Embodied Mathematical Imagination and Cognition: Professional Development for Undergraduate Mathematics Instructors

该讲习班将使数学教师能够在STEM教育研究的一个新兴领域建立新的知识和技能，该领域被称为体现数学想象力和认知(EMIC)。EMIC概念的一个示例说明需要让学习者以代表基本数学概念(如旋转)的方式移动他们的身体。类似地，学习者可能会操纵其他物理对象来表示更复杂的变换；这个想法扩展到虚拟操纵和模拟。这一研究领域为设计和创造新的资源、活动和方法提供了信息，这些资源、活动和方法可以促进广泛的数学内容的教和学，包括比率、斜率和频率等概念，或者表达等式或其他代数关系的工具，甚至几何和复杂分析中的定理。通过这一专业发展经验，本科生、数学教师和研究生将把最近出版的美国数学协会教学实践指南中的想法与EMIC的研究成果结合起来。这次为期两天半的研讨会的50名参与者将(1)熟悉EMIC研究，(2)参与各种EMIC活动，(3)为自己的课堂创建/构建EMIC活动和材料，包括教案和评估策略，以及(4)建立一个了解EMIC知识的本科数学教师的全国实践社区。选定的产品将通过为该项目创建的网站向更广泛的数学教育界提供。研讨会提供了一个机会，通过向教师介绍具体活动和相关研究，并提供空间来创建他们自己的活动，以满足他们自己的学生的需求，从而在大学层面上架起研究与实践的桥梁。这些具体化的活动提供了帮助学习者深入钻研数学思想的承诺，这些思想有时可能会被教授的算法和程序所掩盖。研讨会还将允许项目团队增加研究人员的数量和多样性，他们是与具身认知和设计相关的研究和实践的桥梁。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This workshop will enable mathematics instructors to build new knowledge and skills in an emerging area of STEM education research known as embodied mathematical imagination and cognition (EMIC). A sample illustration of the idea of EMIC entails having learners move their bodies in a way that represents an underlying mathematical concept such as rotation. Similarly, learners might manipulate other physical objects to represent more complex transformations; and the idea extends to virtual manipulations and simulations. This area of research has informed the design and creation of new resources, activities, and methodologies that can promote teaching and learning of a breadth of mathematical content, including concepts such as ratio, slope, and frequency, or tools to express equality or other algebraic relationships, or even theorems from geometry and complex analysis. Through this professional development experience undergraduate mathematics faculty and graduate students will weave ideas from the recently published Mathematical Association of America Instructional Practices Guide with EMIC research results. The fifty participants of this two and a half-day workshop will (1) become familiar with EMIC research, (2) engage in a variety of EMIC activities, (3) create/build EMIC activities and materials for their own classrooms, including lesson plans and assessment strategies, and (4) seed a national community of practice of EMIC-informed undergraduate mathematics instructors. Selected products will be available to the wider mathematics education community via a website created for this project. The workshop presents an opportunity to bridge research and practice at the collegiate level by introducing faculty to embodied activities and related research as well as providing a space to create their own activities that meet the needs of their own students. These embodied activities offer promise to help learners delve deeply into mathematical ideas that may sometimes be obscured by the algorithms and procedures they are taught. The workshop will also allow the project team to increase the number and diversity of the community of investigators who are bridging research and practice related to embodied cognition and design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.