The present study aims at developing a mathematic diagnostic and remedial instruction system for multiple problem solving strategies. The present system includes multiple questions and constructive responsive items. Constructive responsive items, in particular, involve the mechanisms of diagnosing problem solving strategies and error patterns automatically. With the mechanisms, multiple problem solving strategies, concepts/skills, and error patterns will be detected and analyzed simultaneously and therefore provide adequate individualized remedial instruction to reconcile misconceptions and error patterns. The contributions and innovations of the present study are: 1. To organize the procedures and tools of mathematics problem solving and design the interface of computer based test, 2. To propose and compare the automatic analyzing processes of computerized constructed response items, 3. To propose more general cognitive diagnostic models (CDMs) to analyze concept/skill, error pattern, and problem solving strategy simultaneously, 4. To propose computerized adaptive algorithms based on the proposed CDMs. 5. To design a mathematic diagnostic and remedial instruction system for multiple problem solving strategies and apply it to real classroom situation.
