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

研究表明，如果学生对数学结构和关系的非正式直觉要转化为更正式的数学思维方式，那么他们需要在整个K-12年级的数学教育中持续进行代数教学。然而，目前还没有基于研究的模型来指导幼儿代数思维的发展、表征和评估，特别是在正规学校的开始阶段。这项研究将设计一个从K-2年级发展儿童代数思维的课程框架，重点是了解如何支持处于危险环境中的学生的代数教与学。研究结果将包括K-2年级的原型教学序列、相关的评估，以及学生在教学序列中的思维进步的特征。这项工作的影响将是为K-2年级的代数教学和学习提供一个关键的路线图，可以澄清和深化代数在小学年级中的作用，加强当前大学和职业准备的标准和实践，并为小学教师系统地发展儿童的代数思维提供课程支持。本研究将使用设计研究来开发和实证测试K-2早期代数学习进展原型，供不同的学习者使用。这项研究的背景是北卡罗来纳州的一所小学，该小学由的非白人学生组成，其中63%的学生属于低社会经济地位，27%的学生是英语学习者。样本包括大约60名K-2年级的学生。为了经验性地测试原型的框架、学习目标和教学顺序，课堂教学实验(CTE)将与个别学生访谈一起进行。这些面谈将在CTE期间的三个时间点(前、中和后)进行。定性的分析方法将被用来确定关于儿童对CTE和访谈数据中核心代数思维实践和概念的理解的主题。定量方法也将被用来从面试数据中确定学生代数思维的成长模式。结果将被用来改进框架、目标和序列，并在孩子们在序列中前进的过程中识别他们思维的复杂程度。将分析在CTE期间进行的面试评估的心理测量学合理性，以确保它们是有效和可靠的。特别是，将使用评分员之间的可靠性措施确保面试数据的编码一致，将计算可靠性的内部一致性估计并用于删除或修改项目，将通过共同项目的科目内相关性检查评估项目的稳定性，并用于删除或修改项目。在有效性方面，观察到的项目难度与预测的项目难度将由项目的专家顾问委员会进行关联，以确定需要修改或删除的项目。探索研究K-12项目(DRK-12)旨在通过研究和开发创新资源、模型和工具(RMT)，显著提高K-12年级学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发努力的基础上，这些研究和开发工作为拟议的项目提供了理论和经验证明。

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.