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Ed's primary pedagogical aim is to show you how you can perform difficult rhythms, either by tapping or vocalizing them, or on a musical instrument. In order for the time onsets to be correct, you have to be able to hear whether they are right or not. When you are performing the rhythm correctly, you also must know that you are performing it correctly. In one of Ed's classes I learned that, when you are rehearsing in a group with a conductor and the conductor asks you whether you played a rhythm correctly or not, your correct answer is, tautologically, “yes".
Some of the examples ask you to listen for ESPIT: equally spaced onsets in time. Others ask you to notice that complicated-looking rhythms are often well approximated by much simpler ones. Yet others require a sort of figure/ground reversal in which one rhythm (regular or not) becomes the beat against which another rhythm is played. There is sometimes a puline (punch line) - a complicated-looking rhythm is in fact ESPIT, or two very different-looking examples are identical as sounded.
There is usually more than one possible strategy for performing a rhythm, and as mentioned above, it often pays to learn to employ more than one strategy simultaneously. In some complicated situations it pays to re-notate a rhythm in a variety of ways, both approximate and exact, in order to find a way of understanding the rhythm that allows you to verify the correctness of your performance. On many occasions the same rhythmic fragment is examined from several different points of view. Not all of them will be useful to any one practitioner, but an open-minded performer will find many possible paths to explore on their way to mastering a difficult rhythm.