Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K through Middle School

这个项目研究的是从学前班到八年级的测量实践，作为STEM数学和科学学科的协调。这个为期四年的混合方法研究项目测试、修订和扩展了儿童在十年人类发展过程中的几何测量知识的学习轨迹(LTS)。具体地说，来自伊利诺伊州立大学和丹佛大学的研究团队正在与城市和郊区学校的儿童合作，以(1)验证和扩展先前NSF资助的研究的先前发现，该研究开发了学龄前儿童到5年级的测量学习轨迹，以及(2)生成和扩展6-8年级的几何测量轨迹的部分。该项目采用了一种微遗传学研究的形式，从学前班到五年级每个年级有24-50名儿童，代表着从一组特定的郊区学校中分层随机抽样。这些研究将检验LTS在长度、面积和体积方面的有效性、可复制性和普适性。目标是验证每个学习轨迹、目标、发展进程和教学任务的所有组成部分，以及修改每个LT以反映实验的结果。在实验/对照设计中，用前后评估对差异测量进行分析将补充微遗传分析的重复会议方法。为了探索和推广6-8年级儿童的LTS，该项目采用了教学实验。这一设计用于生成和扩展用于几何测量的轨迹的部分，并探索临床和课堂环境中测量的关键方面。这项工作与州立学校首席官员委员会/全国州长协会、全国数学教师委员会、全国科学教师协会、美国科学促进会和国家研究委员会发布的教学标准进行了协调，出版了认知和数学/科学教育文献。关于假设的LT水平的新结构与其他研究人员生成的相关框架和标准文件所暗示的建立6-8年级正在进行的实验干预序列的结构正在被比较、评论和评估。本项目基于经验分析提供了关于学龄前到8年级儿童的思维方式和对数学和科学测量概念的理解的纵向描述。由此产生的学习轨迹将代表综合的、跨学科的、以理论和经验为基础的对测量领域日益复杂和复杂的思维水平的最新描述(尽管，对于6-8年级来说，更具试探性)。这一说明将用于验证和/或修改现有的儿童推理发展说明，这些说明来自对学习的短期分析或横断面研究。目前还没有描述这一认知领域的面积或体积测量的综合性纵向研究。这种基于轨迹的发展和教学分析支持对个人和儿童群体的综合形成性评估的设计和测试。这种学习轨迹将有助于执行《国家共同核心标准数学》中所述的以标准为重点的课程，并有助于支持目前正在进行的多个大型评估项目。

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children's knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8. The project employs a form of microgenetic studies with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis. To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments. This design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards issued by the Council of Chief State School Officials/National Governors Association, the National Council of Teachers of Mathematics, the National Science Teachers Association, the American Association of the Advancement of Science, and the National Research Council with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.This project provides a longitudinal account of pre-K to Grade 8 children's ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art integrated, interdisciplinary, theoretically- and empirically-based descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children's development of reasoning from short-term analyses of learning or cross-sectional studies. There are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway.