SBIR Phase I: Tile Farm: A Versatile Math Education App That Promotes the Development of Spatial, Numeracy, and Higher-Order Thinking Skills

这个SBIR第一阶段项目将开发一个基于几何的数学应用程序，让学生在发展高阶计算和思维技能的同时体验数学的优雅和美丽。这个项目挑战了学生如何以传统死记硬背的方式与数学相关的背景，以及有多少人消极地自我认同数学。它提出，设计和基于游戏的活动的动态视觉界面可以改变人们对数学的感知方式，使其更容易获得、更愉快、更有影响力。这个项目已经展示了产生这种影响的潜力，教师、家长和学生(从幼儿园到以项目为中心的大学课程)都认识到该项目吸引所有年龄段的用户并催化这种转变的能力。该项目旨在为早期学习者(从幼儿园前到二年级)提供影响证明，并帮助学生欣赏数学的优雅，特别是对于那些数学背景很少的人。这将为扩大面向所有年龄段的课程奠定基础，并将为通过积极的数学识别和提高表现推动职业生涯铺平更清晰的道路。这种参与和变革影响的平衡将建立一个可持续的公司，能够在国际范围内的公共和教育市场上竞争。该项目正在寻求通过开发可定制的自适应软件来推进其创新界面，以服务于设计、游戏和探索项目独立价值所必需的模式。为了确保可见性，该项目将需要针对Google、Android和iOS设备的跨平台开发。设计模式将允许学生高效地创建美丽而复杂的图案，并允许教师定制可通过游戏模式强化的讲座。游戏模式将允许学生解决谜题，通过参与机械和表示来提高他们的空间和计算技能。它将专注于通过衡量学生通过多种解决方案解决问题的途径的效率，来评估学生的高阶思维技能是否有所提高。探索模式将需要一个简单的人工智能工具来帮助学生发现有趣的模式，并学习如何根据自己的设计进行新的创作。该项目将致力于确保所有游戏模式符合核心课程要求和NCTM标准(全国数学教师委员会)，并将为下一波产品提供基础，包括为初中生提供创新的3-D界面和增强现实功能。该奖项反映了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 SBIR Phase I project will develop a geometry-based mathematics application that allows students to experience the elegance and beauty of math while developing higher order numeracy and thinking skills. This project challenges the context of how students relate to mathematics in traditional rote fashions, and how many populations negatively self-identify with math. It proposes that a dynamic visual interface of design and game-based activities can transform the way math is perceived, making it more accessible, enjoyable, and impactful. This project has already shown the potential for making this impact, and teachers, parents, and students (ranging from Kindergarten to a project-centered college course) have all recognized the project's ability to engage users of all ages and catalyze this transformation. This project is aimed at proof-of-impact for early learners (Pre-K through 2nd grade) and helping students appreciate the elegance of math, especially for those with very little mathematical background. This will establish a foundation for expanded offerings for all ages and will pave clearer paths to STEAM careers through positive math identification and improved performance. This balance of engagement and transformational impact will establish a sustainable company able to compete in public and educational markets on an international scale. This project is seeking to advance its innovative interface by developing adaptive software that can be customized to serve design, game, and explore modes essential for the project's standalone value. To ensure visibility, this project will require cross-platform development for Google, Android, and iOS devices. Design Mode will allow students to efficiently create beautiful and complex patterns and allow teachers to customize lectures that can be reinforced by game mode. Game Mode will allow students to solve puzzles that improve their spatial and numeracy skills through engaging mechanics and representations. It will focus on finding ways of assessing if students are improving their higher order thinking skills by measuring the efficiency of their paths to solving problems with multiple solutions. Explore Mode will require a simple artificial intelligence tool to help students discover interesting patterns and learn how to make new creations based on their own designs. This project will be devoted to ensuring all modes of play meet the core curriculum requirements and NCTM standards (National Council of Teachers of Mathematics) and will provide a foundation for the next wave of offerings, including an innovative 3-D interface and augmented reality functionality for middle and high school students.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.