Collaborative Research: Development of symbolic and non-symbolic representations of exact equality

合作研究：精确平等的符号和非符号表示的发展

基本信息

批准号：
2000827
负责人：
David Barner
金额：
$ 71.19万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-06-15 至 2025-05-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2000827&HistoricalAwards=false
关键词：
Collaborative Research Development symbolic non

项目摘要

The concept of exact numerical equality is central to mathematical reasoning, and learning it in early childhood is a strong predictor of later academic success. Unfortunately, it remains a persistent source of difficulty for many students, with implications for the understanding of number words by preschoolers and even the learning of algebra in middle school. The main goal of this project, led by researchers at the University of California, San Diego, and Brown University, is to understand the social and cognitive factors in early childhood that affect 4- to 5-year-olds’ learning of the concept. Specifically, the researchers will investigate how children reason about numerical equality prior to the acquisition of formal symbols (i.e., numbers and the equal sign), whether this initial understanding is affected by their developing intuitions about fairness, and how their informal intuitions about numerical equality and fairness supports the learning of symbolic representations of mathematical equality in formal early childhood education settings. The investigation of these ideas will create a research foundation that could lead to changes in early childhood mathematical education. 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.Researchers will examine the developmental origins of children’s understandings of the core mathematical concept of equality. They will conduct a series of behavioral studies that will range from behavioral observations to experiments to learning interventions. In one set of studies, they will assess children’s ability to evaluate whether two quantities are equal when they use a strategy that does not require knowing number words or formal mathematical symbols. The researchers will then test whether children are more likely to use this strategy when they are motivated by a social concern: a desire to make sure valuable resources are shared fairly. They will also test whether the ability changes as children learn numerical symbols (e.g., number words). Finally, researchers will test a learning intervention that involves their leveraging their intuitive understandings of equality, addition, and subtraction together with their motivation to ensure fairness. They hypothesize that such an approach will help children to understand the meaning of formal expressions (e.g., “9 + 1 = 10”) that they might otherwise simply memorize and solve by rote. By connecting children’s social and numerical intuitions with understanding of symbolic math, the project will address a central challenge in mathematics education that has important implications for early childhood education practices.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.

精确数字相等的概念是数学推理的核心，在幼儿期学习它是日后学业成功的有力预测因素，不幸的是，它仍然是许多学生的持续困难来源，对学龄前儿童对数字词的理解产生影响。该项目由加州大学圣地亚哥分校和布朗大学的研究人员领导，其主要目标是了解影响 4 至 5 岁幼儿的社会和认知因素。 - 岁儿童对概念的学习。研究人员将调查儿童在获得正式符号（即数字和等号）之前如何推理数字平等，这种最初的理解是否受到他们发展中的关于公平的特定直觉的影响，以及他们对数字平等的非正式直觉如何影响公平性支持在正规幼儿教育环境中学习数学平等的符号表示。对这些想法的研究将为幼儿数学教育的变革奠定基础。该项目由 EHR 核心研究 (EHR Core Research) 共同资助。 ECR）计划，支持推进工作有关 STEM 学习的基础研究文献，以及 Discovery Research K-12 计划 (DRK-12)，该计划支持创新资源、模型和工具的研究和开发，以通过 Pre-K-12 加强 STEM 学习和教学研究人员将研究儿童对平等核心数学概念的理解的发展起源，他们将进行一系列行为研究，从行为观察到实验再到学习干预。他们将在一组研究中进行评估。儿童评估是否有能力当他们使用不需要了解数字单词或正式数学符号的策略时，两个数量相等。然后，研究人员将测试当孩子受到社会关注（渴望确保有价值的愿望）时，他们是否更有可能使用这种策略。最后，研究人员将测试一种学习干预措施，其中包括利用他们对等式、加法和减法的直观理解。确保公平的动力。该方法将帮助孩子们理解正式表达式（例如“9 + 1 = 10”）的含义，否则他们可能只是死记硬背并解决这些问题。该项目将解决这些问题，将孩子们的社交和数字直觉与对符号数学的理解联系起来。这是数学教育的一个核心挑战，对幼儿教育实践具有重要影响。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。