# Diagrammatic Reasoning for Geometry ITS to Teach Auxiliary Line Construction Problems

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## Abstract

A new model of problem solver for geometric theorems with construction of auxiliary lines is discussed. The problem solver infers based on schematic knowledge with diagrammatic information (diagrammatic schema, DS for short). The inference algorithm invokes forward and backward chaining. The diagrammatic schema as well as the inference algorithm was designed through a series of observations of human problem solving. This paper also describes that DS is beneficial for instructions, especially for teaching students how to draw auxiliary lines.

## Keywords

Problem Solver Semantic Network Tutoring System Problem Figure Cognitive Science Society
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