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，让学生体验数学的优雅和美丽，同时发展高阶算术和思维能力。该项目挑战了学生如何以传统的死记硬背的方式与数学联系起来的背景，以及有多少人对数学有负面的自我认同。它提出，设计和基于游戏的活动的动态视觉界面可以改变数学的感知方式，使其更容易获得，更愉快，更有影响力。该项目已经显示出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）都认识到该项目能够吸引所有年龄段的用户并促进这种转变。该项目旨在为早期学习者（Pre-K到二年级）提供影响力证明，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学生。这将为所有年龄段的扩展产品奠定基础，并将通过积极的数学识别和提高性能为STEAM职业铺平更清晰的道路。这种参与和转型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自适应软件来推进其创新界面，这些软件可以定制为设计，游戏和探索项目独立价值所必需的模式。为了确保可见性，该项目将需要为Google，Android和iOS设备进行跨平台开发。设计模式将允许学生有效地创建美丽而复杂的图案，并允许教师定制可以通过游戏模式加强的讲座。游戏模式将允许学生解决难题，提高他们的空间和算术技能，通过从事力学和表示。它将侧重于寻找评估方法，如果学生正在提高他们的高阶思维能力，通过测量他们的路径，以解决问题的多个解决方案的效率。探索模式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（全国数学教师理事会），并将为下一波的课程提供基础，包括创新的3-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智力优点和更广泛的影响审查标准。

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.