Ilvermorny and Wandless Magic
Everyone knows that the most difficult form of sorcery to master is that without a wand. Nevertheless, Ilvermorny, along with most of the American schools, teach some form of this, however small. This allows witches and wizards to potentially never be caught defenseless simply because they lack their wand.
True wandless magic is far different in nature than accidental magic, the foremost distinction being the magician’s ability to control it. During most cases of accidental magic, the magic lashes out in an attempt to protect the magician from physical, mental, or emotional harm. Controlled magic is entirely intentional and requires concious thought to operate, as seen in the cases of Animagi, Metamorphmagi, Legilimens, Seers, and Parselmouths (it is important to note that the process of becoming an Animagus does require a wand, and that Parselmouths and Seers can access their abilities without meaning to or often even realizing it).
A common staple of wandless magic taught in America is that of potion-making. By the end of their third year, students in any of the major American schools of magic are expected to be able to create simple potions entirely wandless by waving their hand rather than their wand (all potions call for a wave of the wand to finish the potion, and often several other points throughout the brewing process, in order to bind the ingredients together magically). This is due to the Native American history of magic without wands, particularly in such potion-making.
Witches and wizards who are interested in controlled wandless magic will note that some spells are easier to master than others as would be expected, though sometimes, this happens even among simple spells. One wizard might find that they can cast a wandless Levitation Charm with relative ease, while another can more easily make a fire spring to life in their hands. Common studies in wandless magic include Levitation, Summoning, and other Motion Charms, as well as elemental magic.
Although wandless magic is taught in America, it is foolish to rely on it. Charms and Transfiguration are nearly impossible to do without use of a wand, and only the most powerful witches and wizards can consistently cast reliable wandless magic. Wands, as focusing and amplifying tools, create the precision and power in spells generally not possible through intent, words, and hands alone. Wandless magic is a useful and respected skill to have as many are not capable of even the smallest feats without a wand, but it is highly discouraged to neglect training with a wand in favor of that without.