Seeing the World through a Mathematical Lens: A Place-Based Mobile App for Creating Math Walks

该奖项全部或部分由2021年美国救援计划法案（公法117-2）资助。数学在世界各地，但年轻人可能会认为数学与他们的日常经验脱节，并想知道数学与他们的生活有何关系。有证据表明，孩子们做的非正式数学是非常有效的，涉及效率，灵活性和社交。然而，需要更多的了解教育工作者如何支持校外的数学参与，以及这些校外经验相对于课堂和终身STEM学习可以发挥的作用。这个创新和发展项目旨在研究一个基于位置的移动的应用程序，用于非正式数学学习。这项研究在9个非正式学习站点进行，涉及迭代设计一个应用程序，学习者可以在其中查看并贡献这些站点的数学步行“站点”的交互式地图。学习者将能够选择地点并观看短视频或查看带有文字的图片，这些文字描述了数学原理如何在他们的周围环境中存在。例如，学习者可以使用该应用程序来发现当地拉丁美洲艺术家的绘画如何使用比例和比例，或者市中心的坡道如何设计有特定的坡度以容纳轮椅。研究将检查增强现实（AR）覆盖的启示，学习者可以举起他们的移动终端的相机，并看到数学表示（例如，线、正方形）在其相机馈送中层叠在真实世界对象上。研究还将研究让学习者在当地的非正式学习网站上创建自己的数学步行站，上传图片，描述和链接他们叙述的音频，在那里他们观察数学如何出现在他们的周围环境中，并提出关于STEM想法和他们想知道的联系的有趣问题的影响。该项目借鉴了对非正式数学学习，提出问题和文化支持的方法的研究，对技术支持的数学行走进行基于参与式设计的研究周期。研究问题是：在社区嵌入式数学散步中提出数学情景如何影响学习者的数学态度？如何在真实的世界物体上体验AR叠加，突出数学原理，并让学习者在周围的世界中看到数学？学习者和非正式教育者如何能够作为他们所创造的内容的传播者和其他人所创造的数学内容的评论者参与进来？为了回答这些问题，我们将进行五项研究，让学习者创建数学步行站：没有技术（研究1），有应用程序的原型版本（研究2），有或没有AR覆盖（研究3）。研究还将比较儿童接受数学步行停止与创建自己的停止（研究4）的经验，并探索学习者审查他们的同龄人（研究5）的数学步行停止。使用社区人种学方法，以及青年如何与应用程序和彼此互动的定性和定量过程数据，该项目将确定如何促进数学兴趣的发展，如何构建学习者驱动的问题生成，以及在什么情况下基于应用程序的数学行走最有效。研究结果将有助于研究兴趣的发展，提出问题，非正式数学学习以及STEM学习的数字支持，如AR。该项目将通过数字基础设施促进创新并产生战略影响，该基础设施可以扩大规模以支持世界任何地方的STEM行走，同时还在专注于非正式数学的非正式学习网站中建立本地STEM学习生态系统。这个项目是南卫理公会大学，一个非营利性的，talkSTEM，促进社区数学散步的创建，和9个非正式学习提供者之间的合作伙伴关系。该项目将直接为大约500名4-8年级学生和30-60名非正规教育工作者提供服务。该项目将在9个非正式学习点进行能力建设，每年为数十万学生提供课程服务。这一发展中的创新项目得到了促进非正式STEM学习（AISL）计划的支持，该计划旨在（a）促进非正式环境中STEM学习设计和发展的新方法和基于证据的理解;（B）提供多种途径，以扩大获得和参与STEM学习经验的机会;（c）推进非正式环境中STEM学习的创新研究和评估;以及（d）鼓励所有年龄段的公众在非正式环境中学习STEM。该奖项反映了NSF的法定使命，并被认为值得通过以下方式获得支持：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。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Math is everywhere in the world, but youth may see math as disconnected from their everyday experiences and wonder how math is relevant to their lives. There is evidence that informal math done by children is highly effective, involving efficiency, flexibility, and socializing. Yet, more is needed to understand how educators can support math engagement outside of school, and the role these out-of-school experiences can play relative to the classroom and lifelong STEM learning. This Innovations and Development Project seeks to conduct research on a location-based mobile app for informal mathematics learning. This research takes place at 9 informal learning sites and involves iteratively designing an app in which learners can view and contribute to an interactive map of math walk “stops” at these sites. Learners will be able to select locations and watch short videos or view pictures with text that describe how mathematical principles are present in their surroundings. For example, learners could use the app to discover how a painting by a local Latino artist uses ratio and scale, or how a ramp in downtown was designed with a specific slope to accommodate wheelchairs. Research studies will examine the affordances of augmented reality (AR) overlays where learners can hold up the camera of their mobile device, and see mathematical representations (e.g., lines, squares) layered over real-world objects in their camera feed. Research studies will also examine the impact of having learners create their own math walk stops at local informal learning sites, uploading pictures, descriptions, and linking audio they narrate, where they make observations about how math appears in their surroundings and pose interesting questions about STEM ideas and connections they wonder about. This project draws on research on informal math learning, problem-posing, and culturally-sustaining pedagogies to conduct cycles of participatory design-based research on technology-supported math walks. The research questions are: How does posing mathematical scenarios in community-imbedded math walks impact learners’ attitudes about mathematics? How can experiencing AR overlays on real world objects highlight mathematical principles and allow learners to see math in the world around them? How can learners and informal educators be engaged as disseminators of content they create and as reviewers of mathematical content created by others? To answer these questions, five studies will be conducted where learners create math walk stops: without technology (Study 1), with a prototype version of the app (Study 2), and with or without AR overlays (Study 3). Studies will also compare children's experiences receiving math walk stops vs. creating their own stops (Study 4) and explore learners reviewing math walk stops made by their peers (Study 5). Using a community ethnography approach with qualitative and quantitative process data of how youth engage with the app and with each other, the project will determine how the development of math interest can be facilitated, how learner-driven problem generation can be scaffolded, and under what circumstances app-based math walks are most effective. The results will contribute to research on the development of interest, problem-posing, informal mathematics learning, and digital supports for STEM learning such as AR. This project will promote innovation and have strategic impact through a digital infrastructure that could be scaled up to support STEM walks anywhere in the world, while also building a local STEM learning ecosystem among informal learning sites focused on informal mathematics. This project is a partnership between Southern Methodist University, a nonprofit, talkSTEM that facilitates the creation of community math walks, and 9 informal learning providers. The project will directly serve approximately 500 grades 4-8 learners and 30-60 informal educators. The project will build capacity at 9 informal learning sites, which serve hundreds of thousands of students per year in their programming.This Innovations in Development project is supported by the Advancing Informal STEM Learning (AISL) program, which seeks to (a) advance new approaches to and evidence-based understanding of the design and development of STEM learning in informal environments; (b) provide multiple pathways for broadening access to and engagement in STEM learning experiences; (c) advance innovative research on and assessment of STEM learning in informal environments; and (d) engage the public of all ages in learning STEM in informal environments.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.