Exploring K-2 Children Understandings of Visual Representations in Algebraic Reasoning

探索 K-2 儿童对代数推理中视觉表征的理解

• 批准号: 2201095
• 负责人: Barbara Brizuela
• 金额: $ 45万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2201095&HistoricalAwards=false
• 关键词: Exploring; Children; Understandings; Visual; Representations

Algebra is a foundational topic in mathematics and STEM. As research has demonstrated how arithmetic is connected to algebra, there is more need to explore how K-2 children understand and use visual representations such as graphs and tables. This project will explore how children in grades K-2 understand visual representations of algebraic concepts. For instance, children might create tables or graphs to organize information about the relationship between two quantities. They might use graphs and diagrams to explain their mathematical thinking and develop their understanding of relationships in numbers and operations. The project will use data gathered in K-2 classrooms and via interviews with children to describe their use of the visual representations. This exploratory project aims to develop learning trajectories as cognitive models of how children in grades K–2 understand visual representations for algebraic relationships. Generalized arithmetic involves generalizing arithmetic relationships and reasoning explicitly with these generalizations. These relationships include field properties of number and operations (e.g., the Commutative Property of Addition) as well as relationships on classes of numbers, such as evens and odds. It entails reasoning about the structure of arithmetic expressions and equations rather than their computational value. The project has three guiding research questions. First, what are trajectories of learning in how grades K–2 children understand visual representations such as tables, graphs, and diagrams of algebraic relationships? Second, what features of tasks or instruction facilitate movement in students’ thinking within the trajectories? Third, what are similarities and differences in how children understand visual representations of algebraic relationships across the content dimensions of functional thinking and generalized arithmetic? The study will use a design-based research methodological framework to organize data collection via classroom teaching experiments, semi-clinical interviews, classroom observations, and children’s written work. The research will produce cognitive models that can be used to design further interventions for algebra learning in grades K-2. The Discovery Research preK-12 program (DRK-12) 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 projects. 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.

代数是数学和STEM的基础主题。研究表明，算术如何与代数相连，因此更多需要探讨K-2孩子如何理解和使用诸如图形和表格之类的视觉表示。该项目将探讨K-2年级的儿童如何理解代数概念的视觉表示。例如，儿童可能会创建表或图表来组织有关两个数量之间关系的信息。他们可能会使用图形和图表来解释他们的数学思维，并发展他们对数字和操作关系的理解。该项目将使用在K-2教室中收集的数据，并通过与儿童的访谈来描述他们对视觉表示的使用。这个探索性项目旨在发展学习轨迹作为K – 2年级儿童如何理解代数关系的视觉表示的认知模型。广义算术涉及通过这些概括明确地推广算术关系和推理。这些关系包括数字和操作的现场属性（例如，加法的交换属性）以及数字类别（例如evens和赔率）的关系。 IT官员推论算术表达式和方程的结构，而不是其计算价值。该项目有三个指导研究问题。首先，在K – 2年级的孩子如何理解诸如代数关系的表，图和图表之类的视觉表示形式中，学习的轨迹是什么？第二，在轨迹中，学生思维中的任务或指导设施运动的哪些特征？第三，孩子如何理解功能思维内容和广义算术内容的代数关系的视觉表示方面的相似之处和差异？该研究将使用基于设计的研究方法框架来通过课堂教学实验，半临床访谈，课堂观察和儿童书面工作来组织数据收集。该研究将产生认知模型，可用于设计K-2年级的代数学习的进一步干预措施。 Discovery Research Prek-12计划（DRK-12）试图通过研究和开发创新资源，模型和工具来显着增强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计划中的项目基于STEM教育和先前的研发工作的基础研究，为拟议项目提供了理论和经验的理由。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛的影响来通过评估来支持的珍贵支持。