A generic term such as "traditional textbooks" nearly demands an imprecise answer. There are thousands of different textbooks, written in different languages, from a variety of perspectives. Without knowing specifically what "tradition" you refer to, the only way to give a simple answer to to be reductionist to the point of outright wrong.
Instead, it is better to say that there are certain common factual elements shared by the vast majority of textbook portraits, such as the dates of his voyages, the names of his ships, and the bibliographic details concerning his own first person accounts of his travels.
The main area of variation is whether the textbook authors admire him as a great explorer who confirmed the scientific hypothesis that the earth was round, or whether they treat him as a bumbling adventurer who mistook the Americas for India, and was a tool of imperialism. Scholars also disagree about his importance, with some earlier scholars crediting him with "discovery" of the Americas, and other pointing out that native populations had discovered the Americas long before his voyages, and that medieval Viking were actually the first Europeans to reach the continent.