Xanthosoma sagittifolium) is commonly called "arrowleaf elephant ear" in English although it's also sometimes referred to as tannia, and in Spanish it's known as yautia in Puerto Rico and as tiquizque or macal in Costa Rica and Nicaragua. In the cuisines of these countries, the leaves of the plant are sometimes used, but it's cultivated mostly for its edible tubers.
In Brazil, it's the large green leaves that are consumed, and I've been unable to find any reference to the use of the taioba tuber in Brazilian cooking. It's often simply sauteed with garlic and served as an accompaniment to a meal including meat, beans and rice.
Because the large leaves of the taioba plant have large veins, most recipes call for the stems and veins to be stripped out, leaving on the leafy green part to be used in cooking. As these leafy greens can still be quite large, most commonly the greens are shredded or cut into thin strips before cooking, as is also done in Minas Gerais with kale (couve).