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

这个SBIR二期项目将开发软件，教4 -10年级的学生如何解决数学问题，这些问题一开始看起来很难，甚至可能毫无希望。问题，顾名思义，是很难解决的。它们需要密集的思考和开放式的实验，这在今天的课堂上往往是不可能的。在这个软件中，一个专家化身带着学生在视频游戏质量的3D中进行数学探索，在那里他们想象并发现令人大开眼界的数学真理。该项目帮助教师将数学变成学生们会喜欢的令人兴奋的探索。例如，当学生驾驶一架大型喷气式飞机从纽约飞往东京时，他们毫不费力地发现了在球体表面上寻找两点之间最短路径的方法，这是一个困难的几何问题。教师可以很容易地将该程序融入到日常教学中，并获得每个学生弱点的关键细节。发现的乐趣旨在提高学生对数学、科学和工程的兴趣，并显著减少他们的数学焦虑。除了创造就业机会和税收外，该项目还有望显著提高全国13.2万所学校5800万学生的数学成绩。在这个项目中开发的软件的独特之处在于，它模拟了学生和数学专家老师之间的自然交流方式，让学生沉浸在3D虚拟世界中，在那里他们发展了深刻的数学洞察力，并解决了令人着迷的现实问题。该项目同时发展数学内容知识和解决问题的能力，以及在数学探索过程中对学生进行非侵入性评估的能力也是无与伦比的。在第二期项目中，将充分开发具有商业可行性的软件，并深入研究其对提高学生数学解决问题能力的功效。在真实的教育环境中进行前测后测对照组实验，以确定效果。软件的教学模式和内容可以根据研究结果进行必要的调整。

This SBIR Phase II project will develop software that teaches 4th-10th grade students how to solve mathematical problems that seem difficult, maybe even hopeless at first. Problems, by definition, are hard to solve. They require intensive thinking and open-ended experimentation, which are often not possible in today's classrooms. In the software, an expert avatar takes students on math explorations in video-game-quality 3D where they visualize and discover eye-opening mathematical truths. The program helps teachers turn math into exciting explorations that students will love. For example, as students fly a jumbo jet from New York to Tokyo, they effortlessly discover methods for finding the shortest path between two points on the surface of a sphere, which is a difficult geometry problem. Teachers can easily fit the program into their daily instruction and get crucial details about the weak spots of each student. The joy of discovery is envisioned to increase students' interest in math, science, and engineering and to significantly reduce their math anxiety. Besides creating jobs and tax revenue, the project is expected to contribute to measurably improved math scores across the nation's 132,000 schools educating 58 million students. The software being developed in this project is unique in that it emulates the natural style of communication between a student and an expert math teacher and immerses students in 3D virtual worlds where they develop deep mathematical insight and solve fascinating real-world problems. The program's ability to develop both mathematical content knowledge and problem-solving skills at the same time, as well as its capability to non-intrusively assess students during the mathematical explorations is also unmatched. During the Phase II project, the commercially viable software will be fully developed and its efficacy to improve students' mathematical problem-solving skills will be thoroughly researched. A pretest-posttest control group experiment will be conducted in authentic education settings to determine efficacy. The software's educational model and content may be adjusted if necessary based on the outcome of the research.