Collaborative Research: Paving the Way for Fractions: Identifying Foundational Concepts in First Grade

虽然分数是幼儿教育中的一个重要话题，但许多学生对分数概念的掌握还很薄弱，即使经过几年符合现行标准的分数教学之后也是如此。这个项目由特拉华大学和坦普尔大学的一组研究人员领导，目的是回答一些重要的问题，即幼儿在入学前对分数的非正式理解，以及它们与在更正式的教学环境中学习分数的关系。对分数的熟练掌握极大地增加了学生在数学方面取得成功的可能性，这反过来又增加了STEM劳动力的参与度。重要的是，在中年级开始分数教学时，分数理解上的巨大个体差异是明显的。早期对分数的误解会在后来的年级发展成更严重的数学弱点，特别是当教学可能突然从整数转移到分数的时候。在正式教学发生之前，迫切需要了解个体差异产生的根源。幼儿在入学前对分数有重要的非正式理解，但这些能力的范围以及它们在正式分数学习和发展中的作用还没有被很好地理解。该项目的目标是：(A)调查一年级儿童在分数相关非正式知识方面的个体差异与短期和长期分数和数学成绩之间的关系；(B)了解分数相关非正式知识水平与从直接建立在这些知识基础上的分数教学中获利的能力之间是否存在因果联系。该项目的发现有望告诉幼儿教育工作者如何以新的、有意义的方式将分数纳入一年级课程。尽管调查结果对所有学生都有利，但该项目将专门针对STEM领域代表性不足的群体成员，包括少数民族和种族少数以及低收入学生。该项目由EHR核心研究(ECR)计划和探索研究K-12计划(DRK-12)共同资助，ECR计划支持推进STEM学习基础研究文献的工作，探索研究K-12计划支持创新资源、模式和工具的研究和开发，以加强K-12之前的学生和教师的STEM学习和教学。项目设计包括观测研究和实验研究。这项观察性研究将：(1)记录一年级非正式分数相关知识的个体差异；(2)确定这种非正式知识与一般认知能力和整数能力之间的并行关系；(3)检验一年级开始时的非正式分数相关知识是否唯一地预测一年级结束时的数学成绩。这项实验研究将探索培训对一年级学生的非正式和正式分数概念的影响程度。研究人员将测试数字线上的训练是否会帮助学生利用他们对比例、比例和均等分享的非正式分数理解，以及他们与整数的经验来学习关键的分数概念。数字线是连续的，与所有实数的大小在心理上表现得密切一致。综上所述，协同研究将明确非正式分数知识在学习关键分数概念中的作用。所有数据将在特拉华州的学校收集，这些学校为不同社会经济和种族的学生群体服务。主要措施包括对非正式分数知识(比例推理、空间比例、平等分享)、执行功能、词汇、整数知识、整数/分数数线估计、正式分数知识和广泛的数学成就(计算、流利性、应用题)的评估。该奖项反映了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，被认为值得支持。

Although fractions represent a crucial topic in early childhood education, many students develop only a tenuous grasp of fraction concepts, even after several years of fraction instruction that is aligned with current standards. The goal of this project, led by a team of researchers at the University of Delaware and Temple University, is to answer important questions about the informal understandings of fractions young children have before they come to school and what their relations are to fraction learning in more formal instructional settings. Proficiency with fractions dramatically increases the likelihood of students succeeding in math, which in turn increases participation in the STEM workforce. Importantly, large individual differences in fraction understandings are apparent at the start of fractions instruction in the intermediate grades. Early fraction misunderstandings cascade into more severe math weaknesses in later grades, especially when instruction may shift abruptly from whole numbers to fractions. There is a critical need to understand the roots of individual differences that arise before formal instruction takes place. Young children possess important informal fraction understandings before they come to school, but the range of these abilities and their role in formal fraction learning and development is not well understood. The goal of this project is: a) to investigate the extent to which individual differences in informal fraction-related knowledge in first-grade children are associated with short- and longer-term fractions and math outcomes; and b) to see whether there is a causal link between level of informal fraction-related knowledge and the ability to profit from fractions instruction that directly builds on this knowledge. The findings from the project hold promise for informing early childhood educators how fractions can be incorporated in the first-grade curriculum in new and meaningful ways. Though the findings should be beneficial to all students, the project will specifically target members of groups underrepresented in STEM fields, including ethnic and racial minority and low-income students. The project is jointly funded by the EHR Core Research (ECR) program, which supports work that advances the fundamental research literature on STEM learning, and by the Discovery Research K-12 program (DRK-12), which supports the research and development of innovative resources, models and tools in order to enhance STEM learning and teaching by pre-K-12 students and teachers. The project design includes both an observational study and an experimental study. The observational study will: (1) document individual differences in informal fraction-related knowledge in first grade; (2) determine concurrent relations between this informal knowledge and general cognitive and whole number competencies; and (3) examine whether informal fraction-related knowledge at the beginning of first grade uniquely predicts math outcomes at the end. The experimental study will explore the extent to which first graders’ informal and formal fraction concepts can be affected by training. The researchers will test whether training on the number line, which is continuous and closely aligned with the mental representation of the magnitude of all real numbers, will help students capitalize on their informal fraction understandings of proportionality, scaling, and equal sharing as well as their experience with integers to learn key fraction concepts. Together, the synergistic studies will pinpoint the role informal fraction knowledge in learning key fraction concepts. All data will be collected in Delaware schools serving socioeconomically and ethnically diverse populations of students. Primary measures include assessments of informal fraction knowledge (proportional reasoning, spatial scaling, equal sharing), executive functioning, vocabulary, whole number knowledge, whole number/fraction number line estimation, formal fraction knowledge, and broad mathematics achievement (calculation, fluency, applied problems).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.