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.

确切的数值平等的概念对于数学推理至关重要，在童年时期学习它是后来学术成功的有力预测指标。不幸的是，对于许多学生来说，这仍然是一个持久的困难来源，这对学龄前儿童的数字单词甚至在中学中的代数学习都有意义。该项目的主要目标是由加利福尼亚大学，圣地亚哥大学和布朗大学的研究人员领导的，是要了解幼儿期的社会和认知因素，影响了4至5岁儿童对该概念的学习。具体来说，研究人员将研究孩子如何在获取形式符号（即数字和平等符号）之前如何理解数值平等，这是否会受到对公平性发展的直觉以及他们对数值平等和公平性的非正式直觉的影响，如何支持对正式儿童范围内数学等等的符号的学习符号来体现。这些想法的投资将创造一个研究基础，可能导致幼儿数学教育的变化。该项目由EHR核心研究（ECR）计划共同资助，该计划支持有关STEM学习的基础研究的发展，并由Discovuly Research K-12计划（DRK-12）（DRK-12）提供了支持，该研究支持创新资源的研究和开发，模型和工具，以增强Pre-K-12学生和教师的STEM学习和教学的核心构建构建核心的核心启发的构图。他们将进行一系列行为研究，范围从行为观察到实验到学习干预措施。在一组研究中，他们将评估儿童在使用不需要知道数字单词或正式数学符号的策略时评估两个数量是否相等的能力。然后，研究人员将在社会关注的激励时测试孩子是否更有可能使用这种策略：确保有价值的资源得到公平共享的愿望。他们还将测试能力是否会随着儿童学习数字符号（例如，数字单词）而变化。最后，研究人员将测试一种学习干预措施，涉及他们利用他们对平等，加法和减法的直观理解，以及确保公平性的动机。他们假设这种方法将帮助孩子理解形式表达的含义（例如，“ 9 + 1 = 10”），否则他们可能会简单地记住死记硬背。通过将儿童的社会和数值直觉与对象征数学的了解联系起来，该项目将解决数学教育中的核心挑战，对幼儿教育习惯具有重要意义。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子和更广泛影响的审查标准来通过评估来通过评估来支持的。