potential in K-2 classrooms. This project will develop cognitive foundations regarding how children learn to generalize, represent, and reason with algebraic relationships. Such findings will inform both the design of new interventions and resources to strengthen algebra learning in grades K-2 and the improvement of educational policies, practices, and resources. The project will use design research to identify: (1) learning trajectories as cognitive models of how grades K-2 children learn to generalize, represent, and reason with algebraic relationships within content dimensions where these practices can occur (e.g., generalized arithmetic); (2) critical junctures in the development of these trajectories; and (3) characteristics of tasks and instruction that facilitate movement along the trajectories. The project's design will include the use of classroom teaching experiments that incorporate: (1) instructional design and planning; (2) ongoing analysis of classroom events; and (3) retrospective analysis of all data sources generated in the course of the experiment. This will allow for the development and empirical validation of hypothesized trajectories in students' understanding of algebraic relationships. This exploratory research will contribute critical early-grade cognitive foundations of K-12 teaching and learning algebra that can help democratize access to student populations historically marginalized by a traditional approach to teaching algebra. Moreover, the project will occur in demographically diverse school districts, thereby increasing the generalizability of findings across settings.

代数是学校数学教育中的一个中心问题。它在限制学生职业和生活选择方面的历史守门人作用得到了很好的证明。近年来，人们的反应是将代数重新定义为K-12的努力。为此，对3-5年级儿童代数思维的研究表明，学生在小学年级就可以开始理解代数概念，他们将在以后更正式地探索这些概念。然而，关于K-2年级的孩子如何理解适合他们年龄的代数概念，还有很多未知的东西。本项目旨在了解K-2年级儿童开始进行代数思维的具体方式。它将确定孩子们如何理解数学关系，他们如何表达他们注意到的关系，以及他们如何将这些关系作为更复杂思维的基石。该项目将利用课堂研究向孩子们传授重要的代数概念，并仔细探索孩子们是如何理解这些概念的。主要目标是确定儿童思维在通过教学发展过程中的成熟程度。了解儿童思维的发展将为设计课程、制定内容标准和制定教育政策提供重要的基础，所有这些都可以帮助儿童在代数方面取得成功，并有更广泛的机会从事与STEM相关的职业。虽然大学和职业准备标准表明代数从幼儿园就开始发挥作用，但K-2年级有限的研究基础限制了代数在K-2课堂上的潜力。这个项目将开发关于儿童如何学习概括、表示和用代数关系进行推理的认知基础。这些发现将有助于设计新的干预措施和资源，以加强K-2年级的代数学习，并改进教育政策、实践和资源。该项目将使用设计研究来确定：(1)学习轨迹作为认知模型，说明K-2年级的儿童如何在内容维度内学习概括、表示和推理这些实践(例如，广义算术)；(2)这些轨迹发展的关键节点；(3)促进沿轨迹移动的任务和教学的特点。该项目的设计将包括使用课堂教学实验，其中包括：(1)教学设计和规划；(2)正在进行的课堂事件分析；(3)对实验过程中产生的所有数据来源的回顾分析。这将允许在学生对代数关系的理解中开发和实验验证假设的轨迹。这项探索性研究将有助于K-12代数教学和学习的关键早期年级认知基础，有助于民主化进入历史上被传统方法教学代数边缘化的学生群体。此外，该项目将在人口结构不同的学区开展，从而增加调查结果在不同环境中的普适性。

项目成果

Exploring Kindergarten Students’ Early Understandings of the Equal Sign

探索幼儿园学生对等号的早期理解

• DOI: 10.1080/10986065.2018.1474534
• 发表时间: 2018
• 期刊: Mathematical thinking and learning
• 影响因子: 1.6
• 作者: Blanton, Maria;Otálora, Yenny;Brizuela, Bárbara M.;Gardiner, Angela Murphy;Sawrey, Katharine B.;Gibbins, Aliska;& Kim, Yangsook.
• 通讯作者: & Kim, Yangsook.