Being a woman I perform taraweeh prayer at home in a way that first make a neeah for 4 rakah sunnah taraweeh reciting last surahs from qoran in each rakah.then i sit for a while and recite a quarter of qoran .I do this in test of the taraweeh prayers .pl suggestvif I am doing it right
You can make one intention of all 20 Rak'aat of Taraweeh but when you perform these Rak'aat of Taraweeh prayer then you have perform them in sets of two. You should perform two Rak'ah of Taraweeh and then make Salam and start again.
You are allowed to go to the Masjid to perform Taraweeh prayers as well.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America