Integrating Rational Number Sense

该奖项是美国国家科学基金会社会、行为和经济科学博士后研究奖学金（SPRF）计划的一部分。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事业准备有前途的早期职业博士级科学家。SPRF奖励包括在知名科学家的赞助下进行为期两年的培训，并鼓励博士后进行独立研究。美国国家科学基金会寻求促进科学界各阶层的科学家，包括那些未被充分代表的群体的科学家，参与其研究项目和活动；博士后阶段被认为是实现这一目标的一个重要的专业发展阶段。每个博士后必须解决各自学科领域的重要科学问题。在哥伦比亚大学教师学院的罗伯特·西格勒博士和肯特州立大学的克拉丽莎·汤普森博士的赞助下，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符号（分数、小数和百分比）之间关系的理解。早期的研究表明，有理数，尤其是分数，对代数很重要，而代数反过来又能预测生活结果。不幸的是，儿童对有理数的理解相当差。这项研究的最终目的是了解儿童对数字系统的概念，并确定改进的方法。本研究对中小学课程设置和教学具有重要的启示意义。目前的项目建立在Siegler， Thompson和Schneider（2011）的数值发展综合理论的基础上，该理论认为分数是数值发展的核心。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，我们称之为综合数字感。我们对儿童的交叉符号理解知之甚少。初步研究结果（Schiller, 2020）表明，综合数字感是一项关键技能，但在很大程度上被课程和研究所忽视。具体来说，综合数字感，通过对不同符号的数量级比较来衡量，可以独特地预测分数数量级表示之外的数学成绩。此外，综合数感预测分数算术估计，而分数大小表示没有。然而，学生们对交叉符号的理解很少。例如，学生倾向于认为百分比比分数和小数更大（例如，40% vs. 1/4比2/5 vs. 25%的准确性更高）。拟议的项目旨在通过以下方式开发构建综合数感的指导：1)更详细地研究综合数感及其在其他数学结果中的作用，2)通过研究符号内和符号间大小的策略使用来检查心理数线的使用，3)测试使用孤立或集成的方法来构建心理数线的交叉符号抽象是否更有效。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。

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.