Collaborative Research: Cognitive Mechanisms of Early Math Learning - Improving Outcomes by Harnessing Multiple Memory Representations

该提案是针对电子病历核心研究(ECR)计划公告NSF 15-509而提交的。ECR STEM教育基础研究计划为关键的研究领域提供资金，这些领域是基本的、广泛的和持久的。EHR寻求的建议将有助于综合、建立和/或扩大以下重点领域的研究基础：STEM学习、STEM学习环境、STEM劳动力发展和扩大STEM的参与。ECR项目的特点是强调积累可靠的证据，为以下努力提供信息：(A)理解，(B)建立解释理论，(C)提出干预措施(和创新)，以解决STEM兴趣、教育、学习和参与方面的持续挑战。该研究将调查将手势和数学学习联系起来的过程。手势是数学教学中一个重要而又缺乏研究的方面。它们会影响学生对数学表示法的记忆和理解。这一系列研究将通过测试结合常用语言解释和手势的教学来检验学生对数学等价性概念的学习。数学等价包括理解等号的含义和确定两个表达式是否相等。二年级和三年级的孩子将参加。这些研究特别感兴趣的是手势对先前存在的程序知识的影响，手势如何支持学习，而不仅仅是强调信息和引导学习者的注意力，以及程序知识的创造。这一系列的实验研究将考察手势与数学等价性的程序性理解之间的联系机制。研究从第一阶段开始，考察手势如何与数学等价性的程序性知识相联系。随后的研究调查了手势如何作为一种学习机制发挥作用，而不仅仅是强调或引导注意力到相关信息上。收集的数据将学生对等值问题的反应和眼球跟踪数据跟踪学生是否从等号的一边看到另一边。在这项工作的第二阶段，这些研究将考察手势如何对数学学习产生更广泛的有益影响。为了考察手势在不同个体中的作用，将对工作记忆进行评估。分数任务将被用来检验之前关于手势的结果对其他数学概念的概括。

This proposal was submitted in response to EHR Core Research (ECR) program announcement NSF 15-509. The ECR program of fundamental research in STEM education provides funding in critical research areas that are essential, broad and enduring. EHR seeks proposals that will help synthesize, build and/or expand research foundations in the following focal areas: STEM learning, STEM learning environments, STEM workforce development, and broadening participation in STEM. The ECR program is distinguished by its emphasis on the accumulation of robust evidence to inform efforts to (a) understand, (b) build theory to explain, and (c) suggest interventions (and innovations) to address persistent challenges in STEM interest, education, learning, and participation.The study will investigate the processes that connect gestures and mathematics learning. Gestures are an important yet under-investigated aspect of mathematics teaching. They can influence students' memory and understanding of mathematical representations. The series of studies will examine students' learning of the concept of mathematical equivalence by testing instruction that incorporates commonly used verbal explanations and gestures. Mathematical equivalence includes understanding the meaning of the equal sign and determining if two expressions are equal. Second and third grade children will be participants. Of particular interest in the studies is the influence of gestures on preexisting knowledge of procedures, how gestures support learning beyond emphasizing information and direct learners' attention, and the creation of procedural knowledge. The series of experimental studies will examine the mechanisms that connect gestures and procedural understanding of mathematical equivalence. The studies begin in the first phase with examining how gesture is connected to procedural knowledge of mathematical equivalence. Subsequent studies investigate how gesture functions as a mechanism for learning beyond emphasizing or directing attention to relevant information. Data collected will students' responses to equivalence problems and eye tracking data to follow whether students are looking from one side of the equal sign to the other. In the second phase of the work, the studies will examine how gesture has beneficial effects on learning more generally in mathematics. Working memory will be assessed in order to examine the role of gesture across different individuals. Fraction tasks will be used to examine the generalization of the previous results regarding gestures to other mathematics concepts.