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We present Newton's Pen, a statics tutor implemented on a "pentop computer," a writing instrument with an integrated digitizer and embedded processor. The tutor, intended for undergraduate education, scaffolds students in the construction of free body diagrams and equilibrium equations. This project entailed the development of sketch understanding techniques and user interface principles for creating pedagogically-sound instructional tools for pentop computers. Development on the pentop platform presented novel challenges because of limited computational resources and a visually static, ink-on-paper display (the only dynamic output device is an audio speaker).We show that a system architecture based on a finite state machine reduces the computational complexity, and serves as a convenient means for providing context-sensitive tutorial help. Our pilot study suggests that Newton's Pen has potential as an effective teaching tool.

Kirchhoff's Pen is a pen-based tutoring system that teaches students to apply Kirchhoff's voltage law (KVL) and current law (KCL). To use the system, the student sketches a circuit schematic and annotates it to indicate component labels, mesh currents, and nodal voltages. The student then selects either mesh (KVL) or nodal (KCL) analysis, and writes the appropriate equations. The system interprets the equations, compares them to the correct equations (which are automatically derived from the circuit), and provides tutorial feedback about errors. Unlike traditional tutoring systems that work from input provided with a keyboard and mouse, our system works from ambiguous, hand-drawn input. The goal of our work is to create computational techniques to enable natural, pen-based tutoring systems that scaffold students in solving problems in the same way they would ordinarily solve them with paper and pencil. Kirchhoff's Pen is an important first step toward this goal.