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

本课题旨在加深对学生分数知识与代数知识之间关系的理解。从高中毕业到上大学，再到事业和经济前景，代数方面的成功是人生成就的重要决定因素。不幸的是，大量研究记录了学生在学习代数时所面临的困难。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条途径。这两个领域的研究人员都发现分数和代数能力密切相关，但这种关系的基础尚不清楚。这个项目将设计有效地捕捉学生分数和代数知识的广度和深度的措施，并在从7年级到9年级的三年时间里调查分数和代数知识之间的关系。通过调查学生的理解如何随着时间的推移而发展，这项研究将确定关键的时间点，在这些时间点上，教学可能被证明是特别有成效的。该项目将分两个阶段进行。第一阶段是一个测量项目，在这个项目中，7-9年级的学生将使用从先前研究改编的评估方法，对代数知识和分数知识进行学科内评估。一部分学生也将接受采访，以更深入地了解他们解决问题的方法。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。这允许对分数和代数域的因子结构进行经验检验，并开发具有最优结构覆盖面的有效工具。第二阶段将使用改进的措施在三个学年(7-9年级)对新的儿童样本进行纵向跟踪。交叉滞后面板模型将被用来同时检验分数知识对代数知识的影响，反之亦然，同时还考虑了协变量的作用。结果将得到分数和代数知识之间发展关系的信息。数据将在两个阶段在线收集。该项目由NSF的EDU核心研究(ECR)计划支持。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，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.