A Longitudinal Exploration of Relations Between Fractions and Algebra Knowledge: An Interdisciplinary Approach

这个项目旨在提高学生的分数知识和他们的代数知识之间的关系的理解。代数的成功是人生成果的重要决定因素，从高中毕业到大学入学以及职业和经济前景。不幸的是，大量的研究记录了学生学习代数所面临的困难。心理学和数学教育研究的结果表明，加强学生的分数学习可能是提高代数学习的一个途径。这两个领域的研究人员都发现分数和代数能力密切相关，但这种关系的基础仍然不清楚。该项目将设计有效地捕捉学生的分数和代数知识的广度和深度的措施，并调查分数和代数知识之间的关系，从7年级到9年级，为期三年。通过调查学生的理解如何随着时间的推移而发展，本研究将确定关键的时间点，在这些时间点上，教学可能会证明特别有成效。第一阶段是一个测量项目，7-9年级的参与者将使用根据先前研究改编的评估进行代数知识和分数知识的学科内评估。学生的子集也将接受采访，以获得更深入的了解他们的解决问题的方法。关键的协变量，包括儿童的数学焦虑，整数技能和一般认知技能，将被测量，以隔离分数和代数知识之间的关系。这使得实证检验的因素结构的分数和代数域和开发有效的工具与最佳覆盖的结构。第二阶段将使用改进后的措施，在三个学年（7-9年级）纵向跟踪新的儿童样本。交叉滞后面板模型将被用来同时检查分数知识对代数知识的影响，反之亦然，同时也考虑协变量的作用。研究结果将提供分数和代数知识之间发展关系的信息。这两个阶段的数据都将在网上收集。这个项目是由美国国家科学基金会的EDU核心研究（ECR）计划的支持。ECR计划强调基础STEM教育研究，产生该领域的基础知识。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响力审查标准进行评估，被认为值得支持。

This project aims to improve understanding of the relationships between students’ knowledge of fractions and their knowledge of algebra. Success in algebra is an important determinant of life outcomes, from high school graduation to college access and career and economic prospects. Unfortunately, a broad swath of research has documented the struggles students face learning algebra. Findings from both psychology and mathematics education research suggest that enhancing students’ fraction learning may be one route to improving algebra learning. Researchers from both fields have found that fractions and algebra competence are closely related, but the basis of this relationship remains unclear. This project will design measures that efficiently capture the breadth and depth of students’ fractions and algebra knowledge and investigate relations between fractions and algebra knowledge over a three-year period, from grades 7 to 9. By investigating how students’ understanding develops over time, this study will identify critical time points at which instruction might prove especially fruitful.The project will take place in two phases. Phase 1 is a measurement project in which participants in grades 7-9 will engage in within-subjects assessments of algebra knowledge and fractions knowledge using assessments adapted from prior research. A subset of students will also be interviewed to gain greater insight into their problem-solving approaches. Key covariates, including children’s mathematics anxiety, whole number skills, and general cognitive skills, will be measured in order to isolate the relations between fractions and algebra knowledge. This allows for empirical examination of the factor structure of the fractions and algebra domains and for development of efficient instruments with optimal coverage of the constructs. Phase 2 will use the refined measures to follow a new sample of children longitudinally over three school years (grades 7–9). Cross-lagged panel models will be used to simultaneously examine effects of fractions knowledge on algebra knowledge and vice versa, while also considering the role of covariates. Results will yield information about the developmental relations between fractions and algebra knowledge. Data will be collected online in both phases.This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.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.