Collaborative Research: Using Cognitive Science Principles to Help Children Learn Place Value

探索研究K-12计划（DRK-12）旨在通过研究和开发创新资源，模型和工具，显着提高学前班学生和教师的科学，技术，工程和数学（STEM）的学习和教学。DRK-12项目中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，这些研究和开发工作为拟议的项目提供了理论和经验依据。许多儿童难以理解多位数的含义，这可能导致长期的数学问题。 对位置价值的理解不佳困扰着所有社会经济背景的儿童，并不仅限于那些有学习障碍的儿童。这个问题是普遍存在的，甚至可能比目前所理解的更普遍，因为一些测试可能高估了孩子们的知识。 长期成功所需的关键技能，也是一个不总是衡量的技能，被称为分解。 它涉及到知道如何将一个多位数按位置（个位、十位、百位）分解成它的组成部分，并解释它的含义（例如，642 = 6个百位、4个十位和2个一位）。这个项目将针对这一关键技能，并测试基于类比推理原理的教授位置值的新方法，这些原理是从几十年的认知科学研究中收集到的。这些新方法将通过突出显示和调整其结构，使位值在口语数字名称，书面数字和对象集合中更加透明。通过利用这些强大的类比学习机制，有可能比通常更早地教授位置值，因此该项目将针对K-1学生。 如果成功的话，这种方法可以避免目前在年龄较大的儿童中常见的误解。该项目还将跟踪儿童随着时间的推移，使用测试，衡量分解和其他地方价值的概念，看看他们如何相互关联。 该项目的活动被设计成成本低廉，适合日常教育实践，使结果可以很容易地由教师实施。该项目将测试新的教学方法，旨在帮助K-1学生理解位置值。该项目是创新的，它将强调潜在的关系结构的地方价值符号，并针对这一结构的教学材料和技术从结构映射文献。它的作用理论是，为位值构建结构映射的教学将更好地为儿童准备面对高级操作的挑战，例如多位数计算。 该项目专门针对分解，因为这已被确定为儿童的一个特别的绊脚石。 此外，分解技能与更好的长期数学成果有关。将有三项研究。研究1将跟踪从幼儿园到二年级的地方价值理解的发展，使用一些明确需要分解的措施，以及其他广泛使用但可能不需要分解的措施，如数字线估计和大小判断。这项研究将展示这些措施是如何与发展时间相关的，以及测试对分解的坚定理解是否能预测以后的数学学习。 研究二和研究三将采用前测-训练-后测的设计，测试六种结构映射活动对K-1学生位置价值的有效性。研究2中的培训将集中在一个活动上，为期三周，而研究3中的培训将包括整个学期的所有六个活动。

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.Many children have trouble understanding what multidigit numbers mean and this can lead to long-term problems in mathematics. Poor place value understanding plagues children from all socioeconomic backgrounds and is not limited to those with learning disabilities. This problem is widespread and pervasive; indeed, perhaps more widespread than currently understood because some tests may overestimate what children know. The critical skill needed for long-term success, and one not always measured, is called decomposition. It involves knowing how to break a multi-digit number down into its components by place (ones, tens, hundreds) and interpret its meaning (e.g., 642 = 6 hundreds, 4 tens, and 2 ones). This project will target that crucial skill and test new ways of teaching place value based on principles of analogical reasoning, gleaned from decades of cognitive science research. These new approaches will make place value more transparent by highlighting and aligning its structure across spoken number names, written numerals, and sets of objects. By leveraging these powerful analogical learning mechanisms, it may be possible to teach place value earlier than is typical, so the project will target K-1 students. If successful, this approach could head off the misconceptions that are currently common among older children. The project will also track children over time, using tests that measure decomposition and other place value concepts to see how they interrelate. The project's activities have been designed to be inexpensive and fit into everyday educational practice, so that the results may be easily implemented by teachers.The project will test new instructional approaches designed to help K-1 students comprehend place value. The project is innovative in that it will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation. The project specifically targets decomposition, as this has been identified as a particular stumbling block for children. Also, decomposition skill has been linked to better long-term mathematics outcomes. There will be three studies. Study 1 will track the development of place value understanding from kindergarten to 2nd grade, using some measures that clearly require decomposition, and others that are in wide use but may not require decomposition, such as number line estimation and magnitude judgments. The study will show how these measures are related over developmental time, as well as testing whether a firm understanding of decomposition predicts later mathematics learning. Studies 2 and 3 will use a pretest-training-posttest design to test the efficacy of six structure mapping activities for place value in K-1 students. The training in Study 2 will be focused on one activity for three weeks, whereas the training in Study 3 will include all six activities presented over an entire semester.