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

该项目研究了从学前班到8年级的测量实践，作为数学和科学STEM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几何测量知识的学习轨迹（lt）。具体来说，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孩子们一起工作，以：(1)验证和扩展先前由美国国家科学基金会资助的研究成果，这些研究开发了学龄前儿童到五年级儿童的测量学习轨迹，(2)生成并扩展了6-8年级几何测量轨迹的一部分。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，代表了一组特定郊区学校的分层随机样本。这些研究将测试LTs在长度、面积和体积方面的有效性、可复制性和普遍性。我们的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，并修改每个学习记录以反映实验结果。在实验/控制设计中采用前后评估的方差分析措施将补充微遗传分析的重复会议方法。为了探索和拓展6-8年级儿童的学习能力，本项目采用教学实验的方式。该设计用于生成和扩展几何测量的轨迹部分，并探索临床和课堂环境中测量的关键方面。这项工作与各州首席学校官员委员会/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关于认知和数学/科学教育文献的教学标准相协调。与其他研究者提出的相关框架和标准文件所暗示的建立6-8年级实验干预持续序列的相关框架相关的假设低水平的新兴结构正在被比较、批评和评估。本项目在实证分析的基础上，对学前班至八年级儿童的思维方式和对数学和科学测量概念的理解进行了纵向分析。由此产生的学习轨迹将代表最先进的、综合的、跨学科的、基于理论和经验的对测量领域中日益复杂和复杂的思维水平的描述（尽管，对6-8年级来说更具试探性）。这种说法将用于验证和/或修改现有的关于儿童推理能力发展的说法，这些说法来自对学习的短期分析或横断面研究。目前还没有综合的纵向研究描述这种认知领域的面积或体积测量。这种基于发展和教学轨迹的分析支持对个人和儿童群体进行综合、形成性评估的设计和测试。这样的学习轨迹将有助于实施《共同核心州数学标准》中所描述的以标准为重点的课程，并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.