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

《空间数学、工程和科学：走向综合STEM教育》的目标是开发一个跨越K-5年级的临时学习进度，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、数学和工程的学科边界内和跨领域具有广泛的范围，该项目将为基础教学创造一种连贯的方法，在这种方法中系统地培养关于空间的数学推理。同时，研究人员正在探索空间数学的潜力，作为运动机械工程设计的资源，以及关于这些机器行为的机械推理的发展。跨这些学科的工作定位和激励了数学工作，也提供了机会来研究标志性学科实践之间的交叉点和对比，例如数学中的定义和证明，工程中的设计和科学中的建模。这项研究和开发是在一所中学进行的，这所中学是该项目的全面合作伙伴。通过合作，研究人员和参与的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角色。该研究包括在12个参与的幼儿园-五年级教室进行的设计研究，以及对同一年级的儿童进行的小规模教学实验。这项研究将建立关于空间学习的临时途径和里程碑，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是新颖的。首先，它为儿童提供了早期和系统的多种几何（例如，平面，圆柱体，球体），以发展对强大的，但可通过实验获得的概念的复杂理解，例如直线，以及与stem相关的实践，例如模型，定义和证明。第二，国家研究委员会科学/工程和共同核心国家标准数学都强调了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实用的途径。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中，这为生成式STEM整合提供了坚实的基础——这种整合不会忽视不同学科的独特实践，而是利用这些差异来产生多种了解空间的方式。研究和开发是在代表性不足的学生群体中进行的，这些学生通常在STEM教育中得不到充分的服务。虽然在这一阶段的工作中接触到的学生人数相对较少，但长期的潜力是巨大的，因为对于那些在传统形式的数学教育中挣扎的学生来说，以空间为基础的教学可能更容易获得。在国家一级对综合STEM教育的日益关注也确保了这一努力可能有助于建立推进跨学科教育形式所需的知识基础。

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.