SBIR Phase I: Avatar-guided system to develop mastery in mathematical problem solving.

这个SBIR第一阶段的项目将开发一个原型系统，教孩子们如何解决看似无望的数学问题。问题与练习的不同之处在于，如何解决问题并不能立即明确。它们需要认真思考，而不是复杂的计算。例如，该系统的智能化身将帮助学生发现一种计算地月距离的方法，只需要基本的几何知识和大量的思考和实验。问题是由2D或迷人的3D虚拟世界中的化身提出的。（引导）发现的乐趣旨在提高学生对数学和其他STEM学科的兴趣，并显着减少数学焦虑。新的严格的数学教育标准要求每个学生都有很强的解决问题的能力，包括高危人群。学生人数的稳步增长也给学校带来了巨大的压力，要求他们协助老师的工作。据设想，该系统相对于竞争解决方案的独特优势，最终可能使其成为教育5800万K-12学生的全国13.2万所学校的“必备”。该项目有望显著改善数学教育。该项目最重要的技术创新是模拟数学教育领域自然风格的师生互动，由专家化身教授经过验证的解决问题策略，以及使用沉浸式3D虚拟世界来帮助培养深入的洞察力和高级的解决问题的技能。第一阶段研究的目标是开发一个原型系统，并科学评估其在共同核心州标准规定的数学实践内容领域和标准的背景下提高6-8年级学生解决问题能力的前景。该系统的苏格拉底化身会针对给定问题向学生提出有目的的问题。学生们以各种受限的方式做出反应：通过将单词拖拽到正确的位置来构建书面答案，或者通过操纵虚拟环境中的物体来构建书面答案。学生的推理能力在教学化身的过程中被持续和非侵入性地测试，在这个过程中，角色互换，学生向一个新手化身演示如何解决给定的问题。这将揭示在概念理解和使用特定数学方法方面的广泛知识差距。研究人员将在前测后测的对照组实验中分析学生的进步。

This SBIR Phase I project will develop a prototype system that teaches children how to solve seemingly hopeless mathematical problems. Problems differ from exercises in that it is not immediately clear how to approach them. They require hard thinking, not complicated calculations. For example, the system's intelligent avatar will help students discover a method to calculate the Earth-Moon distance with nothing more than basic geometry and a lot of thinking and experimentation. Problems are presented by the avatar in 2D or in captivating 3D virtual worlds. The joy of (guided) discovery is envisioned to increase students' interest in math and other STEM disciplines and to significantly reduce math anxiety. The new rigorous math education standards require strong problem solving skills from each student including at-risk populations. The steady increase of student population also puts enormous pressure on schools to assist the work of their teachers. It is envisioned that the system's unique advantages over competitive solutions could ultimately make it a "must have" for the nation's 132,000 schools educating 58 million K-12 students. The project is expected to contribute to a markedly better math education.The most important technical innovations of this project are the emulation of natural-style teacher-student interactions in the domain of mathematics education, the teaching of proven problem solving strategies by an expert avatar, and the use of immersive 3D virtual worlds to help develop deep insight and advanced problem solving skills. The goal of the Phase I research is to develop a prototype system and scientifically evaluate its promise to improve students' problem solving skills in grades 6-8 within the context of the content domains and standards of mathematical practice specified by the Common Core State Standards. The system's Socratic avatar asks students purposeful questions in relation to a given problem. Students respond in a variety of constrained ways: construct written answers by dragging and dropping words into the right place, or by manipulating objects in the virtual environment. Student reasoning skills are tested continuously and non-intrusively during teach the avatar sessions in which roles are reversed and students demonstrate to a novice avatar how to solve a given problem. This will reveal a wide range of knowledge gaps in conceptual understanding and the use of particular mathematical methods. The researchers will analyze students' improvement in a pretest-posttest control group experiment.