Foregrounding Agency versus Structure as Models for Designing Integrated Mathematics and Computational Thinking Curriculum

该项目将设计和研究融合数学和计算思维的新学习环境。虽然整合内容被认为是学生学习的一种策略，但关于数学和计算思维在学习经验中应该如何联系的调查有限。计算思维是STEM职业生涯的一项基本技能，包括算法和编程、数据收集和分析、使用抽象和解决问题等概念。这些计算思维概念和实践可以与数学概念相关。这个项目将研究如何设计放置数学概念的学习模块。通过探索不同类型的设计如何支持学习和参与，该项目将建立一套支持数学和计算思维的设计原则。该项目由STEM+计算计划资助，该计划寻求通过将计算思维和计算活动应用于学科STEM教与学的整合来应对计算STEM领域中新出现的挑战，并将其应用于从高中到高中的幼儿教育(Pre-K-12)。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(RMT)，显著提高K-12学龄前学生和教师在科学、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，为拟议的项目提供理论和经验证明。该项目将使用基于设计的研究作为支持迭代设计和研究的方法论，该项目将探索与数学和计算思维相结合的两个核心紧张关系。每一种紧张都涉及如何平衡相互竞争的目标，并调查突出一个目标对另一个目标的影响。具体地说，该项目将设计、测试并开始在学校应用一组模块，这些模块对比：1)突出数学与计算思维；2)突出机构与结构。实施模式包括两个夏季的中学生夏令营课程和一年的课堂实施，从而允许超越数学和计算思维整合潜力的探索，并延伸到这种整合在学校机构背景下的样子。要研究的问题包括：(1)通过计算思维(前景化数学)教授数学的模块与通过数学(前景化计算思维)教学计算思维的模块相比有什么优势？(2)通过开放探索(代理)教学计算思维的模块与通过游戏(结构)教学的模块有什么优势？(3)数学教师在教处于计算思维和数学交叉的学生时需要或要求什么样的教学支持？该项目将导致(A)一套中学教学序列，提出计算思维和数学的有效交叉；(B)理解这些教学序列如何以及为什么支持不同的参与；以及(C)关于数学教师在课堂上整合计算思维所需的支持的猜想。将为学生创建不同的部分，以比较将突出数学、计算思维、结构或代理的不同条件。收集的数据将包括对学生学习的测量、访谈、对学生作业的分析，以及用来检查学生参与度和兴趣的视频分析。

The project will design and study new learning environments integrating mathematical and computational thinking. While integrating content has been suggested as a strategy for students' learning, there has been limited investigation about how mathematics and computational thinking should be connected in learning experiences. Computational thinking is an essential skill for STEM careers including concepts such as algorithms and programming, data collection and analysis, using abstractions, and problem solving. These computational thinking concepts and practices can be related to mathematics concepts. This project will examine how to design learning modules that place mathematics concepts. By exploring how different kinds of designs support learning and engagement, the project will establish a set of design principles for supporting mathematical and computational thinking. The project is funded by the STEM+Computing program, which seeks to address emerging challenges in computational STEM areas through the applied integration of computational thinking and computing activities within disciplinary STEM teaching and learning in early childhood education through high school (preK-12). 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 (RMTs). 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.Using design-based research as a methodology to support iterative design and research, the project will explore two core tensions that are relevant to the integration of mathematics and computational thinking. Each tension deals with how to balance competing goals, and investigates the influence of foregrounding one goal over another. Specifically, the project will design, test, and begin to apply in schools a set of modules that contrast: 1) foregrounding mathematics vs. computational thinking; and 2) foregrounding agency vs. structure. The model of implementation includes two summers of camp sessions for middle school students, and a year of implementation in classrooms, thus allowing exploration beyond the potential for math and computational thinking to be integrated, and extending into what such integration looks like in the institutional context of schools. The research questions to be investigated include: (1) What are the advantages of modules that teach mathematics through computational thinking (foregrounding mathematics) vs. those that teach computational thinking through mathematics (foregrounding computational thinking)? (2) What are the advantages of modules that teach computational thinking through open exploration (agency) vs. game play (structure)? (3) What kinds of instructional supports do math teachers need or request as they are teaching students at the intersection of computational thinking and mathematics? The project will result in (a) a set of instructional sequences for middle school that propose productive intersections of computational thinking and mathematics, (b) an understanding of how and why these instructional sequences support diverse participation, and (c) conjectures about the support math teachers need to integrate computational thinking in their classrooms. Different sections for students will be created to compare different conditions that will foreground mathematics, computational thinking, structure or agency. Data collected will include measures of student learning, interviews, analysis of student work, and video analysis to examine student engagement and interest.