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

精确数字相等的概念是数学推理的核心，在儿童早期学习它是日后学业成功的一个强有力的预测因素。不幸的是，对许多学生来说，这仍然是一个持续的困难来源，对学龄前儿童对数字单词的理解甚至中学代数的学习都有影响。这个项目由加州大学圣地亚哥分校（University of California, San Diego）和布朗大学（Brown University）的研究人员领导，其主要目标是了解影响4至5岁儿童对概念学习的早期儿童的社会和认知因素。具体而言，研究人员将调查儿童如何在获得正式符号（即数字和等号）之前对数字平等进行推理，这种初步理解是否受到他们关于公平的发展直觉的影响，以及他们关于数字平等和公平的非正式直觉如何支持在正规幼儿教育环境中学习数学平等的符号表征。对这些想法的研究将为早期儿童数学教育的改变奠定研究基础。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。研究人员将研究儿童对核心数学概念平等的理解的发展起源。他们将进行一系列的行为研究，从行为观察到实验再到学习干预。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，研究人员将测试当孩子们受到社会关注的激励时，他们是否更有可能使用这种策略：他们希望确保有价值的资源得到公平分享。他们还将测试孩子们在学习数字符号（如数字单词）时，这种能力是否会发生变化。最后，研究人员将测试一种学习干预，包括利用他们对相等、加法和减法的直觉理解以及他们确保公平的动机。他们假设，这种方法将帮助孩子理解形式表达式的含义（例如，“9 + 1 = 10”），否则他们可能只是简单地记忆和死记硬背。通过将儿童的社会和数字直觉与对符号数学的理解联系起来，该项目将解决数学教育中的核心挑战，这对幼儿教育实践具有重要意义。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。

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.