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An important and challenging problem in data clustering is the determination of the best number of clusters. A variety of estimation methods has been proposed over the years to address this problem. Most of these methods depend on several nontrivial assumptions about the data structure; and such methods may thus fail to discover the true clusters in a dataset that does not satisfy those assumptions. We develop a new approach that takes as a starting point the simple and intuitive observation that close objects should fall within the same cluster, whereas distant ones should not. Based on this simple notion we utilize a new measurement of good clustering called disconnectivity as well as existing goodness measurements; and we embed these measures into a meta-learning approach for estimating the number of clusters. A simulation experiment based on 13 representative models and an application to real world datasets are conducted to show the effectiveness of the proposed method.