All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We do not know any evidence from the Sunnah which indicates that it is a Sunnah to complete the whole Qur'aan during Taraaweeh prayers (optional night prayers during Ramadan). Imaam Maalik said: 'It is not a Sunnah to recite the whole Qur'aan in Taraaweeh prayers.' However, other scholars are of the view that it is desirable to recite the whole Qur'aan during Taraaweeh in the month of Ramadan so that the people would listen to the whole Qur'aan in this prayer. Anyway, if the case is either reciting a chapter of the Qur'aan without observing the correct pronunciation of it, or reading less than a chapter while observing the correct pronunciation and pondering over it, then there is no doubt that reciting less than a chapter is better. The Imaam has to keep in mind the circumstances of the people praying behind him. The Prophet said: "Whoever among you leads people in prayer should shorten it because among them are the sick, the weak and those who might have important matters to attend to." [Al-Bukhari and Muslim] Therefore, if reciting the whole Qur'aan causes many people to stay behind because of the length of the night prayers, or this quick recitation prevents pondering over it, then it is more appropriate not to finish the whole Qur'aan.
Allaah knows best.