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

该项目将设计和研究整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如何在学习经验中联系起来的研究却很有限。计算思维是STEM职业的基本技能，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。这些计算思维的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+Computing项目资助，该项目旨在通过将计算思维和计算活动应用于STEM学科的教学和学习中，解决计算STEM领域的新挑战。探索研究K-12项目（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pre -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教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据。使用基于设计的研究作为一种方法来支持迭代设计和研究，该项目将探索与数学和计算思维整合相关的两个核心紧张关系。每个张力都涉及如何平衡相互竞争的目标，并探讨将一个目标置于另一个目标之上的影响。具体来说，该项目将设计、测试并开始在学校应用一系列模块，这些模块对比如下：1)前景数学与计算思维；前景代理vs.结构。实施模式包括两个夏天的中学生夏令营，以及一年的课堂实施，从而允许探索超越数学和计算思维的潜力，并扩展到这种整合在学校制度背景下的样子。要调查的研究问题包括：(1)通过计算思维教授数学的模块（前景数学）与通过数学教授计算思维的模块（前景计算思维）的优势是什么？(2)通过开放探索（代理）和游戏玩法（结构）教授计算思维的模块有什么优势？(3)数学教师在教授计算思维与数学交叉的学生时，需要或要求什么样的教学支持？该项目将产生(a)一套中学教学序列，提出计算思维和数学的富有成效的交叉点，(b)理解这些教学序列如何以及为什么支持多样化的参与，以及(c)关于数学教师在课堂上整合计算思维所需支持的猜想。将为学生创建不同的部分，以比较不同的条件，将前景数学，计算思维，结构或机构。收集的数据将包括学生学习、访谈、学生作业分析和视频分析，以检查学生的参与度和兴趣。

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.