Spatial Mathematics, Engineering, and Science: Toward an Integrated STEM Education

空间数学，工程和科学的目标：走向综合STEM教育是制定一个临时的学习进度跨越等级K-5，阐明和测试体验，描述和代表空间的潜力作为综合STEM教育的核心。空间科学在科学、数学和工程的学科界限内和跨学科界限具有广泛的范围，该项目将创造一种连贯的小学教学方法，系统地培养关于空间的数学推理。与此同时，研究人员正在探索空间数学的潜力，作为一种资源的工程设计的运动机器和发展的机械推理的行为，这些机器。跨这些学科的工作定位和激励数学工作，也提供了机会来调查签名学科实践之间的交叉点和对比，如数学中的定义和证明，工程设计和科学建模。研究和开发正在一所中学进行，该中学是该项目的正式合作伙伴。在伙伴关系，研究人员和参与教师正在设计和实施旨在支持空间知识和推理的课程方法。专业发展将加强和利用教师作为学生思维专家的作用。本研究包括在12个参与的教室进行的设计研究，K-5，和小规模的教学实验进行了跨年级的儿童。该研究将建立学习空间的临时途径和地标，以及支持综合STEM学习所需的课程活动和教师实践。 这个项目在三个方面都很新颖。首先，它为儿童提供了早期和系统的访问多种几何形状（例如，平面，圆柱体，球体），以发展强大的，但经验上可访问的概念，如直，和STEM相关的做法，如模型，定义和证明复杂的理解。第二，国家研究理事会科学/工程和共同核心国家标准数学都强调实践在学科知识发展中的作用，该项目为协调学科实践和知识的共同发展提供了一个切实可行的途径。第三，空间的统一主题贯穿于数学，科学和工程中的问题和背景，为生成STEM集成提供了坚实的基础-集成不会忽视不同学科中的独特实践，而是利用这些区别来产生了解空间的多种方式。研究和开发正在与代表性不足的学生群体进行，这些学生通常在STEM教育中得不到充分的服务。虽然这一阶段的学生人数相对较少，但长期潜力很大，因为定位于空间的教学可能更适合那些与传统数学教育形式作斗争的学生。在国家一级对STEM综合教育的日益关注也确保了这一努力有可能有助于促进跨学科形式的学校教育所需的知识基础。

The goal of Spatial Mathematics, Engineering, and Science: Toward an Integrated STEM Education is to develop a provisional learning progression spanning grades K-5 that articulates and tests the potential of experiencing, describing, and representing space as the core of an integrated STEM education. The science of space has an extensive scope within and across disciplinary boundaries of science, mathematics and engineering, the project will create a coherent approach to elementary instruction in which mathematical reasoning about space is systematically cultivated. Simultaneously, researchers are exploring the potential of spatial mathematics as a resource for engineering design of kinematic machines and for the development of mechanistic reasoning about the behavior of these machines. Work across these disciplines situates and motivates the mathematical work and also provides opportunities to investigate the intersections and contrasts among signature disciplinary practices, such as definition and proof in mathematics, design in engineering, and modeling in science. The research and development is being conducted in a middle school which is a full partner in the project. In partnership, researchers and participating teachers are designing and implementing curricular approaches intended to support spatial knowledge and reasoning. Professional development will enhance and capitalize on teachers' roles as specialists in student thinking. The research consists of design studies conducted in 12 participating classrooms, K-5, and small-scale teaching experiments conducted with children across the same grade span. The research will establish provisional pathways and landmarks in learning about space, as well as the curricular activities and teacher practices necessary to support integrated STEM learning. The project is novel in three ways. First, it provides children with early and systematic access to multiple geometries (e.g., plane, cylinder, sphere) to develop sophisticated understandings of powerful, yet experientally accessible concepts, such as straight, and STEM-related practices, such as model, definition and proof. Second, both the National Research Council Science/Engineering and the Common Core State Standards Mathematics highlight the role of practices in the development of disciplinary knowledge, and this project is providing a practical avenue for coordinating the co-development of disciplinary practices and knowledge. Third, the unifying theme of space is threaded through problems and contexts in mathematics, science and engineering, which provide a sound basis for generative STEM integration-integration that does not lose sight of the distinctive practices in different disciplines, but, instead, leverages these distinctions to produce multiple ways of knowing about space. Research and development is being conducted with underrepresented populations of students who are typically underserved in STEM education. Although the numbers of students reached in this phase of the work are relatively modest, the longer-term potential is great, because instruction anchored in space may be more accessible to students who struggle with traditional forms of mathematics education. The increased attention to integrated STEM education at the national level also ensures that this effort is likely to contribute to the knowledge base required to advance interdisciplinary forms of schooling.