Integrating Rational Number Sense

该奖项是作为NSF社会、行为和经济学博士后研究奖学金(SPRF)计划的一部分提供的。SPRF计划的目标是为学术界、工业界或私营部门和政府的科学职业生涯培养有前途的、早期职业博士水平的科学家。SPRF奖项包括在知名科学家的赞助下进行两年的培训，并鼓励博士后研究员进行独立研究。国家科学基金会致力于促进科学界所有阶层的科学家参与其研究方案和活动，包括那些来自代表性不足的群体的科学家；博士后阶段被认为是实现这一目标的专业发展的一个重要水平。每个博士后研究员都必须解决推动各自学科领域向前发展的重要科学问题。在哥伦比亚大学师范学院的Robert Siegler博士和肯特州立大学的Clarissa Thompson博士的赞助下，这项博士后奖学金奖支持一位早期职业科学家，研究儿童对有理数表示法(分数、小数和百分比)之间的关系的理解。早期的研究表明，有理数，尤其是分数，对代数很重要，而代数又是人生结局的预言者。不幸的是，儿童的有理数理解能力相当差。这项研究的最终目的是了解儿童对我们的数字系统的概念，并找出改进的方法。这项工作可能会对中小学的课程和教学产生重要的影响。目前的项目建立在西格勒、汤普森和施奈德(2011)的数字发展综合理论的基础上，该理论认为分数是数字发展的核心。在这里，我们重点关注儿童对分数、小数和百分比之间关系的理解，我们称之为综合数感。人们对儿童交叉符号的理解知之甚少。最初的发现(席勒，2020)表明，综合数感是一项关键技能，但在很大程度上被课程和研究忽视。具体地说，综合数感，通过跨符号的大小比较来衡量，唯一地预测了分数大小表示之外的数学成绩。此外，综合数感预测分数算术估计，而分数大小表征不能。然而，学生们很少表现出对交叉记法的理解。例如，学生倾向于认为百分比大于分数和小数(例如，比较40%对1/4比2/5对25%的准确率更高)。这项拟议的项目旨在通过以下方式开发建立综合数感的教学：1)更详细地调查综合数感及其在其他数学结果中所起的作用；2)通过调查符号内部和符号之间大小的策略性使用来检查心理数字线的使用；3)测试使用孤立或综合的方法来建立心理数字线的交叉符号抽象是否更有效。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。

This award was provided as part of NSF's Social, Behavioral and Economic Sciences Postdoctoral Research Fellowships (SPRF) program. The goal of the SPRF program is to prepare promising, early career doctoral-level scientists for scientific careers in academia, industry or private sector, and government. SPRF awards involve two years of training under the sponsorship of established scientists and encourage Postdoctoral Fellows to perform independent research. NSF seeks to promote the participation of scientists from all segments of the scientific community, including those from underrepresented groups, in its research programs and activities; the postdoctoral period is considered to be an important level of professional development in attaining this goal. Each Postdoctoral Fellow must address important scientific questions that advance their respective disciplinary fields. Under the sponsorship of Dr. Robert Siegler at Teachers College, Columbia University and Dr. Clarissa Thompson at Kent State University this postdoctoral fellowship award supports an early career scientist investigating children’s understanding of the relations among rational number notations (fractions, decimals, and percentages). Earlier work has shown that rational numbers, particularly fractions, are important for algebra, which in turn, is predictive of life outcomes. Unfortunately, children’s rational number understanding is quite poor. The ultimate goal of the proposed research is to understand children’s conceptions of our number system and to identify methods for improvement. This work may have important implications for curriculum and instruction across elementary and middle school. The current project builds on Siegler, Thompson, and Schneider’s (2011) Integrated Theory of Numerical Development, which argues that fractions are central to numerical development. Here, we focus on children’s understanding of the relations among fractions, decimals, and percentages, what we call, integrated number sense. Very little is known about children’s cross-notation understandings. Initial findings (Schiller, 2020) suggest that integrated number sense is a critical skill that is largely ignored by curriculum and research. Specifically, integrated number sense, as measured by magnitude comparison across notations, uniquely predicted math achievement beyond fraction magnitude representations. Additionally, integrated number sense predicted fraction arithmetic estimation, whereas fraction magnitude representation did not. However, students demonstrate little cross-notation understanding. For example, students are biased towards perceiving percentages as larger than fractions and decimals (e.g., higher accuracy for comparing 40% vs. 1/4 than 2/5 vs. 25%). The proposed project aims to develop instruction to build integrated number sense by: 1) investigating integrated number sense in much greater detail and the role it plays in other math outcomes, 2) examining use of the mental number line by investigating strategic use of magnitude within and across notations, 3) testing whether it is more effective to use an isolated or integrated approach to build this cross-notation abstraction of the mental number line.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.