Building a Grades K-2 Early Algebra Learning Progression Prototype for Diverse Populations

为不同人群构建 K-2 年级早期代数学习进展原型

• 批准号: 1720129
• 负责人: Maria Blanton
• 金额: $ 161.8万
• 依托单位: TERC Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720129&HistoricalAwards=false
• 关键词: Building; Grades; Early; Algebra; Learning

Research indicates that students need sustained algebra instruction throughout Grades K-12 mathematics education, if their informal intuitions about mathematical structure and relationships are to be transformed into the more formal ways of mathematical thinking. Currently, however, no research-based models are available to guide the development, characterization, and assessment of young children's algebraic thinking, particularly at the start of formal schooling. This study will design a curricular framework for developing children's algebraic thinking across Grades K-2, with a particular focus on understanding how to support the teaching and learning of algebra with students in at-risk settings. Study outcomes will include a prototype Grades K-2 instructional sequence, related assessments, and characterizations of progressions in students' thinking as they advance through the instructional sequence. The impact of this work would be to provide a critical roadmap for teaching and learning algebra in Grades K-2 that can clarify and deepen the role of algebra in the elementary grades, strengthen current college and career readiness standards and practices, and provide curricular support for elementary teachers in systematically developing children's algebraic thinking.The study will use design research to develop and empirically test a K-2 Early Algebra Learning Progression prototype for diverse learners. The context for this study is a North Carolina elementary school, which consists of a student population that is 64% non-white, with 63% categorized as low SES and 27% as English Language Learners. The sample consists of approximately 60 Grades K-2 students. To empirically test the prototype's framework, learning goals, and instructional sequence, classroom teaching experiments (CTEs) will be conducted in conjunction with individual student interviews. These interviews will be conducted at three time points (pre, mid, and post) during the CTEs. Qualitative methods of analysis will be used to identify themes regarding children's understanding of core algebraic thinking practices and concepts in CTE and interview data. Quantitative methods will also be used to identify patterns of growth in students' algebraic thinking from interview data. Results will be used to refine the framework, goals, and sequence, as well as to identify levels of sophistication in children's thinking as they advance through the sequence. Interview assessments conducted during the CTEs will be analyzed for psychometric soundness to ensure they are valid and reliable. In particular, inter-rater reliability measures will be used to ensure that coding of interview data is consistent, internal consistency estimates of reliability will be calculated and used to remove or modify items, and stability of the assessment items will be examined through within-subject correlations of common items and used to remove or modify items. For validity, observed item difficulty will be correlated with predicted item difficulty by the project's expert advisory board to identify items that need modification or deletion.The Discovery Research K-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 (RMTs). 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.

研究表明，学生需要持续的代数教学整个年级K-12数学教育，如果他们的非正式的直觉数学结构和关系要转化为更正式的数学思维方式。然而，目前，没有研究为基础的模式，以指导幼儿的代数思维的发展，表征和评估，特别是在正式学校教育的开始。本研究将设计一个课程框架，以发展儿童的代数思维在K-2年级，特别侧重于了解如何支持代数的教学和学习与学生在风险设置。研究成果将包括一个原型等级K-2教学序列，相关的评估，并在学生的思维进展的特点，因为他们通过教学序列前进。这项工作的影响将是为K-2年级的代数教学提供一个关键的路线图，可以澄清和深化代数在小学年级的作用，加强当前的大学和职业准备标准和实践，并提供课程支援，让国小教师有系统地发展儿童的代数思维。本研究将以设计研究的方式，发展并实证检验一个以数学为基础，2适合不同学习者的早期代数学习进展原型。本研究的背景是北卡罗来纳州的一所小学，其中64%的学生是非白人，63%被归类为低社会经济地位，27%为英语学习者。样本由大约60名K-2学生组成。为了实证检验原型的框架，学习目标和教学序列，课堂教学实验（CTE）将结合个别学生访谈进行。这些访谈将在CTE期间的三个时间点（前、中、后）进行。定性分析的方法将被用来确定有关儿童的理解的核心代数思维的做法和概念CTE和访谈数据的主题。定量方法也将被用来确定增长的模式，学生的代数思维从采访数据。结果将被用来完善框架，目标和序列，以及确定在儿童的思维复杂程度，因为他们通过序列推进。将对CTE期间进行的面试评估进行心理测量学分析，以确保其有效和可靠。特别是，将使用评估者间可靠性措施来确保访谈数据的编码是一致的，将计算可靠性的内部一致性估计并用于删除或修改项目，将通过共同项目的受试者内相关性检查评估项目的稳定性并用于删除或修改项目。为了有效性，项目专家顾问委员会将观察到的项目难度与预测的项目难度相关联，以确定需要修改或删除的项目。发现研究K-12计划（DRK-12）旨在通过研究和开发创新资源，显著提高学前学生和教师对科学，技术，工程和数学（STEM）的学习和教学，模型和工具（RMT）。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，这些研究和开发工作为拟议项目提供了理论和经验依据。

项目成果

The role of balance scales in supporting productive thinking about equations among diverse learners

平衡量表在支持不同学习者对方程进行富有成效的思考方面的​​作用

• DOI: 10.1080/10986065.2020.1793055
• 发表时间: 2020
• 期刊: Mathematical Thinking and Learning
• 影响因子: 1.6
• 作者: Stephens, Ana;Sung, Yewon;Strachota, Susanne;Torres, Ranza Veltri;Morton, Karisma;Gardiner, Angela Murphy;Blanton, Maria;Knuth, Eric;Stroud, Rena
• 通讯作者: Stroud, Rena

Positive Emotions in Early Algebra Meaning-Making

早期代数意义建构中的积极情绪

• DOI: 10.14708/dm.v43i1.7115
• 发表时间: 2022
• 期刊: Didactica Mathematicae
• 作者: Sung, Yewon;Stephen, Ana;Knuth, Eric;Blanton, Maria;Murphy Gardiner, Angela;Stroud, Rena
• 通讯作者: Stroud, Rena