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

合作研究：利用认知科学原理帮助孩子学习位置价值

• 批准号: 1621093
• 负责人: Linda Smith
• 金额: $ 71.36万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1621093&HistoricalAwards=false
• 关键词: Collaborative; Research; Using; Cognitive; Science

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.

Discovery Research K-12 计划 (DRK-12) 旨在通过创新资源、模型和工具的研究和开发，显着增强 PreK-12 学生和教师对科学、技术、工程和数学 (STEM) 的学习和教学。 DRK-12 计划中的项目建立在 STEM 教育的基础研究以及先前的研究和开发工作的基础上，为拟议项目提供理论和实证依据。许多孩子难以理解多位数的含义，这可能会导致长期的数学问题。 对地方价值的理解不佳困扰着所有社会经济背景的儿童，而且不仅限于那些有学习障碍的儿童。这个问题是普遍存在的；事实上，它可能比目前所理解的更广泛，因为一些测试可能高估了儿童所知道的知识。 长期成功所需的一项关键技能（但并不总是可以衡量）称为分解。 它涉及了解如何按位置（个位、十位、百位）将多位数字分解为各个组成部分并解释其含义（例如，642 = 6 个百位、4 个十位和 2 个个位）。该项目将针对这一关键技能，并根据数十年认知科学研究中收集到的类比推理原则，测试教授位置价值的新方法。这些新方法将通过突出显示和调整口头数字名称、书面数字和对象集的结构，使位置值更加透明。通过利用这些强大的类比学习机制，有可能比典型情况更早地教授位置价值，因此该项目将针对 K-1 学生。 如果成功的话，这种方法可能会消除目前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值概念的测试来了解它们如何相互关联。 该项目的活动成本低廉，适合日常教育实践，因此教师可以轻松实施其成果。该项目将测试旨在帮助 K-1 学生理解位置价值的新教学方法。该项目的创新之处在于，它将强调位值符号的底层关系结构，并利用从结构映射文献中提取的教学材料和技术来瞄准这一结构。其作用理论是，为位值构建结构映射的教学将更好地让孩子们准备好面对高级运算的挑战，例如多位数计算。 该项目特别针对分解，因为这已被认为是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果有关。将进行三项研究。研究 1 将跟踪从幼儿园到二年级的位值理解的发展，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，例如数轴估计和量级判断。该研究将展示这些指标在发展过程中如何相互关联，并测试对分解的牢固理解是否可以预测以后的数学学习。 研究 2 和 3 将使用预测-训练-后测设计来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 的培训将重点关注一项为期三周的活动，而研究 3 的培训将包括整个学期的所有六项活动。