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

精确数字等式的概念是数学推理的核心，在幼儿时期学习它是未来学业成功的有力预测。不幸的是，对于许多学生来说，它仍然是一个持续的困难来源，这对学龄前儿童理解数字词甚至中学的代数学习都有影响。这项由加州大学圣地亚哥分校和布朗大学的研究人员领导的项目的主要目标是了解幼儿时期影响4至5岁儿童学习这一概念的社会和认知因素。具体地说，研究人员将调查儿童在获得正式符号(即数字和等号)之前是如何对数字平等进行推理的，这种最初的理解是否受到他们对公平的直觉的发展的影响，以及他们关于数字平等和公平的非正式直觉如何支持正规幼儿教育环境中数学平等的符号表示法的学习。对这些思想的调查将创造一个研究基础，可能会导致幼儿数学教育的变化。该项目由EHR核心研究(ECR)计划和发现研究K-12计划(DRK-12)共同资助，ECR计划支持推进STEM学习基础研究文献的工作，发现研究K-12计划支持创新资源、模型和工具的研究和开发，以加强K-12之前的学生和教师的STEM学习和教学。研究人员将探讨儿童对平等核心数学概念理解的发展根源。他们将进行一系列的行为研究，范围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了解数字单词或正式数学符号的策略时，评估两个量是否相等的能力。然后，研究人员将测试孩子们是否更有可能在受到社会问题的激励时使用这一策略：确保有价值的资源得到公平分享的愿望。他们还将测试这种能力是否会随着儿童学习数字符号(例如数字单词)而发生变化。最后，研究人员将测试一项学习干预，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，这样的方法将有助于儿童理解他们原本可能简单地记住和死记硬背的正式表达(例如，“9+1=10”)的含义。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一个核心挑战，这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优势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.