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，显著提高K-12学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划中的项目建立在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证明。许多儿童难以理解多位数数字的含义，这可能会导致长期的数学问题。对位置价值的理解不佳困扰着来自所有社会经济背景的儿童，并不局限于那些学习障碍的儿童。这个问题很普遍，而且无处不在；事实上，可能比目前所理解的更普遍，因为一些测试可能高估了儿童所知道的东西。长期成功所需的关键技能称为分解，这是一种不总是被衡量的技能。它包括知道如何按位置(一、十、百)将多位数字分解成其组成部分，并解释其含义(例如，642=6个百、4个十和2个一)。这个项目将针对这一关键技能，并测试基于类比推理原则的地点价值教学的新方法，这些原则是从几十年的认知科学研究中收集的。这些新方法将通过在口语数字名称、书面数字和对象集之间突出显示和对齐Place Value的结构，使Place Value更加透明。通过利用这些强大的类比学习机制，有可能比通常情况下更早地教授地点价值，因此该项目将以K-1学生为目标。如果成功，这种方法可以防止目前在年龄较大的儿童中普遍存在的误解。该项目还将随着时间的推移跟踪儿童，使用测量分解和其他位置值概念的测试来了解它们是如何相互关联的。该项目的活动被设计为廉价并适合日常教育实践，以便教师可以轻松地实施。该项目将测试旨在帮助K-1学生理解场所价值的新教学方法。该项目的创新之处在于，它将强调地价符号的基本关系结构，并以结构映射文献中的教学材料和技术为目标。它的作用原理是，支架式结构映射的位置值将使儿童更好地准备迎接高级运算的挑战，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殊绊脚石。此外，分解技能与更好的长期数学成绩有关。将进行三项研究。研究一将跟踪从幼儿园到二年级的地点价值理解的发展，使用一些明显需要分解的测量方法，以及其他广泛使用但可能不需要分解的测量方法，如数字线估计和量值判断。这项研究将展示这些措施是如何随着发展时间的推移而联系在一起的，并测试对分解的坚定理解是否预示着以后的数学学习。研究二和研究三将使用前测-训练-后测设计来检验六种结构映射活动对K-1学生位置价值的有效性。研究2的培训将集中在一项活动上，为期三周，而研究3的培训将包括整个学期的所有六项活动。

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.