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

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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.