Most existing visualization systems stress either the original data visualization or the discovered knowledge visualization, such as decision tree, neural network, rules, etc., but lack the abilities to visualize the entire process of knowledge discovery. We propose an interactive model, RuleViz, for visualizing the process of knowledge discovery and data mining. The RuleViz model consists of five components, each of which can be interacted and visualized by using different visualization techniques. According to this model, two interactive systems, AViz and CViz, for visualizing the process of discovering numerical association rules and the process of learning classification rules have been implemented, respectively. To preprocess the data, each system provides users with three approaches for discretizing numerical attributes and the corresponding rule discovery algorithms. The discretization approaches and the algorithms for discovering association rules and learning classification rules are presented, and the approaches to visualizing discretized data and discovered rules are developed. The discovery of numerical association rules in AViz is based on image-based mining algorithm, while, in CViz, the classification rules are learned in terms of a logical rule induction algorithm. We also demonstrate our experimental results with AViz and CViz on the census data sets, UCI data sets, and artificial data sets.