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

体现数学想象力和认知：本科数学教师的专业发展

• 批准号: 1835409
• 负责人: Hortensia Soto
• 金额: $ 4.93万
• 依托单位: University of Northern Colorado
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-06-01 至 2020-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1835409&HistoricalAwards=false
• 关键词: Embodied; Mathematical; Imagination; Cognition; Professional

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.

该研讨会将使数学教师能够在被称为体现数学想象力和认知（EMIC）的新兴STEM教育研究领域建立新的知识和技能。EMIC概念的一个示例说明需要学习者以一种代表基本数学概念（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建新的资源，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学和学习，包括比率，斜率和频率等概念，或表达等式或其他代数关系的工具，甚至是几何和复分析的定理。通过这种专业的发展经验，本科数学教师和研究生将编织从最近出版的美国数学协会教学实践指南与EMIC研究成果的想法。这个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）为自己的教室创建/构建EMIC活动和材料，包括课程计划和评估策略，以及（4）播种一个全国性的EMIC知情本科数学教师实践社区。选定的产品将通过为该项目创建的网站提供给更广泛的数学教育界。 研讨会提供了一个机会，通过向教师介绍具体的活动和相关研究，以及提供一个空间来创建自己的活动，满足自己的学生的需求，在大学一级的研究和实践的桥梁。这些具体的活动提供了承诺，以帮助学习者深入研究数学思想，有时可能会被他们教的算法和程序所掩盖。该研讨会还将使项目团队能够增加研究人员社区的数量和多样性，这些研究人员正在连接与具体认知和设计相关的研究和实践。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。