In visual exploration and analysis of data, determining how to select and transform the data for visualization is a challenge for data-unfamiliar or inexperienced users. Our main hypothesis is that for many data sets and common analysis tasks, there are relatively few "data slices" that result in effective visualizations. By focusing human users on appropriate and suitably transformed parts of the underlying data sets, these data slices can help the users carry their task to correct completion. To verify this hypothesis, we develop a framework that permits us to capture exemplary data slices for a user task, and to explore and parse visual-exploration sequences into a format that makes them distinct and easy to compare. We develop a recommendation system, DataSlicer, that matches a "currently viewed" data slice with the most promising "next effective" data slices for the given exploration task. We report the results of controlled experiments with an implementation of the DataSlicer system, using four common analytical task types. The experiments demonstrate statistically significant improvements in accuracy and exploration speed versus users without access to our system.