Billy's Brain

Teaching math with teachable agents

Part of our research focuses on developing a learning environment for sixth-grade students to learn about math. The system centers around a teachable agent (a software-simulated student) named Billy who needs help with graphing skills to solve problems. Initially Billy has only a passing familiarity with key concepts, similar to a real-life sixth-grade student's knowledge. The user first must teach Billy the details of graphs and their components by combining Billy's pre-existing knowledge in meaningful ways. For example, Billy has heard the term "X-Axis", and he knows what it means to be horizontal; however, he does not know the X-Axis is horizontal - the user must teach him that.

After Billy successfully draws a graph, the user can then go on to teach him how a point is mathematically defined, its relationship to the graph just drawn, and how to actually plot a point on a graph. Armed with his new knowledge, Billy is ready to learn how lines are comprised of many points, the definition of slope, and how slope relates to speed in graphs of distance versus time. Ultimately, Billy will learn the analytic relationships between distances, speeds, and times, and how these concepts are represented visually with graphs.

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