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

尽管分数在幼儿教育中是一个至关重要的话题，但许多学生对分数概念的掌握非常薄弱，即使经过几年符合现行标准的分数教学。这个项目由特拉华大学和天普大学的一组研究人员领导，他们的目标是回答一些重要的问题，这些问题是关于儿童在上学之前对分数的非正式理解，以及他们在更正式的教学环境中对分数的学习有什么关系。对分数的精通大大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，在中等年级分数教学开始时，分数理解的巨大个体差异是明显的。早期对分数的误解会在以后的年级演变成更严重的数学缺陷，特别是当教学突然从整数转向分数时。我们迫切需要了解在正式教学之前产生的个体差异的根源。幼儿在上学之前就具有重要的非正式分数理解能力，但这些能力的范围及其在正式分数学习和发展中的作用尚未得到很好的理解。该项目的目标是：a)调查一年级儿童非正式分数相关知识的个体差异与短期和长期分数和数学结果的关联程度；b)看看非正式分数相关知识的水平和从直接建立在这些知识基础上的分数教学中获益的能力之间是否存在因果关系。该项目的研究结果有望为早期儿童教育工作者提供信息，告诉他们如何以新的、有意义的方式将分数纳入一年级课程。尽管研究结果对所有学生都有益，但该项目将专门针对STEM领域中代表性不足的群体，包括少数民族和种族以及低收入学生。该项目由EHR核心研究项目（ECR）和发现研究K-12项目（DRK-12）共同资助，前者支持推进STEM学习基础研究文献的工作，后者支持创新资源、模型和工具的研发，以提高K-12学前班学生和教师的STEM学习和教学。项目设计包括观察研究和实验研究。观察性研究将：(1)记录小学生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发关系；(3)检验一年级开始时非正式分数相关知识是否能唯一地预测学生最终的数学成绩。本实验研究将探讨训练对一年级学生非正式分数和正式分数概念的影响程度。研究人员将测试在数轴上的训练，这是连续的，与所有实数的大小的心理表征密切相关，是否有助于学生利用他们对比例、比例、等共享的非正式分数理解，以及他们对整数的经验来学习关键的分数概念。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，这些学校为社会经济和种族多样化的学生提供服务。主要测量包括非正式分数知识（比例推理、空间缩放、平等共享）、执行功能、词汇、整数知识、整数/分数数列估计、正式分数知识和广泛的数学成就（计算、流畅性、应用问题）的评估。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.