Concept maps are widely used in education, and have been acclaimed for their excellent results. For efficiently using concept maps in education, computer-based concept mapping systems have been developed. However these computer-based concept mapping systems are limited in their assessment algorithms. The assessment takes only concept nodes as the primary basis, with relation links playing only a minor role. To address this problem, this study proposes a new style of concept map, called the weighted concept map, which assigns a weight to each proposition in a concept map to represent its importance. This study proposes a new assessment based on a weighted concept map and diagnosis analysis. Two studies are conducted to evaluate the methods of assessment. (Contains 8 tables and 6 figures.)